TSTP Solution File: SWW390+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW390+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 : Mon Jun 24 18:09:08 EDT 2024
% Result : Theorem 15.02s 14.78s
% Output : CNFRefutation 15.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW390+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 06:24:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.55/0.57 start to proof:theBenchmark
% 14.60/14.63 %-------------------------------------------
% 14.60/14.63 % File :CSE---1.7
% 14.60/14.63 % Problem :theBenchmark
% 14.60/14.63 % Transform :cnf
% 14.60/14.63 % Format :tptp:raw
% 14.60/14.63 % Command :java -jar mcs_scs.jar %d %s
% 14.60/14.63
% 14.60/14.63 % Result :Theorem 0.480000s
% 14.60/14.63 % Output :CNFRefutation 0.480000s
% 14.60/14.63 %-------------------------------------------
% 14.60/14.64 %------------------------------------------------------------------------------
% 14.60/14.64 % File : SWW390+1 : TPTP v8.2.0. Released v5.2.0.
% 14.60/14.64 % Domain : Software Verification
% 14.60/14.64 % Problem : Hoare's Logic with Procedures 435737, 5000 axioms selected
% 14.60/14.64 % Version : Especial.
% 14.60/14.64 % English :
% 14.60/14.64
% 14.60/14.64 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 14.60/14.64 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 14.60/14.64 % Source : [Bla11]
% 14.60/14.64 % Names : hoare_435737.5000.p [Bla11]
% 14.60/14.64
% 14.60/14.64 % Status : ContradictoryAxioms
% 14.60/14.64 % Rating : 0.50 v8.2.0, 0.53 v8.1.0, 0.61 v7.5.0, 0.59 v7.4.0, 0.63 v7.3.0, 0.62 v7.2.0, 0.66 v7.1.0, 0.65 v7.0.0, 0.70 v6.4.0, 0.65 v6.3.0, 0.62 v6.2.0, 0.72 v6.1.0, 0.77 v6.0.0, 0.74 v5.5.0, 0.67 v5.4.0, 0.71 v5.3.0, 0.70 v5.2.0
% 14.60/14.64 % Syntax : Number of formulae : 5228 (1675 unt; 0 def)
% 14.60/14.64 % Number of atoms : 12734 (4447 equ)
% 14.60/14.64 % Maximal formula atoms : 13 ( 2 avg)
% 14.60/14.64 % Number of connectives : 8498 ( 992 ~; 150 |; 718 &)
% 14.60/14.64 % ( 901 <=>;5737 =>; 0 <=; 0 <~>)
% 14.60/14.64 % Maximal formula depth : 22 ( 6 avg)
% 14.60/14.64 % Maximal term depth : 19 ( 2 avg)
% 14.60/14.64 % Number of predicates : 150 ( 149 usr; 0 prp; 1-6 aty)
% 14.60/14.64 % Number of functors : 384 ( 384 usr; 49 con; 0-7 aty)
% 14.60/14.64 % Number of variables : 16657 (16499 !; 158 ?)
% 14.60/14.64 % SPC : FOF_THM_RFO_SEQ
% 14.60/14.64
% 14.60/14.64 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 14.60/14.64 % 2011-03-01 13:06:16
% 14.60/14.64 %------------------------------------------------------------------------------
% 14.60/14.64 %----Relevant facts (4985)
% 14.60/14.64 fof(fact_ext,axiom,
% 14.60/14.64 ! [V_g_2,V_f_2] :
% 14.60/14.64 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 14.60/14.64 => V_f_2 = V_g_2 ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_empty,axiom,
% 14.60/14.64 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 14.60/14.64 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_triple_Oinject,axiom,
% 14.60/14.64 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 14.60/14.64 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
% 14.60/14.64 <=> ( V_fun1_2 = V_fun1_H_2
% 14.60/14.64 & V_com_2 = V_com_H_2
% 14.60/14.64 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_cut,axiom,
% 14.60/14.64 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 14.60/14.64 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 14.60/14.64 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 14.60/14.64 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_hoare__derivs_Oinsert,axiom,
% 14.60/14.64 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 14.60/14.64 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.64 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 14.60/14.64 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_derivs__insertD,axiom,
% 14.60/14.64 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 14.60/14.64 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
% 14.60/14.64 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.64 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_triple_Orecs,axiom,
% 14.60/14.64 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_triple_Osimps_I2_J,axiom,
% 14.60/14.64 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_b,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_empty__not__insert,axiom,
% 14.60/14.64 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_insert__not__empty,axiom,
% 14.60/14.64 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_doubleton__eq__iff,axiom,
% 14.60/14.64 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.60/14.64 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.60/14.64 <=> ( ( V_a_2 = V_ca_2
% 14.60/14.64 & V_b_2 = V_d_2 )
% 14.60/14.64 | ( V_a_2 = V_d_2
% 14.60/14.64 & V_b_2 = V_ca_2 ) ) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_singleton__inject,axiom,
% 14.60/14.64 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.64 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 14.60/14.64 => V_a_2 = V_b_2 ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_bot__apply,axiom,
% 14.60/14.64 ! [V_x_2,T_c,T_b] :
% 14.60/14.64 ( class_Orderings_Obot(T_b)
% 14.60/14.64 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_hoare__derivs_OSkip,axiom,
% 14.60/14.64 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 14.60/14.64 ! [V_a2_2,V_a1_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_conseq2,axiom,
% 14.60/14.64 ! [V_Q_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 14.60/14.64 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.64 => ( ! [B_Z,B_s] :
% 14.60/14.64 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 14.60/14.64 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 14.60/14.64 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 14.60/14.64
% 14.60/14.64 fof(fact_conseq1,axiom,
% 14.60/14.64 ! [V_Pa_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 14.60/14.64 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.65 => ( ! [B_Z,B_s] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 14.60/14.65 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 14.60/14.65 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Comp,axiom,
% 14.60/14.65 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 14.60/14.65 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.65 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.65 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_insert__code,axiom,
% 14.60/14.65 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 14.60/14.65 <=> ( V_y_2 = V_x_2
% 14.60/14.65 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_insert__commute,axiom,
% 14.60/14.65 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_insert__absorb2,axiom,
% 14.60/14.65 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_the__elem__eq,axiom,
% 14.60/14.65 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ).
% 14.60/14.65
% 14.60/14.65 fof(fact_com_Osimps_I12_J,axiom,
% 14.60/14.65 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_com_Osimps_I13_J,axiom,
% 14.60/14.65 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 14.60/14.65
% 14.60/14.65 fof(fact_com_Osimps_I3_J,axiom,
% 14.60/14.65 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 14.60/14.65 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 14.60/14.65 <=> ( V_com1_2 = V_com1_H_2
% 14.60/14.65 & V_com2_2 = V_com2_H_2 ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_hoare__sound,axiom,
% 14.60/14.65 ! [V_ts_2,V_Ga_2,T_b] :
% 14.60/14.65 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 14.60/14.65 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_conseq12,axiom,
% 14.60/14.65 ! [V_Q_2,V_Pa_2,V_Q_H_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 14.60/14.65 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 14.60/14.65 => ( ! [B_Z,B_s] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 14.60/14.65 => ! [B_s_H] :
% 14.60/14.65 ( ! [B_Z_H] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s))
% 14.60/14.65 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) )
% 14.60/14.65 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) )
% 14.60/14.65 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_subset__singletonD,axiom,
% 14.60/14.65 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 14.60/14.65 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.65 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_singletonE,axiom,
% 14.60/14.65 ! [V_a_2,V_b_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 14.60/14.65 => V_b_2 = V_a_2 ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_singleton__iff,axiom,
% 14.60/14.65 ! [V_a_2,V_b_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 14.60/14.65 <=> V_b_2 = V_a_2 ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_folding__one_Osingleton,axiom,
% 14.60/14.65 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 14.60/14.65 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.65 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_fold1Set__sing,axiom,
% 14.60/14.65 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
% 14.60/14.65 <=> V_a_2 = V_b_2 ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_insert__is__Un,axiom,
% 14.60/14.65 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_order__refl,axiom,
% 14.60/14.65 ! [V_x,T_a] :
% 14.60/14.65 ( class_Orderings_Opreorder(T_a)
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_equalityCE,axiom,
% 14.60/14.65 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 14.60/14.65 ( V_A_2 = V_B_2
% 14.60/14.65 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.65 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 14.60/14.65 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_equalityI,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.65 => V_A_2 = V_B_2 ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_emptyE,axiom,
% 14.60/14.65 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_insertE,axiom,
% 14.60/14.65 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 14.60/14.65 => ( V_a_2 != V_b_2
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_insertCI,axiom,
% 14.60/14.65 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 14.60/14.65 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 14.60/14.65 => V_a_2 = V_b_2 )
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_subsetD,axiom,
% 14.60/14.65 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.65 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_UnE,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.65 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_UnCI,axiom,
% 14.60/14.65 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 14.60/14.65 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_empty__subsetI,axiom,
% 14.60/14.65 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_subset__refl,axiom,
% 14.60/14.65 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__upper1,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__upper2,axiom,
% 14.60/14.65 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__absorb,axiom,
% 14.60/14.65 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 14.60/14.65
% 14.60/14.65 fof(fact_le__fun__def,axiom,
% 14.60/14.65 ! [V_g_2,V_f_2,T_b,T_c] :
% 14.60/14.65 ( class_Orderings_Oord(T_c)
% 14.60/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 14.60/14.65 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_mem__def,axiom,
% 14.60/14.65 ! [V_A_2,V_x_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.65 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__commute,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_linorder__linear,axiom,
% 14.60/14.65 ! [V_y,V_x,T_a] :
% 14.60/14.65 ( class_Orderings_Olinorder(T_a)
% 14.60/14.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_subset__Un__eq,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.65 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_set__eq__subset,axiom,
% 14.60/14.65 ! [T_b,V_B_2,V_A_2] :
% 14.60/14.65 ( V_A_2 = V_B_2
% 14.60/14.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_order__eq__iff,axiom,
% 14.60/14.65 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.65 ( class_Orderings_Oorder(T_b)
% 14.60/14.65 => ( V_x_2 = V_y_2
% 14.60/14.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__left__absorb,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__left__commute,axiom,
% 14.60/14.65 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__iff,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.65 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.65 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_Un__assoc,axiom,
% 14.60/14.65 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_bex__Un,axiom,
% 14.60/14.65 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 14.60/14.65 ( ? [B_x] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.60/14.65 <=> ( ? [B_x] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.60/14.65 | ? [B_x] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 14.60/14.65 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_ball__Un,axiom,
% 14.60/14.65 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 14.60/14.65 ( ! [B_x] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.60/14.65 <=> ( ! [B_x] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.60/14.65 & ! [B_x] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 14.60/14.65 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_equalityD1,axiom,
% 14.60/14.65 ! [T_b,V_B_2,V_A_2] :
% 14.60/14.65 ( V_A_2 = V_B_2
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_equalityD2,axiom,
% 14.60/14.65 ! [T_b,V_B_2,V_A_2] :
% 14.60/14.65 ( V_A_2 = V_B_2
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_order__eq__refl,axiom,
% 14.60/14.65 ! [V_y,V_x,T_a] :
% 14.60/14.65 ( class_Orderings_Opreorder(T_a)
% 14.60/14.65 => ( V_x = V_y
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_UnI1,axiom,
% 14.60/14.65 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_UnI2,axiom,
% 14.60/14.65 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 14.60/14.65 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 14.60/14.65 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.60/14.65
% 14.60/14.65 fof(fact_le__funD,axiom,
% 14.60/14.65 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 14.60/14.66 ( class_Orderings_Oord(T_c)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__absorb1,axiom,
% 14.60/14.66 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__absorb2,axiom,
% 14.60/14.66 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_eqset__imp__iff,axiom,
% 14.60/14.66 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 14.60/14.66 ( V_A_2 = V_B_2
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_eqelem__imp__iff,axiom,
% 14.60/14.66 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 14.60/14.66 ( V_x_2 = V_y_2
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_in__mono,axiom,
% 14.60/14.66 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_order__antisym__conv,axiom,
% 14.60/14.66 ! [V_x_2,V_y_2,T_b] :
% 14.60/14.66 ( class_Orderings_Oorder(T_b)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.66 <=> V_x_2 = V_y_2 ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_eq__mem__trans,axiom,
% 14.60/14.66 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 14.60/14.66 ( V_a_2 = V_b_2
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_ord__eq__le__trans,axiom,
% 14.60/14.66 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.66 ( class_Orderings_Oord(T_a)
% 14.60/14.66 => ( V_a = V_b
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_xt1_I3_J,axiom,
% 14.60/14.66 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.66 ( class_Orderings_Oorder(T_a)
% 14.60/14.66 => ( V_a = V_b
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_set__rev__mp,axiom,
% 14.60/14.66 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_set__mp,axiom,
% 14.60/14.66 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_subset__trans,axiom,
% 14.60/14.66 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_ord__le__eq__trans,axiom,
% 14.60/14.66 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.66 ( class_Orderings_Oord(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.66 => ( V_b = V_c
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_xt1_I4_J,axiom,
% 14.60/14.66 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.66 ( class_Orderings_Oorder(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.60/14.66 => ( V_b = V_c
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_order__antisym,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Orderings_Oorder(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.66 => V_x = V_y ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_order__trans,axiom,
% 14.60/14.66 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.66 ( class_Orderings_Opreorder(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_xt1_I5_J,axiom,
% 14.60/14.66 ! [V_x,V_y,T_a] :
% 14.60/14.66 ( class_Orderings_Oorder(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.66 => V_x = V_y ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_xt1_I6_J,axiom,
% 14.60/14.66 ! [V_z,V_x,V_y,T_a] :
% 14.60/14.66 ( class_Orderings_Oorder(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__least,axiom,
% 14.60/14.66 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__mono,axiom,
% 14.60/14.66 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_equalityE,axiom,
% 14.60/14.66 ! [T_b,V_B_2,V_A_2] :
% 14.60/14.66 ( V_A_2 = V_B_2
% 14.60/14.66 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_le__funE,axiom,
% 14.60/14.66 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 14.60/14.66 ( class_Orderings_Oord(T_c)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_linorder__le__cases,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Orderings_Olinorder(T_a)
% 14.60/14.66 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_subset__insert,axiom,
% 14.60/14.66 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 14.60/14.66 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 14.60/14.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insert__subset,axiom,
% 14.60/14.66 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
% 14.60/14.66 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_empty__fold1SetE,axiom,
% 14.60/14.66 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_fold1Set__nonempty,axiom,
% 14.60/14.66 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 14.60/14.66 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__empty__left,axiom,
% 14.60/14.66 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__empty__right,axiom,
% 14.60/14.66 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__empty,axiom,
% 14.60/14.66 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.66 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.66 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__insert__right,axiom,
% 14.60/14.66 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_Un__insert__left,axiom,
% 14.60/14.66 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_bot__least,axiom,
% 14.60/14.66 ! [V_x,T_a] :
% 14.60/14.66 ( class_Orderings_Obot(T_a)
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_all__not__in__conv,axiom,
% 14.60/14.66 ! [V_A_2,T_b] :
% 14.60/14.66 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.66 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_ex__in__conv,axiom,
% 14.60/14.66 ! [V_A_2,T_b] :
% 14.60/14.66 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.66 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_empty__iff,axiom,
% 14.60/14.66 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_equals0D,axiom,
% 14.60/14.66 ! [V_a_2,T_b,V_A_2] :
% 14.60/14.66 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.66 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_subset__empty,axiom,
% 14.60/14.66 ! [V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.60/14.66 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insertI1,axiom,
% 14.60/14.66 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insert__iff,axiom,
% 14.60/14.66 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 14.60/14.66 <=> ( V_a_2 = V_b_2
% 14.60/14.66 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insert__ident,axiom,
% 14.60/14.66 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 14.60/14.66 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.66 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.66 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
% 14.60/14.66 <=> V_A_2 = V_B_2 ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insertI2,axiom,
% 14.60/14.66 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insert__absorb,axiom,
% 14.60/14.66 ! [V_A_2,V_a_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.66 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_subset__insertI,axiom,
% 14.60/14.66 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_subset__insertI2,axiom,
% 14.60/14.66 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_insert__mono,axiom,
% 14.60/14.66 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_asm,axiom,
% 14.60/14.66 ! [V_Ga_2,V_ts_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
% 14.60/14.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_weaken,axiom,
% 14.60/14.66 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 14.60/14.66 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 14.60/14.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_thin,axiom,
% 14.60/14.66 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 14.60/14.66 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
% 14.60/14.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup1CI,axiom,
% 14.60/14.66 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 14.60/14.66 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 14.60/14.66 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 14.60/14.66 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup1E,axiom,
% 14.60/14.66 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 14.60/14.66 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 14.60/14.66 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__apply,axiom,
% 14.60/14.66 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 14.60/14.66 ( class_Lattices_Olattice(T_b)
% 14.60/14.66 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__bot__left,axiom,
% 14.60/14.66 ! [V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Obounded__lattice__bot(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__bot__right,axiom,
% 14.60/14.66 ! [V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Obounded__lattice__bot(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__eq__bot__iff,axiom,
% 14.60/14.66 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.66 ( class_Lattices_Obounded__lattice__bot(T_b)
% 14.60/14.66 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 14.60/14.66 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 14.60/14.66 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_le__supE,axiom,
% 14.60/14.66 ! [V_x,V_b,V_a,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
% 14.60/14.66 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 14.60/14.66 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__mono,axiom,
% 14.60/14.66 ! [V_d,V_b,V_c,V_a,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__least,axiom,
% 14.60/14.66 ! [V_z,V_x,V_y,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_le__supI,axiom,
% 14.60/14.66 ! [V_b,V_x,V_a,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 14.60/14.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__absorb1,axiom,
% 14.60/14.66 ! [V_x,V_y,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__absorb2,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_eq__mem,axiom,
% 14.60/14.66 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.66 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 14.60/14.66 <=> V_x_2 = V_y_2 ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup_Oidem,axiom,
% 14.60/14.66 ! [V_a,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__idem,axiom,
% 14.60/14.66 ! [V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup_Ocommute,axiom,
% 14.60/14.66 ! [V_b,V_a,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_inf__sup__aci_I5_J,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Olattice(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__commute,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup_Oleft__idem,axiom,
% 14.60/14.66 ! [V_b,V_a,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_inf__sup__aci_I8_J,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Olattice(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup__left__idem,axiom,
% 14.60/14.66 ! [V_y,V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_sup_Oleft__commute,axiom,
% 14.60/14.66 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.66 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ).
% 14.60/14.66
% 14.60/14.66 fof(fact_inf__sup__aci_I7_J,axiom,
% 14.60/14.66 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.66 ( class_Lattices_Olattice(T_a)
% 14.60/14.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup__left__commute,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup_Oassoc,axiom,
% 14.60/14.67 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__aci_I6_J,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup__assoc,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_rev__predicate1D,axiom,
% 14.60/14.67 ! [V_Q_2,T_b,V_x_2,V_Pa_2] :
% 14.60/14.67 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 14.60/14.67 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_predicate1D,axiom,
% 14.60/14.67 ! [V_x_2,V_Q_2,V_Pa_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 14.60/14.67 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 14.60/14.67 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup1I1,axiom,
% 14.60/14.67 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 14.60/14.67 ( hBOOL(hAPP(V_A_2,V_x_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup1I2,axiom,
% 14.60/14.67 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 14.60/14.67 ( hBOOL(hAPP(V_B_2,V_x_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__ord_I3_J,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup__ge1,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__ord_I4_J,axiom,
% 14.60/14.67 ! [V_x,V_y,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_sup__ge2,axiom,
% 14.60/14.67 ! [V_x,V_y,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_le__iff__sup,axiom,
% 14.60/14.67 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.67 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_le__sup__iff,axiom,
% 14.60/14.67 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
% 14.60/14.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 14.60/14.67 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_le__supI1,axiom,
% 14.60/14.67 ! [V_b,V_a,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_le__supI2,axiom,
% 14.60/14.67 ! [V_a,V_b,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold1Set_Ointros,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one_Oinsert,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_diff__single__insert,axiom,
% 14.60/14.67 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_subset__insert__iff,axiom,
% 14.60/14.67 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 14.60/14.67 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 14.60/14.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_nonempty__iff,axiom,
% 14.60/14.67 ! [T_b,V_A_2] :
% 14.60/14.67 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 <=> ? [B_x,B_B] :
% 14.60/14.67 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B)
% 14.60/14.67 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oidem,axiom,
% 14.60/14.67 ! [V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Powp__mono,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_subsetI,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( ! [B_x] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__insert,axiom,
% 14.60/14.67 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__singleton__eq,axiom,
% 14.60/14.67 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 14.60/14.67 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_insert__Diff,axiom,
% 14.60/14.67 ! [V_A_2,V_a_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite_OemptyI,axiom,
% 14.60/14.67 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite_OinsertI,axiom,
% 14.60/14.67 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_DiffI,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_DiffE,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.67 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__Diff,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimageI,axiom,
% 14.60/14.67 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 14.60/14.67 ( hAPP(V_f_2,V_a_2) = V_b_2
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_minus__apply,axiom,
% 14.60/14.67 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 14.60/14.67 ( class_Groups_Ominus(T_b)
% 14.60/14.67 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__Diff,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__idemp,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__code,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 14.60/14.67 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite,axiom,
% 14.60/14.67 ! [V_A_2,T_b] :
% 14.60/14.67 ( class_Finite__Set_Ofinite(T_b)
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__code,axiom,
% 14.60/14.67 ! [V_A_2,T_b] :
% 14.60/14.67 ( class_Finite__Set_Ofinite(T_b)
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__Diff2,axiom,
% 14.60/14.67 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.67 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold__graph__imp__finite,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__Diff__insert,axiom,
% 14.60/14.67 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
% 14.60/14.67 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__iff,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.67 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.67 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_DiffD1,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_DiffD2,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__eq,axiom,
% 14.60/14.67 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 14.60/14.67 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimageD,axiom,
% 14.60/14.67 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimageI2,axiom,
% 14.60/14.67 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_empty__Diff,axiom,
% 14.60/14.67 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__empty,axiom,
% 14.60/14.67 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__cancel,axiom,
% 14.60/14.67 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__empty,axiom,
% 14.60/14.67 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__subset,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__mono,axiom,
% 14.60/14.67 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_double__diff,axiom,
% 14.60/14.67 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__mono,axiom,
% 14.60/14.67 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Un__Diff__cancel,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Un__Diff__cancel2,axiom,
% 14.60/14.67 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Un__Diff,axiom,
% 14.60/14.67 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_vimage__Un,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite_Oequations_I1_J,axiom,
% 14.60/14.67 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__insert,axiom,
% 14.60/14.67 ! [V_A_2,V_a_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 14.60/14.67 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__subset,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_rev__finite__subset,axiom,
% 14.60/14.67 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__UnI,axiom,
% 14.60/14.67 ! [V_Ga_2,V_F_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__Un,axiom,
% 14.60/14.67 ! [V_Ga_2,V_F_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
% 14.60/14.67 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 14.60/14.67 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold__graph_OemptyI,axiom,
% 14.60/14.67 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_empty__fold__graphE,axiom,
% 14.60/14.67 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
% 14.60/14.67 => V_x_2 = V_z_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff1__fold__graph,axiom,
% 14.60/14.67 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one_Oinsert__remove,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.60/14.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_insert__Diff1,axiom,
% 14.60/14.67 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_insert__Diff__if,axiom,
% 14.60/14.67 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 14.60/14.67 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
% 14.60/14.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__insert,axiom,
% 14.60/14.67 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__insert2,axiom,
% 14.60/14.67 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_insert__Diff__single,axiom,
% 14.60/14.67 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__subset__conv,axiom,
% 14.60/14.67 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 14.60/14.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__partition,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one_Oremove,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 14.60/14.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold__graph_OinsertI,axiom,
% 14.60/14.67 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 14.60/14.67 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Diff__insert__absorb,axiom,
% 14.60/14.67 ! [V_A_2,V_x_2,T_b] :
% 14.60/14.67 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__image__simple_Oremove,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 14.60/14.67 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oremove,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 14.60/14.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_diff__eq__diff__less__eq,axiom,
% 14.60/14.67 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.60/14.67 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.60/14.67 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 14.60/14.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one_Oclosed,axiom,
% 14.60/14.67 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__empty__induct,axiom,
% 14.60/14.67 ! [V_Pa_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 14.60/14.67 => ( ! [B_a,B_A] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 14.60/14.67 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 14.60/14.67 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 14.60/14.67 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__subset__induct,axiom,
% 14.60/14.67 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.60/14.67 => ( ! [B_a,B_F] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 14.60/14.67 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 14.60/14.67 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 14.60/14.67 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.60/14.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one__idem_Oidem,axiom,
% 14.60/14.67 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.60/14.67 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__image__simple_Oempty,axiom,
% 14.60/14.67 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.67 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Osingleton,axiom,
% 14.60/14.67 ! [V_x_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_diff__eq__diff__eq,axiom,
% 14.60/14.67 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.60/14.67 ( class_Groups_Oab__group__add(T_b)
% 14.60/14.67 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 14.60/14.67 => ( V_a_2 = V_b_2
% 14.60/14.67 <=> V_ca_2 = V_d_2 ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oin__idem,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__one__idem_Oin__idem,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Osubset__idem,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Ounion__idem,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__image__simple_Oinsert,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oinsert,axiom,
% 14.60/14.67 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Oclosed,axiom,
% 14.60/14.67 ! [V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_insert__fold1SetE,axiom,
% 14.60/14.67 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
% 14.60/14.67 => ~ ! [B_a,B_A] :
% 14.60/14.67 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold1Set_Oequations,axiom,
% 14.60/14.67 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
% 14.60/14.67 <=> ? [B_a,B_A] :
% 14.60/14.67 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 14.60/14.67 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 14.60/14.67 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_setsum__diff1__ring,axiom,
% 14.60/14.67 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 14.60/14.67 ( class_Rings_Oring(T_c)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_setsum__diff1,axiom,
% 14.60/14.67 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 14.60/14.67 ( class_Groups_Oab__group__add(T_c)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 14.60/14.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_fold__graph__permute__diff,axiom,
% 14.60/14.67 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 14.60/14.67 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Sup__fin_Ounion__inter,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.67 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_psubset__insert__iff,axiom,
% 14.60/14.67 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 14.60/14.67 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 14.60/14.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 14.60/14.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) )
% 14.60/14.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.60/14.67 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.67 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf1I,axiom,
% 14.60/14.67 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 14.60/14.67 ( hBOOL(hAPP(V_A_2,V_x_2))
% 14.60/14.67 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf1E,axiom,
% 14.60/14.67 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 14.60/14.67 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 14.60/14.67 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_IntI,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_IntE,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.67 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_finite__Int,axiom,
% 14.60/14.67 ! [V_Ga_2,V_F_2,T_b] :
% 14.60/14.67 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.67 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 14.60/14.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 14.60/14.67 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.67 ( class_Groups_Oab__semigroup__mult(T_a)
% 14.60/14.67 => 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)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_times_Oidem,axiom,
% 14.60/14.67 ! [V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_mult__idem,axiom,
% 14.60/14.67 ! [V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf_Oidem,axiom,
% 14.60/14.67 ! [V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__idem,axiom,
% 14.60/14.67 ! [V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf_Ocommute,axiom,
% 14.60/14.67 ! [V_b,V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__aci_I1_J,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__commute,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_mult__left__idem,axiom,
% 14.60/14.67 ! [V_b,V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 14.60/14.67 => 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) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf_Oleft__idem,axiom,
% 14.60/14.67 ! [V_b,V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__aci_I4_J,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__left__idem,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf_Oleft__commute,axiom,
% 14.60/14.67 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__aci_I3_J,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__left__commute,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf_Oassoc,axiom,
% 14.60/14.67 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__sup__aci_I2_J,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Olattice(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__assoc,axiom,
% 14.60/14.67 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf__apply,axiom,
% 14.60/14.67 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 14.60/14.67 ( class_Lattices_Olattice(T_b)
% 14.60/14.67 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_less__infI1,axiom,
% 14.60/14.67 ! [V_b,V_x,V_a,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_less__infI2,axiom,
% 14.60/14.67 ! [V_a,V_x,V_b,T_a] :
% 14.60/14.67 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf1D1,axiom,
% 14.60/14.67 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 14.60/14.67 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_inf1D2,axiom,
% 14.60/14.67 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 14.60/14.67 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 14.60/14.67 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_order__less__irrefl,axiom,
% 14.60/14.67 ! [V_x,T_a] :
% 14.60/14.67 ( class_Orderings_Opreorder(T_a)
% 14.60/14.67 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_linorder__neq__iff,axiom,
% 14.60/14.67 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.67 ( class_Orderings_Olinorder(T_b)
% 14.60/14.67 => ( V_x_2 != V_y_2
% 14.60/14.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.67 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_not__less__iff__gr__or__eq,axiom,
% 14.60/14.67 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.67 ( class_Orderings_Olinorder(T_b)
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 14.60/14.67 | V_x_2 = V_y_2 ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Int__absorb,axiom,
% 14.60/14.67 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Int__commute,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_linorder__less__linear,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Orderings_Olinorder(T_a)
% 14.60/14.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.67 | V_x = V_y
% 14.60/14.67 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Int__left__absorb,axiom,
% 14.60/14.67 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Int__left__commute,axiom,
% 14.60/14.67 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_Int__assoc,axiom,
% 14.60/14.67 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_linorder__antisym__conv3,axiom,
% 14.60/14.67 ! [V_x_2,V_y_2,T_b] :
% 14.60/14.67 ( class_Orderings_Olinorder(T_b)
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.67 <=> V_x_2 = V_y_2 ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_linorder__neqE,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Orderings_Olinorder(T_a)
% 14.60/14.67 => ( V_x != V_y
% 14.60/14.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 14.60/14.67
% 14.60/14.67 fof(fact_less__imp__neq,axiom,
% 14.60/14.67 ! [V_y,V_x,T_a] :
% 14.60/14.67 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => V_x != V_y ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__not__sym,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__imp__not__less,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__imp__not__eq,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => V_x != V_y ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__imp__not__eq2,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => V_y != V_x ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__asym_H,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I9_J,axiom,
% 14.60/14.68 ! [V_a,V_b,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_ord__eq__less__trans,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Oord(T_a)
% 14.60/14.68 => ( V_a = V_b
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I1_J,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( V_a = V_b
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_psubset__trans,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_ord__less__eq__trans,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Oord(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.68 => ( V_b = V_c
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I2_J,axiom,
% 14.60/14.68 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 14.60/14.68 => ( V_b = V_c
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__trans,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I10_J,axiom,
% 14.60/14.68 ! [V_z,V_x,V_y,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__asym,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__cases,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_a)
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => ( V_x != V_y
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oidem,axiom,
% 14.60/14.68 ! [V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 14.60/14.68 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.68 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__infE,axiom,
% 14.60/14.68 ! [V_b,V_a,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
% 14.60/14.68 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__mono,axiom,
% 14.60/14.68 ! [V_d,V_b,V_c,V_a,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__greatest,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__infI,axiom,
% 14.60/14.68 ! [V_b,V_a,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__absorb2,axiom,
% 14.60/14.68 ! [V_x,V_y,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__absorb1,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__infI2,axiom,
% 14.60/14.68 ! [V_a,V_x,V_b,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__infI1,axiom,
% 14.60/14.68 ! [V_b,V_x,V_a,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__inf__iff,axiom,
% 14.60/14.68 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__iff__inf,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__le2,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__sup__ord_I2_J,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__le1,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_a)
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__sup__ord_I1_J,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__bot__left,axiom,
% 14.60/14.68 ! [V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Obounded__lattice__bot(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__bot__right,axiom,
% 14.60/14.68 ! [V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Obounded__lattice__bot(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_sup__inf__distrib2,axiom,
% 14.60/14.68 ! [V_x,V_z,V_y,T_a] :
% 14.60/14.68 ( class_Lattices_Odistrib__lattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__sup__distrib2,axiom,
% 14.60/14.68 ! [V_x,V_z,V_y,T_a] :
% 14.60/14.68 ( class_Lattices_Odistrib__lattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_sup__inf__distrib1,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Odistrib__lattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__sup__distrib1,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Odistrib__lattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_sup__inf__absorb,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__sup__absorb,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__iff,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.68 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_IntD1,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_IntD2,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_less__fun__def,axiom,
% 14.60/14.68 ! [V_g_2,V_f_2,T_b,T_c] :
% 14.60/14.68 ( class_Orderings_Oord(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 14.60/14.68 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__not__less,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_b)
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__not__le,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_b)
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__le__less__linear,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.68 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__le,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Oorder(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 & V_x_2 != V_y_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_less__le__not__le,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__le__less,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Oorder(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.68 | V_x_2 = V_y_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_leI,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_a)
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_not__leE,axiom,
% 14.60/14.68 ! [V_x,V_y,T_a] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_a)
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__antisym__conv1,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_b)
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> V_x_2 = V_y_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__neq__le__trans,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( V_a != V_b
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I12_J,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( V_a != V_b
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_leD,axiom,
% 14.60/14.68 ! [V_x,V_y,T_a] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__imp__le,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__antisym__conv2,axiom,
% 14.60/14.68 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.68 ( class_Orderings_Olinorder(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> V_x_2 = V_y_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__le__imp__less__or__eq,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 | V_x = V_y ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__le__neq__trans,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.68 => ( V_a != V_b
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I11_J,axiom,
% 14.60/14.68 ! [V_a,V_b,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.60/14.68 => ( V_a != V_b
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__less__le__trans,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I7_J,axiom,
% 14.60/14.68 ! [V_z,V_x,V_y,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_order__le__less__trans,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Orderings_Opreorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_xt1_I8_J,axiom,
% 14.60/14.68 ! [V_z,V_x,V_y,T_a] :
% 14.60/14.68 ( class_Orderings_Oorder(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_psubsetD,axiom,
% 14.60/14.68 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__empty__left,axiom,
% 14.60/14.68 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__empty__right,axiom,
% 14.60/14.68 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_disjoint__iff__not__equal,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 <=> ! [B_x] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.68 => ! [B_xa] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 14.60/14.68 => B_x != B_xa ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_insert__inter__insert,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_not__psubset__empty,axiom,
% 14.60/14.68 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__lower1,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__lower2,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__absorb2,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__absorb1,axiom,
% 14.60/14.68 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__greatest,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__mono,axiom,
% 14.60/14.68 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_diff__eq__diff__less,axiom,
% 14.60/14.68 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.60/14.68 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__Un__distrib,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Un__Int__distrib,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__Un__distrib2,axiom,
% 14.60/14.68 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Un__Int__distrib2,axiom,
% 14.60/14.68 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Un__Int__crazy,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_less__supI2,axiom,
% 14.60/14.68 ! [V_a,V_b,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_less__supI1,axiom,
% 14.60/14.68 ! [V_b,V_a,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Osemilattice__sup(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_psubset__eq,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 & V_A_2 != V_B_2 ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_subset__iff__psubset__eq,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 | V_A_2 = V_B_2 ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_psubset__imp__subset,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_psubset__subset__trans,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_subset__psubset__trans,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__Int__distrib,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__Diff,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__Int__distrib2,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__Int2,axiom,
% 14.60/14.68 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_vimage__Int,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_distrib__inf__le,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_distrib__sup__le,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Lattices_Olattice(T_a)
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__insert__left__if1,axiom,
% 14.60/14.68 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__insert__right__if1,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__insert__left__if0,axiom,
% 14.60/14.68 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 14.60/14.68 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__insert__right__if0,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 14.60/14.68 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__insert__left,axiom,
% 14.60/14.68 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 14.60/14.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 14.60/14.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Int__insert__right,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 14.60/14.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 14.60/14.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__triv,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__disjoint,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Un__Int__assoc__eq,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__Int,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Diff__Un,axiom,
% 14.60/14.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Un__Diff__Int,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__diff__nat,axiom,
% 14.60/14.68 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_inf__Sup__absorb,axiom,
% 14.60/14.68 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold__graph__insert__swap,axiom,
% 14.60/14.68 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 14.60/14.68 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 14.60/14.68 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.60/14.68 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__diff1__nat,axiom,
% 14.60/14.68 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 14.60/14.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 14.60/14.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__diff,axiom,
% 14.60/14.68 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Oab__group__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__one_Ounion__inter,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__one_Ounion__disjoint,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 14.60/14.68 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.68 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oremove,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.68 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 14.60/14.68 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__strict__mono,axiom,
% 14.60/14.68 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( ! [B_x] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__diff1_H,axiom,
% 14.60/14.68 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum_Oremove,axiom,
% 14.60/14.68 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Ounion__inter,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.60/14.68 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oinsert,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__Un,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.60/14.68 => ( ! [B_x] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.68 => hAPP(V_g_2,B_x) = V_z_2 )
% 14.60/14.68 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__insert,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.68 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__right__imp__eq,axiom,
% 14.60/14.68 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.68 ( class_Groups_Ocancel__semigroup__add(T_a)
% 14.60/14.68 => ( 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)
% 14.60/14.68 => V_b = V_c ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__imp__eq,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 14.60/14.68 => ( 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)
% 14.60/14.68 => V_b = V_c ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__left__imp__eq,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Ocancel__semigroup__add(T_a)
% 14.60/14.68 => ( 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)
% 14.60/14.68 => V_b = V_c ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__right__cancel,axiom,
% 14.60/14.68 ! [V_ca_2,V_a_2,V_b_2,T_b] :
% 14.60/14.68 ( class_Groups_Ocancel__semigroup__add(T_b)
% 14.60/14.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)
% 14.60/14.68 <=> V_b_2 = V_ca_2 ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__left__cancel,axiom,
% 14.60/14.68 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Groups_Ocancel__semigroup__add(T_b)
% 14.60/14.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)
% 14.60/14.68 <=> V_b_2 = V_ca_2 ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oab__semigroup__add(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__le__cancel__right,axiom,
% 14.60/14.68 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__le__cancel__left,axiom,
% 14.60/14.68 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__right__mono,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__left__mono,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__mono,axiom,
% 14.60/14.68 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__le__imp__le__right,axiom,
% 14.60/14.68 ! [V_b,V_c,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(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)))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__le__imp__le__left,axiom,
% 14.60/14.68 ! [V_b,V_a,V_c,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(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)))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__less__imp__less__left,axiom,
% 14.60/14.68 ! [V_b,V_a,V_c,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(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)))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__less__imp__less__right,axiom,
% 14.60/14.68 ! [V_b,V_c,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(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)))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__strict__mono,axiom,
% 14.60/14.68 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__strict__left__mono,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__strict__right__mono,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__less__cancel__left,axiom,
% 14.60/14.68 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__less__cancel__right,axiom,
% 14.60/14.68 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_OF__eq,axiom,
% 14.60/14.68 ! [V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_diff__add__cancel,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Ogroup__add(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__diff__cancel,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Ogroup__add(T_a)
% 14.60/14.68 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__le__less__mono,axiom,
% 14.60/14.68 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__less__le__mono,axiom,
% 14.60/14.68 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 14.60/14.68 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__singleton__def,axiom,
% 14.60/14.68 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 14.60/14.68 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 14.60/14.68 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__singleton,axiom,
% 14.60/14.68 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Osingleton,axiom,
% 14.60/14.68 ! [V_x_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_folding__one_Oeq__fold,axiom,
% 14.60/14.68 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.68 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__Un__nat,axiom,
% 14.60/14.68 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_sup__Inf__absorb,axiom,
% 14.60/14.68 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oin__idem,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Sup__fin_OF__eq,axiom,
% 14.60/14.68 ! [V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum_Oinsert,axiom,
% 14.60/14.68 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__insert,axiom,
% 14.60/14.68 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__Un__Int,axiom,
% 14.60/14.68 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__belowI,axiom,
% 14.60/14.68 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_below__fold1__iff,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
% 14.60/14.68 <=> ! [B_x] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__insert__idem,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__Un2,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 14.60/14.68 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Osubset__idem,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Ounion__idem,axiom,
% 14.60/14.68 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__le__Sup,axiom,
% 14.60/14.68 ! [V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum_Oinsert__remove,axiom,
% 14.60/14.68 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__Un__disjoint,axiom,
% 14.60/14.68 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_setsum__Un,axiom,
% 14.60/14.68 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.68 ( class_Groups_Oab__group__add(T_c)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.68 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_semilattice__big_OF__eq,axiom,
% 14.60/14.68 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.68 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_less__add__iff2,axiom,
% 14.60/14.68 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Rings_Oordered__ring(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_less__add__iff1,axiom,
% 14.60/14.68 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Rings_Oordered__ring(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__add__iff2,axiom,
% 14.60/14.68 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Rings_Oordered__ring(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_le__add__iff1,axiom,
% 14.60/14.68 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Rings_Oordered__ring(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 14.60/14.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_eq__add__iff2,axiom,
% 14.60/14.68 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Rings_Oring(T_b)
% 14.60/14.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 14.60/14.68 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_eq__add__iff1,axiom,
% 14.60/14.68 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Rings_Oring(T_b)
% 14.60/14.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 14.60/14.68 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_Inf__fin_Oclosed,axiom,
% 14.60/14.68 ! [V_A_2,T_b] :
% 14.60/14.68 ( class_Lattices_Olattice(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_fold1__in,axiom,
% 14.60/14.68 ! [V_A_2,T_b] :
% 14.60/14.68 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.68 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 14.60/14.68 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_linorder__neqE__linordered__idom,axiom,
% 14.60/14.68 ! [V_y,V_x,T_a] :
% 14.60/14.68 ( class_Rings_Olinordered__idom(T_a)
% 14.60/14.68 => ( V_x != V_y
% 14.60/14.68 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.60/14.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 14.60/14.68 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 14.60/14.68 ! [V_d,V_c,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 14.60/14.68 ! [V_d,V_c,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 14.60/14.68 ! [V_c,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 14.60/14.68 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 14.60/14.68 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 14.60/14.68 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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))) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 14.60/14.68 ! [V_rx,V_ly,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 14.60/14.68 ! [V_rx,V_ly,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 14.60/14.68 ! [V_ry,V_rx,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 14.60/14.68 ! [V_ry,V_rx,V_lx,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 14.60/14.68 ! [V_b,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_crossproduct__eq,axiom,
% 14.60/14.68 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 14.60/14.68 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 14.60/14.68 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
% 14.60/14.68 <=> ( V_w_2 = V_x_2
% 14.60/14.68 | V_y_2 = V_z_2 ) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_combine__common__factor,axiom,
% 14.60/14.68 ! [V_c,V_b,V_e,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Osemiring(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 14.60/14.68 ! [V_b,V_m,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_comm__semiring__class_Odistrib,axiom,
% 14.60/14.68 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.68 ( class_Rings_Ocomm__semiring(T_a)
% 14.60/14.68 => 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)) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_crossproduct__noteq,axiom,
% 14.60/14.68 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.60/14.68 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 14.60/14.68 => ( ( V_a_2 != V_b_2
% 14.60/14.68 & V_ca_2 != V_d_2 )
% 14.60/14.68 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)) ) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_diff__add__assoc2,axiom,
% 14.60/14.68 ! [V_i,V_j,V_k] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.68 => hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ) ).
% 14.60/14.68
% 14.60/14.68 fof(fact_add__diff__assoc2,axiom,
% 14.60/14.68 ! [V_i,V_j,V_k] :
% 14.60/14.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.68 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ) ).
% 14.60/14.68
% 14.60/14.69 fof(fact_diff__add__assoc,axiom,
% 14.60/14.69 ! [V_i,V_j,V_k] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.69 => hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__imp__diff__is__add,axiom,
% 14.60/14.69 ! [V_k_2,V_j_2,V_i_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 14.60/14.69 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__add__diff__inverse2,axiom,
% 14.60/14.69 ! [V_m,V_n] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__diff__conv2,axiom,
% 14.60/14.69 ! [V_i_2,V_j_2,V_k_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 14.60/14.69 <=> hBOOL(hAPP(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)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__diff__assoc,axiom,
% 14.60/14.69 ! [V_i,V_j,V_k] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__add__diff__inverse,axiom,
% 14.60/14.69 ! [V_m,V_n] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__add__diff,axiom,
% 14.60/14.69 ! [V_m,V_n,V_k] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__diff__conv,axiom,
% 14.60/14.69 ! [V_i_2,V_k_2,V_j_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
% 14.60/14.69 <=> hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__square,axiom,
% 14.60/14.69 ! [V_m] : hBOOL(hAPP(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))) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__cube,axiom,
% 14.60/14.69 ! [V_m] : hBOOL(hAPP(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)))) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult__le__mono1,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult__le__mono2,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult__le__mono,axiom,
% 14.60/14.69 ! [V_l,V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__antisym,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.60/14.69 => V_m = V_n ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__trans,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_eq__imp__le,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( V_m = V_n
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__le__linear,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__refl,axiom,
% 14.60/14.69 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__or__eq__imp__le,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 | V_m = V_n )
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__neq__implies__less,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => ( V_m != V_n
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__imp__le__nat,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__eq__less__or__eq,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 | V_m_2 = V_n_2 ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__less__le,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 & V_m_2 != V_n_2 ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__right__cancel,axiom,
% 14.60/14.69 ! [V_n_2,V_k_2,V_m_2] :
% 14.60/14.69 ( 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)
% 14.60/14.69 <=> V_m_2 = V_n_2 ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__left__cancel,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.69 ( 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)
% 14.60/14.69 <=> V_m_2 = V_n_2 ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__assoc,axiom,
% 14.60/14.69 ! [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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__left__commute,axiom,
% 14.60/14.69 ! [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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__commute,axiom,
% 14.60/14.69 ! [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) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__add2,axiom,
% 14.60/14.69 ! [V_m,V_n] : hBOOL(hAPP(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))) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__add1,axiom,
% 14.60/14.69 ! [V_m,V_n] : hBOOL(hAPP(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))) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__iff__add,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__left__cancel__le,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.69 ( hBOOL(hAPP(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)))
% 14.60/14.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_trans__le__add1,axiom,
% 14.60/14.69 ! [V_m,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_trans__le__add2,axiom,
% 14.60/14.69 ! [V_m,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__le__mono1,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__le__mono,axiom,
% 14.60/14.69 ! [V_l,V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__leD2,axiom,
% 14.60/14.69 ! [V_n,V_k,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(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))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__leD1,axiom,
% 14.60/14.69 ! [V_n,V_k,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(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))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__leE,axiom,
% 14.60/14.69 ! [V_n,V_k,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(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))
% 14.60/14.69 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_not__add__less1,axiom,
% 14.60/14.69 ! [V_j,V_i] : ~ hBOOL(hAPP(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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_not__add__less2,axiom,
% 14.60/14.69 ! [V_i,V_j] : ~ hBOOL(hAPP(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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__mult__distrib2,axiom,
% 14.60/14.69 ! [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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__mult__distrib,axiom,
% 14.60/14.69 ! [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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__add__left__cancel__less,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.69 ( hBOOL(hAPP(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)))
% 14.60/14.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_trans__less__add1,axiom,
% 14.60/14.69 ! [V_m,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_trans__less__add2,axiom,
% 14.60/14.69 ! [V_m,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__less__mono1,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__less__mono,axiom,
% 14.60/14.69 ! [V_l,V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__add__eq__less,axiom,
% 14.60/14.69 ! [V_n,V_m,V_l,V_k] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 14.60/14.69 => ( 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)
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__lessD1,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(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))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__diff__iff,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 14.60/14.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__less__mono,axiom,
% 14.60/14.69 ! [V_c,V_b,V_a] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__less__mono2,axiom,
% 14.60/14.69 ! [V_l,V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__imp__diff__less,axiom,
% 14.60/14.69 ! [V_n,V_k,V_j] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__mult__distrib,axiom,
% 14.60/14.69 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__mult__distrib2,axiom,
% 14.60/14.69 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__commute,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__le__self,axiom,
% 14.60/14.69 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__le__mono2,axiom,
% 14.60/14.69 ! [V_l,V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__le__mono,axiom,
% 14.60/14.69 ! [V_l,V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__diff__cancel,axiom,
% 14.60/14.69 ! [V_n,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_eq__diff__iff,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
% 14.60/14.69 <=> V_m_2 = V_n_2 ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Nat_Odiff__diff__eq,axiom,
% 14.60/14.69 ! [V_n,V_m,V_k] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_le__diff__iff,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 14.60/14.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_add__diff__inverse,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__diff__conv,axiom,
% 14.60/14.69 ! [V_k_2,V_j_2,V_i_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
% 14.60/14.69 <=> hBOOL(hAPP(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)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__add__inverse2,axiom,
% 14.60/14.69 ! [V_n,V_m] : hAPP(hAPP(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 ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__add__inverse,axiom,
% 14.60/14.69 ! [V_m,V_n] : hAPP(hAPP(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 ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__diff__left,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__cancel,axiom,
% 14.60/14.69 ! [V_n,V_m,V_k] : hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__cancel2,axiom,
% 14.60/14.69 ! [V_n,V_k,V_m] : hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__diff__right,axiom,
% 14.60/14.69 ! [V_i,V_j,V_k] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__le__add__iff1,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 14.60/14.69 => ( hBOOL(hAPP(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)))
% 14.60/14.69 <=> hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__less__add__iff1,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 14.60/14.69 => ( hBOOL(hAPP(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)))
% 14.60/14.69 <=> hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__diff__add__eq1,axiom,
% 14.60/14.69 ! [V_n,V_m,V_u,V_i,V_j] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 14.60/14.69 => hAPP(hAPP(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)) = hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__eq__add__iff1,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 14.60/14.69 => ( 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)
% 14.60/14.69 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__le__add__iff2,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 14.60/14.69 => ( hBOOL(hAPP(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)))
% 14.60/14.69 <=> hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__less__add__iff2,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 14.60/14.69 => ( hBOOL(hAPP(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)))
% 14.60/14.69 <=> hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__diff__add__eq2,axiom,
% 14.60/14.69 ! [V_n,V_m,V_u,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => hAPP(hAPP(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)) = hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__eq__add__iff2,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 14.60/14.69 => ( 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)
% 14.60/14.69 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_termination__basic__simps_I3_J,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__mult__assoc,axiom,
% 14.60/14.69 ! [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)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__mult__commute,axiom,
% 14.60/14.69 ! [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) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__not__refl,axiom,
% 14.60/14.69 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__neq__iff,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2] :
% 14.60/14.69 ( V_m_2 != V_n_2
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_linorder__neqE__nat,axiom,
% 14.60/14.69 ! [V_y,V_x] :
% 14.60/14.69 ( V_x != V_y
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__irrefl__nat,axiom,
% 14.60/14.69 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__not__refl2,axiom,
% 14.60/14.69 ! [V_m,V_n] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 14.60/14.69 => V_m != V_n ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__not__refl3,axiom,
% 14.60/14.69 ! [V_t,V_s] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 14.60/14.69 => V_s != V_t ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__less__cases,axiom,
% 14.60/14.69 ! [V_Pa_2,V_n_2,V_m_2] :
% 14.60/14.69 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 14.60/14.69 => ( ( V_m_2 = V_n_2
% 14.60/14.69 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 14.60/14.69 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 14.60/14.69 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_termination__basic__simps_I2_J,axiom,
% 14.60/14.69 ! [V_y,V_z,V_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_termination__basic__simps_I1_J,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_left__add__mult__distrib,axiom,
% 14.60/14.69 ! [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) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_termination__basic__simps_I5_J,axiom,
% 14.60/14.69 ! [V_y,V_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_termination__basic__simps_I4_J,axiom,
% 14.60/14.69 ! [V_y,V_z,V_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff1__less,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff2__less,axiom,
% 14.60/14.69 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Oremove,axiom,
% 14.60/14.69 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Olattice(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Olattice(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold1__eq__fold,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_finite__induct,axiom,
% 14.60/14.69 ! [V_Pa_2,V_F_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.69 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.60/14.69 => ( ! [B_x,B_F] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 14.60/14.69 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 14.60/14.69 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 14.60/14.69 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 14.60/14.69 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
% 14.60/14.69 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold1__antimono,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oidem,axiom,
% 14.60/14.69 ! [V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__assoc,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf_Oassoc,axiom,
% 14.60/14.69 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__left__commute,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 14.60/14.69 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__left__idem,axiom,
% 14.60/14.69 ! [V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 14.60/14.69 ! [V_b,V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__commute,axiom,
% 14.60/14.69 ! [V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf_Ocommute,axiom,
% 14.60/14.69 ! [V_b,V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf_Oidem,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ofold__inf__insert,axiom,
% 14.60/14.69 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__le1,axiom,
% 14.60/14.69 ! [V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__le2,axiom,
% 14.60/14.69 ! [V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ole__iff__inf,axiom,
% 14.60/14.69 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.69 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ole__inf__iff,axiom,
% 14.60/14.69 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.60/14.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ole__infI1,axiom,
% 14.60/14.69 ! [V_b,V_x,V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ole__infI2,axiom,
% 14.60/14.69 ! [V_a,V_x,V_b,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__absorb1,axiom,
% 14.60/14.69 ! [V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__absorb2,axiom,
% 14.60/14.69 ! [V_x,V_y,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ole__infI,axiom,
% 14.60/14.69 ! [V_b,V_a,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__greatest,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oinf__mono,axiom,
% 14.60/14.69 ! [V_d,V_b,V_c,V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ole__infE,axiom,
% 14.60/14.69 ! [V_b,V_a,V_x,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
% 14.60/14.69 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.60/14.69 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__le__iff__disj,axiom,
% 14.60/14.69 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 14.60/14.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__less__iff__disj,axiom,
% 14.60/14.69 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 14.60/14.69 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__less__iff__conj,axiom,
% 14.60/14.69 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
% 14.60/14.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 14.60/14.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oless__infI2,axiom,
% 14.60/14.69 ! [V_a,V_x,V_b,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Oless__infI1,axiom,
% 14.60/14.69 ! [V_b,V_x,V_a,T_a] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__add__distrib__left,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.69 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__diff__distrib__left,axiom,
% 14.60/14.69 ! [V_z,V_y,V_x,T_a] :
% 14.60/14.69 ( class_Groups_Oordered__ab__group__add(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 14.60/14.69 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 14.60/14.69 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_inf__min,axiom,
% 14.60/14.69 ! [T_b] :
% 14.60/14.69 ( ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.69 & class_Orderings_Olinorder(T_b) )
% 14.60/14.69 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__empty,axiom,
% 14.60/14.69 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__diff,axiom,
% 14.60/14.69 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 14.60/14.69 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__insert__le,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__seteq,axiom,
% 14.60/14.69 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 14.60/14.69 => V_A_2 = V_B_2 ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__mono,axiom,
% 14.60/14.69 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_union__fold__insert,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__sup__insert,axiom,
% 14.60/14.69 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Osemilattice__sup(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__inf__insert,axiom,
% 14.60/14.69 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_psubset__card__mono,axiom,
% 14.60/14.69 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__insert,axiom,
% 14.60/14.69 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Oinsert,axiom,
% 14.60/14.69 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__Un__Int,axiom,
% 14.60/14.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Ounion__inter,axiom,
% 14.60/14.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Un__Int,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card_Ounion__inter,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_sup__le__fold__sup,axiom,
% 14.60/14.69 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Osemilattice__sup(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__inf__le__inf,axiom,
% 14.60/14.69 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff__subset,axiom,
% 14.60/14.69 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff__subset__Int,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_diff__card__le__card__Diff,axiom,
% 14.60/14.69 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Ofold1__belowI,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold1__below__iff,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 14.60/14.69 <=> ? [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 14.60/14.69 <=> ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold1__strict__below__iff,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 14.60/14.69 <=> ? [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_strict__below__fold1__iff,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 14.60/14.69 <=> ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__psubset,axiom,
% 14.60/14.69 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold1__eq__fold__idem,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Olattice(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Lattices_Olattice(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_folding__one_Oeq__fold_H,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Oinsert__remove,axiom,
% 14.60/14.69 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Ounion__disjoint,axiom,
% 14.60/14.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__Un__disjoint,axiom,
% 14.60/14.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Un__disjoint,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff1__le,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 14.60/14.69 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__ord__min,axiom,
% 14.60/14.69 ! [T_b] :
% 14.60/14.69 ( class_Orderings_Oord(T_b)
% 14.60/14.69 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 14.60/14.69 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff__singleton,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff__singleton__if,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 14.60/14.69 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card_Oremove,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oremove,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 14.60/14.69 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 14.60/14.69 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 14.60/14.69 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 14.60/14.69 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 14.60/14.69 | ? [B_x,B_y] :
% 14.60/14.69 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 14.60/14.69 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 14.60/14.69 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 14.60/14.69 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_inf__nat__def,axiom,
% 14.60/14.69 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_one__reorient,axiom,
% 14.60/14.69 ! [V_x_2,T_b] :
% 14.60/14.69 ( class_Groups_Oone(T_b)
% 14.60/14.69 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 14.60/14.69 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 14.60/14.69 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult__1__left,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Groups_Omonoid__mult(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult__1,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult__1__right,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Groups_Omonoid__mult(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_mult_Ocomm__neutral,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_a)
% 14.60/14.69 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__eq__1__iff,axiom,
% 14.60/14.69 ! [V_f_2,V_F_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.69 <=> ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 14.60/14.69 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__mult__eq__1__iff,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2] :
% 14.60/14.69 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.69 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.69 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__mult__1__right,axiom,
% 14.60/14.69 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__1__eq__mult__iff,axiom,
% 14.60/14.69 ! [V_n_2,V_m_2] :
% 14.60/14.69 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 14.60/14.69 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.69 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat__mult__1,axiom,
% 14.60/14.69 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm,axiom,
% 14.60/14.69 ! [T_b] :
% 14.60/14.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 14.60/14.69 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__add__one,axiom,
% 14.60/14.69 ! [V_a,T_a] :
% 14.60/14.69 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.69 => hBOOL(hAPP(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)))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__1__mult,axiom,
% 14.60/14.69 ! [V_n,V_m,T_a] :
% 14.60/14.69 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 14.60/14.69 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 14.60/14.69 ! [V_m,T_a] :
% 14.60/14.69 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.69 => 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) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 14.60/14.69 ! [V_a,V_m,T_a] :
% 14.60/14.69 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.69 => 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) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 14.60/14.69 ! [V_m,V_a,T_a] :
% 14.60/14.69 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.69 => 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) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 14.60/14.69 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 14.60/14.69 => V_y_2 = V_x_2 ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Oempty,axiom,
% 14.60/14.69 ! [V_g_2,T_c,T_b] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__empty,axiom,
% 14.60/14.69 ! [V_f_2,T_c,T_b] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__infinite,axiom,
% 14.60/14.69 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Oinfinite,axiom,
% 14.60/14.69 ! [V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Osingleton,axiom,
% 14.60/14.69 ! [V_x_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 14.60/14.69 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 14.60/14.69 ! [V_x_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min__le,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min__in,axiom,
% 14.60/14.69 ! [V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oin__idem,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 14.60/14.69 ! [V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 14.60/14.69 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_OF__eq,axiom,
% 14.60/14.69 ! [V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min__antimono,axiom,
% 14.60/14.69 ! [V_N_2,V_M_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 14.60/14.69 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min__insert,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Osubset__idem,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min__Un,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 14.60/14.69 ! [V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 14.60/14.69 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card_Oinsert,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.60/14.69 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oinsert,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oinsert__remove,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.60/14.69 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Ounion__inter,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Ounion__disjoint,axiom,
% 14.60/14.69 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oeq__fold_H,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Diff__insert,axiom,
% 14.60/14.69 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card_Oinsert__remove,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 14.60/14.69 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 14.60/14.69 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 14.60/14.69 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.69 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.69 => ? [B_y_H] :
% 14.60/14.69 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 14.60/14.69 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 14.60/14.69 ! [V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Min_Oclosed,axiom,
% 14.60/14.69 ! [V_A_2,T_b] :
% 14.60/14.69 ( class_Orderings_Olinorder(T_b)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 14.60/14.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.60/14.69 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__Un__one,axiom,
% 14.60/14.69 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.60/14.69 => ( ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 14.60/14.69 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_fold__Un__disjoint,axiom,
% 14.60/14.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.69 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__mono__one__right,axiom,
% 14.60/14.69 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 14.60/14.69 => ( ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 14.60/14.69 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_setprod__mono__one__left,axiom,
% 14.60/14.69 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 14.60/14.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 14.60/14.69 => ( ! [B_x] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 14.60/14.69 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 14.60/14.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_card__Suc__Diff1,axiom,
% 14.60/14.69 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.69 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Suc__mono,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_lessI,axiom,
% 14.60/14.69 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Suc__inject,axiom,
% 14.60/14.69 ! [V_y,V_x] :
% 14.60/14.69 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 14.60/14.69 => V_x = V_y ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_nat_Oinject,axiom,
% 14.60/14.69 ! [V_nat_H_2,V_nat_2] :
% 14.60/14.69 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 14.60/14.69 <=> V_nat_2 = V_nat_H_2 ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Suc__n__not__n,axiom,
% 14.60/14.69 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 14.60/14.69
% 14.60/14.69 fof(fact_n__not__Suc__n,axiom,
% 14.60/14.69 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Suc__less__SucD,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_Suc__lessD,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__SucE,axiom,
% 14.60/14.69 ! [V_n,V_m] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 14.60/14.69 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.69 => V_m = V_n ) ) ).
% 14.60/14.69
% 14.60/14.69 fof(fact_less__trans__Suc,axiom,
% 14.60/14.69 ! [V_k,V_j,V_i] :
% 14.60/14.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 14.60/14.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__lessI,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__SucI,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__antisym,axiom,
% 14.60/14.70 ! [V_m,V_n] :
% 14.60/14.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 14.60/14.70 => V_m = V_n ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__less__less__Suc__eq,axiom,
% 14.60/14.70 ! [V_m_2,V_n_2] :
% 14.60/14.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 14.60/14.70 <=> V_n_2 = V_m_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__less__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__Suc__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.70 | V_m_2 = V_n_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__less__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__Suc__shift,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__Suc,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__Suc__right,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__leD,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__SucE,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 14.60/14.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__SucI,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__le__mono,axiom,
% 14.60/14.70 ! [V_m_2,V_n_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__Suc__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.70 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__less__eq__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__n__not__le__n,axiom,
% 14.60/14.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__Suc__Suc,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__diff__diff,axiom,
% 14.60/14.70 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__mult__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
% 14.60/14.70 <=> V_m_2 = V_n_2 ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fold__image__empty,axiom,
% 14.60/14.70 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 14.60/14.70
% 14.60/14.70 fof(fact_min__Suc__Suc,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__add__Suc1,axiom,
% 14.60/14.70 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__add__Suc2,axiom,
% 14.60/14.70 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__iff__Suc__add,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.70 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__le__lessD,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__less__Suc__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 14.60/14.70 <=> V_n_2 = V_m_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__leI,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__imp__less__Suc,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__le__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__Suc__eq__le,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__eq__Suc__le,axiom,
% 14.60/14.70 ! [V_m_2,V_n_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__less__Suc,axiom,
% 14.60/14.70 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__mult__less__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__Suc__right,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(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)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__Suc,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(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)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__diff__le,axiom,
% 14.60/14.70 ! [V_m,V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.60/14.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__mult__le__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__Suc__1,axiom,
% 14.60/14.70 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 14.60/14.70
% 14.60/14.70 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 14.60/14.70 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.70 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__Suc__diff__eq1,axiom,
% 14.60/14.70 ! [V_m,V_j,V_k] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__Suc__diff__eq2,axiom,
% 14.60/14.70 ! [V_m,V_j,V_k] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 14.60/14.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__insert__disjoint,axiom,
% 14.60/14.70 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__insert__if,axiom,
% 14.60/14.70 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
% 14.60/14.70 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fold__image__insert,axiom,
% 14.60/14.70 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Oab__semigroup__mult(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.60/14.70 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setprod_OF__eq,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.70 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) )
% 14.60/14.70 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setprod_Oeq__fold,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__insert,axiom,
% 14.60/14.70 ! [V_x_2,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fold__image__Un__Int,axiom,
% 14.60/14.70 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.60/14.70 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 14.60/14.70 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__eq__plus1__left,axiom,
% 14.60/14.70 ! [V_n] : hAPP(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) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__eq__plus1,axiom,
% 14.60/14.70 ! [V_n] : hAPP(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)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__monoid__big_OF__eq,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 14.60/14.70 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.70 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) )
% 14.60/14.70 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.70 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fold__image__Un__one,axiom,
% 14.60/14.70 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.60/14.70 => ( ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 14.60/14.70 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 14.60/14.70 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__fold__sup,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 14.60/14.70 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
% 14.60/14.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.70 => ~ ! [B_y] :
% 14.60/14.70 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 14.60/14.70 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_finite__UnionD,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_sup__Sup__fold__sup,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__fin__Sup,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.70 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 14.60/14.70 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 14.60/14.70 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__binary,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__insert,axiom,
% 14.60/14.70 ! [V_A_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__singleton,axiom,
% 14.60/14.70 ! [V_a_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__empty,axiom,
% 14.60/14.70 ! [T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__upper,axiom,
% 14.60/14.70 ! [V_A_2,V_x_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_UnionI,axiom,
% 14.60/14.70 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__mono,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__Sup__iff,axiom,
% 14.60/14.70 ! [V_S_2,V_a_2,T_b] :
% 14.60/14.70 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 & class_Orderings_Olinorder(T_b) )
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 14.60/14.70 <=> ? [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__empty,axiom,
% 14.60/14.70 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__upper,axiom,
% 14.60/14.70 ! [V_A_2,V_B_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__insert,axiom,
% 14.60/14.70 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Un__eq__Union,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__Un__distrib,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__disjoint,axiom,
% 14.60/14.70 ! [V_A_2,V_C_2,T_b] :
% 14.60/14.70 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.70 <=> ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 14.60/14.70 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Union__Int__subset,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Sup__le__iff,axiom,
% 14.60/14.70 ! [V_b_2,V_A_2,T_b] :
% 14.60/14.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
% 14.60/14.70 <=> ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_finite__Union,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 14.60/14.70 => ( ! [B_M] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 14.60/14.70 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 14.60/14.70 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_insert__partition,axiom,
% 14.60/14.70 ! [V_F_2,V_x_2,T_b] :
% 14.60/14.70 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 14.60/14.70 => ( ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 14.60/14.70 => ! [B_xa] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 14.60/14.70 => ( B_x != B_xa
% 14.60/14.70 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 14.60/14.70 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_convex__bound__lt,axiom,
% 14.60/14.70 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 14.60/14.70 => hBOOL(hAPP(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)) ) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__partition,axiom,
% 14.60/14.70 ! [V_k_2,V_C_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 14.60/14.70 => ( ! [B_c] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 14.60/14.70 => ( ! [B_c1] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 14.60/14.70 => ! [B_c2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 14.60/14.70 => ( B_c1 != B_c2
% 14.60/14.70 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 14.60/14.70 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fold__image__1,axiom,
% 14.60/14.70 ! [V_f_2,V_S_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.60/14.70 => ( ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 14.60/14.70 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 14.60/14.70 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__Plus,axiom,
% 14.60/14.70 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__zeroE,axiom,
% 14.60/14.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le0,axiom,
% 14.60/14.70 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__Suc,axiom,
% 14.60/14.70 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__reorient,axiom,
% 14.60/14.70 ! [V_x_2,T_b] :
% 14.60/14.70 ( class_Groups_Ozero(T_b)
% 14.60/14.70 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 14.60/14.70 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 14.60/14.70 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 14.60/14.70 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 14.60/14.70 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__0__iff,axiom,
% 14.60/14.70 ! [V_a_2,V_b_2,T_b] :
% 14.60/14.70 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 14.60/14.70 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 14.60/14.70 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__0__left,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Groups_Omonoid__add(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__0,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_double__zero__sym,axiom,
% 14.60/14.70 ! [V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.60/14.70 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 14.60/14.70 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__0__right,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Groups_Omonoid__add(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add_Ocomm__neutral,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_divisors__zero,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Ono__zero__divisors(T_a)
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 14.60/14.70 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 14.60/14.70 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_no__zero__divisors,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Ono__zero__divisors(T_a)
% 14.60/14.70 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 14.60/14.70 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__eq__0__iff,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Rings_Oring__no__zero__divisors(T_b)
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.70 => 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) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__zero__right,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Omult__zero(T_a)
% 14.60/14.70 => 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) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.60/14.70 => 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) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__zero__left,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Omult__zero(T_a)
% 14.60/14.70 => 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) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_right__minus__eq,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Ogroup__add(T_b)
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 <=> V_a_2 = V_b_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_eq__iff__diff__eq__0,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Oab__group__add(T_b)
% 14.60/14.70 => ( V_a_2 = V_b_2
% 14.60/14.70 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__self,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Groups_Ogroup__add(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__0__right,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Groups_Ogroup__add(T_a)
% 14.60/14.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_one__neq__zero,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Ozero__neq__one(T_a)
% 14.60/14.70 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__neq__one,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Ozero__neq__one(T_a)
% 14.60/14.70 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Zero__not__Suc,axiom,
% 14.60/14.70 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat_Osimps_I2_J,axiom,
% 14.60/14.70 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__not__Zero,axiom,
% 14.60/14.70 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat_Osimps_I3_J,axiom,
% 14.60/14.70 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Zero__neq__Suc,axiom,
% 14.60/14.70 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__neq__Zero,axiom,
% 14.60/14.70 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__less0,axiom,
% 14.60/14.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_neq0__conv,axiom,
% 14.60/14.70 ! [V_n_2] :
% 14.60/14.70 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__nat__zero__code,axiom,
% 14.60/14.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_gr__implies__not0,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_gr0I,axiom,
% 14.60/14.70 ! [V_n] :
% 14.60/14.70 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_plus__nat_Oadd__0,axiom,
% 14.60/14.70 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Nat_Oadd__0__right,axiom,
% 14.60/14.70 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__is__0,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__eq__self__zero,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 14.60/14.70 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 14.60/14.70 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__0__eq,axiom,
% 14.60/14.70 ! [V_n_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 14.60/14.70 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diffs0__imp__equal,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 => V_m = V_n ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__self__eq__0,axiom,
% 14.60/14.70 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_minus__nat_Odiff__0,axiom,
% 14.60/14.70 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__0__eq__0,axiom,
% 14.60/14.70 ! [V_n] : hAPP(hAPP(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) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__cancel2,axiom,
% 14.60/14.70 ! [V_n_2,V_k_2,V_m_2] :
% 14.60/14.70 ( 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)
% 14.60/14.70 <=> ( V_m_2 = V_n_2
% 14.60/14.70 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( 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)
% 14.60/14.70 <=> ( V_m_2 = V_n_2
% 14.60/14.70 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__is__0,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__0__right,axiom,
% 14.60/14.70 ! [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) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__0,axiom,
% 14.60/14.70 ! [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) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( 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)
% 14.60/14.70 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 | V_m_2 = V_n_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_min__0R,axiom,
% 14.60/14.70 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_min__0L,axiom,
% 14.60/14.70 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem__insert,axiom,
% 14.60/14.70 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_finite__Plus__iff,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 14.60/14.70 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_finite__Plus,axiom,
% 14.60/14.70 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_finite__PlusD_I1_J,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_finite__PlusD_I2_J,axiom,
% 14.60/14.70 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__Plus__conv__if,axiom,
% 14.60/14.70 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.60/14.70 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) )
% 14.60/14.70 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem,axiom,
% 14.60/14.70 ! [T_b] :
% 14.60/14.70 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 14.60/14.70 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem__sup,axiom,
% 14.60/14.70 ! [T_b] :
% 14.60/14.70 ( class_Lattices_Osemilattice__sup(T_b)
% 14.60/14.70 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_fun__left__comm__idem__inf,axiom,
% 14.60/14.70 ! [T_b] :
% 14.60/14.70 ( class_Lattices_Osemilattice__inf(T_b)
% 14.60/14.70 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 14.60/14.70 ! [T_b] :
% 14.60/14.70 ( class_Orderings_Olinorder(T_b)
% 14.60/14.70 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 14.60/14.70 ! [V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 14.60/14.70 ! [V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__nonneg__nonneg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__nonneg__eq__0__iff,axiom,
% 14.60/14.70 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__increasing,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__increasing2,axiom,
% 14.60/14.70 ! [V_a,V_b,V_c,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__nonpos__nonpos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__le__square,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring(T_a)
% 14.60/14.70 => hBOOL(hAPP(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))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__le__mult__iff,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
% 14.60/14.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 14.60/14.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__le__0__iff,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 14.60/14.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__nonneg__nonneg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__cancel__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__nonneg__nonpos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__cancel__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__nonneg__nonpos2,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__cancel__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__nonpos__nonneg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__cancel__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__nonpos__nonpos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__ring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__right__mono,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__left__mono,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__mult__left__mono,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__comm__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__right__mono__neg,axiom,
% 14.60/14.70 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__ring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__left__mono__neg,axiom,
% 14.60/14.70 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__ring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__mono_H,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__mono,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_split__mult__pos__le,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__ring(T_a)
% 14.60/14.70 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 14.60/14.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_split__mult__neg__le,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Oordered__cancel__semiring(T_a)
% 14.60/14.70 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 14.60/14.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_pos__add__strict,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 14.60/14.70 ! [V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 14.60/14.70 ! [V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__pos__pos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__neg__neg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__strict__left__mono__neg,axiom,
% 14.60/14.70 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__strict__right__mono__neg,axiom,
% 14.60/14.70 ! [V_c,V_a,V_b,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_comm__mult__strict__left__mono,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__strict__left__mono,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__strict__right__mono,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__neg__neg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__neg__pos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__cancel__left__neg,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__mult__pos2,axiom,
% 14.60/14.70 ! [V_a,V_b,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__mult__pos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__pos__neg2,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__pos__neg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__pos__pos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__cancel__left__pos,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__cancel__left__disj,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 14.60/14.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 14.60/14.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__cancel__right__disj,axiom,
% 14.60/14.70 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
% 14.60/14.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 14.60/14.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__square__less__zero,axiom,
% 14.60/14.70 ! [V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring(T_a)
% 14.60/14.70 => ~ hBOOL(hAPP(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))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_le__iff__diff__le__0,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__iff__diff__less__0,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,T_b] :
% 14.60/14.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_sum__squares__eq__zero__iff,axiom,
% 14.60/14.70 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__scale__eq__noteq,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 14.60/14.70 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 14.60/14.70 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 14.60/14.70 => ( ( V_a = V_b
% 14.60/14.70 & V_c != V_d )
% 14.60/14.70 => 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)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__one__le__zero,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__le__one,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__one,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__one__less__zero,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum__empty,axiom,
% 14.60/14.70 ! [V_f_2,T_c,T_b] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum_Oempty,axiom,
% 14.60/14.70 ! [V_g_2,T_c,T_b] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum_Oinfinite,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.70 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum__infinite,axiom,
% 14.60/14.70 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.70 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setprod__zero__iff,axiom,
% 14.60/14.70 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 14.60/14.70 & class_Rings_Ono__zero__divisors(T_c) )
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
% 14.60/14.70 <=> ? [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.70 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setprod__zero,axiom,
% 14.60/14.70 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Rings_Ocomm__semiring__1(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( ? [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.70 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__Suc__eq__0__disj,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 14.60/14.70 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 | ? [B_j] :
% 14.60/14.70 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_less__Suc0,axiom,
% 14.60/14.70 ! [V_n_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 14.60/14.70 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_gr0__conv__Suc,axiom,
% 14.60/14.70 ! [V_n_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 14.60/14.70 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_one__is__add,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hAPP(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)
% 14.60/14.70 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.60/14.70 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__is__1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.60/14.70 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__gr__0,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 14.60/14.70 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card_Oempty,axiom,
% 14.60/14.70 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__infinite,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__eq__1__iff,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__diff,axiom,
% 14.60/14.70 ! [V_m_2,V_n_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__less,axiom,
% 14.60/14.70 ! [V_m,V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__0__less__mult__iff,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__cancel2,axiom,
% 14.60/14.70 ! [V_n_2,V_k_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__mono1,axiom,
% 14.60/14.70 ! [V_k,V_j,V_i] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__mono2,axiom,
% 14.60/14.70 ! [V_k,V_j,V_i] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__mult__less__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__mult__eq__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 => ( 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)
% 14.60/14.70 <=> V_m_2 = V_n_2 ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__add__0,axiom,
% 14.60/14.70 ! [V_m,V_n] : hAPP(hAPP(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) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__is__0__eq_H,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.60/14.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__is__0__eq,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_One__nat__def,axiom,
% 14.60/14.70 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__eq__self__implies__10,axiom,
% 14.60/14.70 ! [V_n,V_m] :
% 14.60/14.70 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 14.60/14.70 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.70 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum__eq__0__iff,axiom,
% 14.60/14.70 ! [V_f_2,V_F_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.60/14.70 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 <=> ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 14.60/14.70 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__nonpos__neg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__neg__nonpos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__strict__increasing2,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__strict__increasing,axiom,
% 14.60/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__nonneg__pos,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_add__pos__nonneg,axiom,
% 14.60/14.70 ! [V_b,V_a,T_a] :
% 14.60/14.70 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__le__cancel__left__pos,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__le__cancel__left__neg,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__strict__mono,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__strict__mono_H,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__le__imp__less,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__le__less__imp__less,axiom,
% 14.60/14.70 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__right__less__imp__less,axiom,
% 14.60/14.70 ! [V_b,V_c,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__imp__less__right,axiom,
% 14.60/14.70 ! [V_b,V_c,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__left__less__imp__less,axiom,
% 14.60/14.70 ! [V_b,V_a,V_c,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__less__imp__less__left,axiom,
% 14.60/14.70 ! [V_b,V_a,V_c,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__right__le__imp__le,axiom,
% 14.60/14.70 ! [V_b,V_c,V_a,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__left__le__imp__le,axiom,
% 14.60/14.70 ! [V_b,V_a,V_c,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__strict(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_sum__squares__ge__zero,axiom,
% 14.60/14.70 ! [V_y,V_x,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring(T_a)
% 14.60/14.70 => hBOOL(hAPP(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)))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_sum__squares__le__zero__iff,axiom,
% 14.60/14.70 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
% 14.60/14.70 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_sum__squares__gt__zero__iff,axiom,
% 14.60/14.70 ! [V_y_2,V_x_2,T_b] :
% 14.60/14.70 ( class_Rings_Olinordered__ring__strict(T_b)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
% 14.60/14.70 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.60/14.70 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_not__sum__squares__lt__zero,axiom,
% 14.60/14.70 ! [V_y,V_x,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__ring(T_a)
% 14.60/14.70 => ~ hBOOL(hAPP(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))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__right__le__one__le,axiom,
% 14.60/14.70 ! [V_y,V_x,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__idom(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__left__le__one__le,axiom,
% 14.60/14.70 ! [V_y,V_x,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__idom(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_zero__less__two,axiom,
% 14.60/14.70 ! [T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semidom(T_a)
% 14.60/14.70 => hBOOL(hAPP(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)))) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__eq__0__iff,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.60/14.70 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.70 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__ge__0__finite,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 14.60/14.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__pred,axiom,
% 14.60/14.70 ! [V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.60/14.70 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_diff__Suc__less,axiom,
% 14.60/14.70 ! [V_i,V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_n__less__m__mult__n,axiom,
% 14.60/14.70 ! [V_m,V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_n__less__n__mult__m,axiom,
% 14.60/14.70 ! [V_m,V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 14.60/14.70 => hBOOL(hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_one__less__mult,axiom,
% 14.60/14.70 ! [V_m,V_n] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(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))) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__diff__split__asm,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_Pa_2] :
% 14.60/14.70 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 14.60/14.70 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 14.60/14.70 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 14.60/14.70 | ? [B_d] :
% 14.60/14.70 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 14.60/14.70 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__diff__split,axiom,
% 14.60/14.70 ! [V_b_2,V_a_2,V_Pa_2] :
% 14.60/14.70 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 14.60/14.70 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 14.60/14.70 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 14.60/14.70 & ! [B_d] :
% 14.60/14.70 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 14.60/14.70 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_one__le__mult__iff,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 14.60/14.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_nat__mult__le__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 => ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__le__cancel1,axiom,
% 14.60/14.70 ! [V_n_2,V_m_2,V_k_2] :
% 14.60/14.70 ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_mult__le__cancel2,axiom,
% 14.60/14.70 ! [V_n_2,V_k_2,V_m_2] :
% 14.60/14.70 ( hBOOL(hAPP(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)))
% 14.60/14.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum__eq__Suc0__iff,axiom,
% 14.60/14.70 ! [V_f_2,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 <=> ? [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.70 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.60/14.70 & ! [B_xa] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 14.60/14.70 => ( B_x != B_xa
% 14.60/14.70 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum__eq__1__iff,axiom,
% 14.60/14.70 ! [V_f_2,V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.70 <=> ? [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.60/14.70 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 14.60/14.70 & ! [B_xa] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 14.60/14.70 => ( B_x != B_xa
% 14.60/14.70 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setprod__pos__nat__iff,axiom,
% 14.60/14.70 ! [V_f_2,V_S_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
% 14.60/14.70 <=> ! [B_x] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 14.60/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_convex__bound__le,axiom,
% 14.60/14.70 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 14.60/14.70 ( class_Rings_Olinordered__semiring__1(T_a)
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 14.60/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 14.60/14.70 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 14.60/14.70 => hBOOL(hAPP(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)) ) ) ) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_card__gt__0__iff,axiom,
% 14.60/14.70 ! [V_A_2,T_b] :
% 14.60/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 14.60/14.70 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.60/14.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum_OF__eq,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.70 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) )
% 14.60/14.70 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_setsum_Oeq__fold,axiom,
% 14.60/14.70 ! [V_g_2,V_A_2,T_b,T_c] :
% 14.60/14.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.60/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.60/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ).
% 14.60/14.70
% 14.60/14.70 fof(fact_Suc__pred_H,axiom,
% 14.60/14.70 ! [V_n] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.70 => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_Suc__diff__1,axiom,
% 14.82/14.70 ! [V_n] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.70 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_add__eq__if,axiom,
% 14.82/14.70 ! [V_n,V_m] :
% 14.82/14.70 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 14.82/14.70 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.70 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_mult__eq__if,axiom,
% 14.82/14.70 ! [V_n,V_m] :
% 14.82/14.70 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.70 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.70 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.70 => 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_even__less__0__iff,axiom,
% 14.82/14.70 ! [V_a_2,T_b] :
% 14.82/14.70 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_setsum__mono2,axiom,
% 14.82/14.70 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 14.82/14.70 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.70 => ( ! [B_b] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 14.82/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 14.82/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_triple_Osize_I1_J,axiom,
% 14.82/14.70 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_Plus__eq__empty__conv,axiom,
% 14.82/14.70 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.70 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
% 14.82/14.70 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.70 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_card_Ounion__inter__neutral,axiom,
% 14.82/14.70 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.70 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.70 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.70 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 14.82/14.70 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.70 => ( ! [B_x] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.70 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 14.82/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_setsum__Un__zero,axiom,
% 14.82/14.70 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 14.82/14.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.82/14.70 => ( ! [B_x] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
% 14.82/14.70 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 14.82/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_setsum__mono3,axiom,
% 14.82/14.70 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 14.82/14.70 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.70 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.70 => ( ! [B_x] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 14.82/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 14.82/14.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_bot__nat__def,axiom,
% 14.82/14.70 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_double__eq__0__iff,axiom,
% 14.82/14.70 ! [V_a_2,T_b] :
% 14.82/14.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.70 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.70 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_triple_Osize_I2_J,axiom,
% 14.82/14.70 ! [V_fun2_2,V_com_2,V_fun1_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_card__Suc__eq,axiom,
% 14.82/14.70 ! [V_k_2,V_A_2,T_b] :
% 14.82/14.70 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 14.82/14.70 <=> ? [B_b,B_B] :
% 14.82/14.70 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 14.82/14.70 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 14.82/14.70 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 14.82/14.70 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.70 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_Ints__odd__less__0,axiom,
% 14.82/14.70 ! [V_a_2,T_b] :
% 14.82/14.70 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_com_Osize_I4_J,axiom,
% 14.82/14.70 ! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_com_Osize_I12_J,axiom,
% 14.82/14.70 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_setprod__diff1,axiom,
% 14.82/14.70 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.70 ( class_Fields_Ofield(T_c)
% 14.82/14.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.70 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 14.82/14.70 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 14.82/14.70 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_ex__least__nat__less,axiom,
% 14.82/14.70 ! [V_n_2,V_Pa_2] :
% 14.82/14.70 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 14.82/14.70 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 14.82/14.70 => ? [B_k] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 14.82/14.70 & ! [B_i] :
% 14.82/14.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 14.82/14.70 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 14.82/14.70 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_divide__zero__left,axiom,
% 14.82/14.70 ! [V_a,T_a] :
% 14.82/14.70 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.70 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_divide__zero,axiom,
% 14.82/14.70 ! [V_a,T_a] :
% 14.82/14.70 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 14.82/14.70 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_add__divide__distrib,axiom,
% 14.82/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.70 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.70 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 14.82/14.70
% 14.82/14.70 fof(fact_times__divide__eq__right,axiom,
% 14.82/14.70 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.70 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_diff__divide__distrib,axiom,
% 14.82/14.71 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__1,axiom,
% 14.82/14.71 ! [V_a,T_a] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nonzero__eq__divide__eq,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_b)
% 14.82/14.71 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 14.82/14.71 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nonzero__divide__eq__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_b)
% 14.82/14.71 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 14.82/14.71 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__eq__imp,axiom,
% 14.82/14.71 ! [V_a,V_b,V_c,T_a] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.71 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__divide__imp,axiom,
% 14.82/14.71 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.71 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 14.82/14.71 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__self__if,axiom,
% 14.82/14.71 ! [V_a,T_a] :
% 14.82/14.71 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 14.82/14.71 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 14.82/14.71 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__self,axiom,
% 14.82/14.71 ! [V_a,T_a] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.71 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_right__inverse__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_b_2,T_b] :
% 14.82/14.71 ( class_Rings_Odivision__ring(T_b)
% 14.82/14.71 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.71 <=> V_a_2 = V_b_2 ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__0,axiom,
% 14.82/14.71 ! [T_b] :
% 14.82/14.71 ( class_Rings_Oring__1(T_b)
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__add,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Rings_Oring__1(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__mult,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Rings_Oring__1(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__diff,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Rings_Oring__1(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__1,axiom,
% 14.82/14.71 ! [T_b] :
% 14.82/14.71 ( class_Rings_Oring__1(T_b)
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osize_I9_J,axiom,
% 14.82/14.71 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osize_I1_J,axiom,
% 14.82/14.71 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__double__eq__0__iff,axiom,
% 14.82/14.71 ! [V_a_2,T_b] :
% 14.82/14.71 ( class_Int_Oring__char__0(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__odd__nonzero,axiom,
% 14.82/14.71 ! [V_a_2,T_b] :
% 14.82/14.71 ( class_Int_Oring__char__0(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__divide__eq,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__le__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_pos__le__divide__eq,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_pos__divide__le__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__imp__div__pos__le,axiom,
% 14.82/14.71 ! [V_z,V_x,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__imp__le__div__pos,axiom,
% 14.82/14.71 ! [V_x,V_z,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__le__divide__eq,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_times__divide__times__eq,axiom,
% 14.82/14.71 ! [V_w,V_z,V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zero__le__divide__iff,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 14.82/14.71 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__le__0__iff,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 14.82/14.71 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__right__mono,axiom,
% 14.82/14.71 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__right__mono__neg,axiom,
% 14.82/14.71 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__strict__right__mono__neg,axiom,
% 14.82/14.71 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__strict__right__mono,axiom,
% 14.82/14.71 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__neg__neg,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__neg__pos,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__pos__neg,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__pos__pos,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__less__0__iff,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 14.82/14.71 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zero__less__divide__iff,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 14.82/14.71 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__divide__eq,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_b)
% 14.82/14.71 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 14.82/14.71 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 )
% 14.82/14.71 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__eq__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_b)
% 14.82/14.71 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 14.82/14.71 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 14.82/14.71 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__divide__mult__cancel__right,axiom,
% 14.82/14.71 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.71 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__divide__mult__cancel__left,axiom,
% 14.82/14.71 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.71 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_frac__eq__eq,axiom,
% 14.82/14.71 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 14.82/14.71 ( class_Fields_Ofield(T_b)
% 14.82/14.71 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
% 14.82/14.71 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__nonneg__pos,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__nonneg__neg,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_frac__less2,axiom,
% 14.82/14.71 ! [V_z,V_w,V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_frac__less,axiom,
% 14.82/14.71 ! [V_z,V_w,V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_frac__le,axiom,
% 14.82/14.71 ! [V_z,V_w,V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__nonpos__pos,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__nonpos__neg,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__strict__left__mono__neg,axiom,
% 14.82/14.71 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => ( hBOOL(hAPP(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)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__strict__left__mono,axiom,
% 14.82/14.71 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.82/14.71 => ( hBOOL(hAPP(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)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__divide__less__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__less__divide__eq,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__imp__less__div__pos,axiom,
% 14.82/14.71 ! [V_x,V_z,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__imp__div__pos__less,axiom,
% 14.82/14.71 ! [V_z,V_x,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_pos__divide__less__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_pos__less__divide__eq,axiom,
% 14.82/14.71 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__less__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__divide__eq,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__num__frac,axiom,
% 14.82/14.71 ! [V_x,V_z,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.71 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__divide__eq__iff,axiom,
% 14.82/14.71 ! [V_y,V_x,V_z,T_a] :
% 14.82/14.71 ( class_Fields_Ofield(T_a)
% 14.82/14.71 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__frac__num,axiom,
% 14.82/14.71 ! [V_z,V_x,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.71 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__add__eq__iff,axiom,
% 14.82/14.71 ! [V_y,V_x,V_z,T_a] :
% 14.82/14.71 ( class_Fields_Ofield(T_a)
% 14.82/14.71 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__frac__eq,axiom,
% 14.82/14.71 ! [V_w,V_x,V_z,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Ofield(T_a)
% 14.82/14.71 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_diff__frac__eq,axiom,
% 14.82/14.71 ! [V_w,V_x,V_z,V_y,T_a] :
% 14.82/14.71 ( class_Fields_Ofield(T_a)
% 14.82/14.71 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__diff__eq__iff,axiom,
% 14.82/14.71 ! [V_y,V_x,V_z,T_a] :
% 14.82/14.71 ( class_Fields_Ofield(T_a)
% 14.82/14.71 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_diff__divide__eq__iff,axiom,
% 14.82/14.71 ! [V_y,V_x,V_z,T_a] :
% 14.82/14.71 ( class_Fields_Ofield(T_a)
% 14.82/14.71 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_gt__half__sum,axiom,
% 14.82/14.71 ! [V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__half__sum,axiom,
% 14.82/14.71 ! [V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__left__mono__neg,axiom,
% 14.82/14.71 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.71 => ( hBOOL(hAPP(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)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__left__mono,axiom,
% 14.82/14.71 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 14.82/14.71 => ( hBOOL(hAPP(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)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__divide__le__eq,axiom,
% 14.82/14.71 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setprod__Un,axiom,
% 14.82/14.71 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.71 ( class_Fields_Ofield(T_c)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.71 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 14.82/14.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setsum__mono__zero__left,axiom,
% 14.82/14.71 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 14.82/14.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 14.82/14.71 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 14.82/14.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setsum__mono__zero__right,axiom,
% 14.82/14.71 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 14.82/14.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 14.82/14.71 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 14.82/14.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_field__le__mult__one__interval,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.71 => ( ! [B_z] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setprod__pos__nat,axiom,
% 14.82/14.71 ! [V_f_2,V_S_2,T_b] :
% 14.82/14.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setsum__SucD,axiom,
% 14.82/14.71 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 14.82/14.71 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 14.82/14.71 => ? [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osize_I5_J,axiom,
% 14.82/14.71 ! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I4_J,axiom,
% 14.82/14.71 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 14.82/14.71 ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
% 14.82/14.71 <=> ( V_fun_2 = V_fun_H_2
% 14.82/14.71 & V_com1_2 = V_com1_H_2
% 14.82/14.71 & V_com2_2 = V_com2_H_2 ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I45_J,axiom,
% 14.82/14.71 ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I44_J,axiom,
% 14.82/14.71 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I15_J,axiom,
% 14.82/14.71 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I14_J,axiom,
% 14.82/14.71 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osize_I13_J,axiom,
% 14.82/14.71 ! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_card_Oneutral,axiom,
% 14.82/14.71 ! [V_A_2,T_b] :
% 14.82/14.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.71 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 14.82/14.71 ( class_Orderings_Olinorder(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_fold__image__cong,axiom,
% 14.82/14.71 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 14.82/14.71 ( class_Groups_Oab__semigroup__mult(T_c)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 14.82/14.71 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Min__eqI,axiom,
% 14.82/14.71 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.71 ( class_Orderings_Olinorder(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( ! [B_y] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.71 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_inf__le__fold__inf,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 14.82/14.71 ( class_Lattices_Osemilattice__inf(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_fold__sup__le__sup,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 14.82/14.71 ( class_Lattices_Osemilattice__sup(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_expand__Suc,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__number__of,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Int_Oring__char__0(T_b) )
% 14.82/14.71 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 14.82/14.71 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__reorient,axiom,
% 14.82/14.71 ! [V_x_2,V_w_2,T_b] :
% 14.82/14.71 ( class_Int_Onumber(T_b)
% 14.82/14.71 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 14.82/14.71 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__number__of,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__number__of,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__number__of__left,axiom,
% 14.82/14.71 ! [V_z,V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__number__of__eq,axiom,
% 14.82/14.71 ! [V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__add,axiom,
% 14.82/14.71 ! [V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__mult,axiom,
% 14.82/14.71 ! [V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_arith__simps_I32_J,axiom,
% 14.82/14.71 ! [V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__number__of__left,axiom,
% 14.82/14.71 ! [V_z,V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__diff,axiom,
% 14.82/14.71 ! [V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__number__of__eq__not__less,axiom,
% 14.82/14.71 ! [V_w_2,V_v_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber(T_b)
% 14.82/14.71 & class_Orderings_Olinorder(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_left__distrib__number__of,axiom,
% 14.82/14.71 ! [V_v,V_b,V_a,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber(T_b)
% 14.82/14.71 & class_Rings_Osemiring(T_b) )
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_right__distrib__number__of,axiom,
% 14.82/14.71 ! [V_c,V_b,V_v,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber(T_b)
% 14.82/14.71 & class_Rings_Osemiring(T_b) )
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__number__of__diff1,axiom,
% 14.82/14.71 ! [V_c,V_w,V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_right__diff__distrib__number__of,axiom,
% 14.82/14.71 ! [V_c,V_b,V_v,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber(T_b)
% 14.82/14.71 & class_Rings_Oring(T_b) )
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_left__diff__distrib__number__of,axiom,
% 14.82/14.71 ! [V_v,V_b,V_a,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber(T_b)
% 14.82/14.71 & class_Rings_Oring(T_b) )
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_min__number__of,axiom,
% 14.82/14.71 ! [V_v,V_u,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber(T_b)
% 14.82/14.71 & class_Orderings_Oord(T_b) )
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 14.82/14.71 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 14.82/14.71 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__number__of,axiom,
% 14.82/14.71 ! [V_w_2,T_b] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__eq__eq__number__of1,axiom,
% 14.82/14.71 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 14.82/14.71 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
% 14.82/14.71 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__eq__eq__number__of,axiom,
% 14.82/14.71 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 14.82/14.71 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) )
% 14.82/14.71 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__divide__eq__number__of,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 14.82/14.71 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2 )
% 14.82/14.71 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__divide__eq__number__of1,axiom,
% 14.82/14.71 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 14.82/14.71 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 )
% 14.82/14.71 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.71 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__less__eq__number__of1,axiom,
% 14.82/14.71 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__less__eq__number__of,axiom,
% 14.82/14.71 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__divide__eq__number__of,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__divide__eq__number__of1,axiom,
% 14.82/14.71 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__divide__eq__number__of1,axiom,
% 14.82/14.71 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__divide__eq__number__of,axiom,
% 14.82/14.71 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__le__eq__number__of,axiom,
% 14.82/14.71 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__le__eq__number__of1,axiom,
% 14.82/14.71 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 14.82/14.71 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.71 & class_Int_Onumber(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osize_I3_J,axiom,
% 14.82/14.71 ! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osize_I11_J,axiom,
% 14.82/14.71 ! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_UnionE,axiom,
% 14.82/14.71 ! [V_C_2,V_A_2,T_b] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 14.82/14.71 => ~ ! [B_X] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 14.82/14.71 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setprod__pos,axiom,
% 14.82/14.71 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_c)
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setprod__nonneg,axiom,
% 14.82/14.71 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_c)
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__succ,axiom,
% 14.82/14.71 ! [V_k,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_field__le__epsilon,axiom,
% 14.82/14.71 ! [V_y,V_x,T_a] :
% 14.82/14.71 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.71 => ( ! [B_e] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__eq__number__of__int__code,axiom,
% 14.82/14.71 ! [V_l_2,V_k_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_plus__numeral__code_I9_J,axiom,
% 14.82/14.71 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_times__numeral__code_I5_J,axiom,
% 14.82/14.71 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__number__of__int__code,axiom,
% 14.82/14.71 ! [V_l_2,V_k_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_odd__nonzero,axiom,
% 14.82/14.71 ! [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) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_odd__less__0,axiom,
% 14.82/14.71 ! [V_z_2] :
% 14.82/14.71 ( hBOOL(hAPP(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)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__0__less__1,axiom,
% 14.82/14.71 hBOOL(hAPP(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))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_pos__zmult__eq__1__iff,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 14.82/14.71 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 14.82/14.71 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 14.82/14.71 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__one__le__iff__zero__less,axiom,
% 14.82/14.71 ! [V_z_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__imp__0__less,axiom,
% 14.82/14.71 ! [V_z] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__0__right,axiom,
% 14.82/14.71 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__0,axiom,
% 14.82/14.71 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__zless__mono2,axiom,
% 14.82/14.71 ! [V_k,V_j,V_i] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__bin__lemma,axiom,
% 14.82/14.71 ! [V_l_2,V_k_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__zless__mono,axiom,
% 14.82/14.71 ! [V_z,V_z_H,V_w,V_w_H] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zless__le,axiom,
% 14.82/14.71 ! [V_w_2,V_z_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 14.82/14.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 14.82/14.71 & V_z_2 != V_w_2 ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zdiff__zmult__distrib,axiom,
% 14.82/14.71 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zdiff__zmult__distrib2,axiom,
% 14.82/14.71 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zless__linear,axiom,
% 14.82/14.71 ! [V_y,V_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 14.82/14.71 | V_x = V_y
% 14.82/14.71 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__commute,axiom,
% 14.82/14.71 ! [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) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__assoc,axiom,
% 14.82/14.71 ! [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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__zmult__distrib2,axiom,
% 14.82/14.71 ! [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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__zmult__distrib,axiom,
% 14.82/14.71 ! [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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__strict__right__mono,axiom,
% 14.82/14.71 ! [V_k,V_j,V_i] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__commute,axiom,
% 14.82/14.71 ! [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) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__left__commute,axiom,
% 14.82/14.71 ! [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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__assoc,axiom,
% 14.82/14.71 ! [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)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__refl,axiom,
% 14.82/14.71 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__linear,axiom,
% 14.82/14.71 ! [V_w,V_z] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 14.82/14.71 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__trans,axiom,
% 14.82/14.71 ! [V_k,V_j,V_i] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__antisym,axiom,
% 14.82/14.71 ! [V_w,V_z] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 14.82/14.71 => V_z = V_w ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__left__mono,axiom,
% 14.82/14.71 ! [V_k,V_j,V_i] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__add1__eq__le,axiom,
% 14.82/14.71 ! [V_z_2,V_w_2] :
% 14.82/14.71 ( hBOOL(hAPP(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))))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add1__zle__eq,axiom,
% 14.82/14.71 ! [V_z_2,V_w_2] :
% 14.82/14.71 ( hBOOL(hAPP(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))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zless__imp__add1__zle,axiom,
% 14.82/14.71 ! [V_z,V_w] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 14.82/14.71 => hBOOL(hAPP(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)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__diff1__eq,axiom,
% 14.82/14.71 ! [V_z_2,V_w_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__1,axiom,
% 14.82/14.71 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__1__right,axiom,
% 14.82/14.71 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zless__add1__eq,axiom,
% 14.82/14.71 ! [V_z_2,V_w_2] :
% 14.82/14.71 ( hBOOL(hAPP(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))))
% 14.82/14.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 14.82/14.71 | V_w_2 = V_z_2 ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_succ__def,axiom,
% 14.82/14.71 ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I2_J,axiom,
% 14.82/14.71 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 14.82/14.71 ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
% 14.82/14.71 <=> ( V_loc_2 = V_loc_H_2
% 14.82/14.71 & V_fun_2 = V_fun_H_2
% 14.82/14.71 & V_com_2 = V_com_H_2 ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I37_J,axiom,
% 14.82/14.71 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I36_J,axiom,
% 14.82/14.71 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I34_J,axiom,
% 14.82/14.71 ! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I35_J,axiom,
% 14.82/14.71 ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I11_J,axiom,
% 14.82/14.71 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 14.82/14.71
% 14.82/14.71 fof(fact_com_Osimps_I10_J,axiom,
% 14.82/14.71 ! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_self__quotient__aux1,axiom,
% 14.82/14.71 ! [V_q,V_r,V_a] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.71 => ( 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))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_self__quotient__aux2,axiom,
% 14.82/14.71 ! [V_q,V_r,V_a] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.71 => ( 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))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 14.82/14.71 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 14.82/14.71 ( 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)
% 14.82/14.71 => ( hBOOL(hAPP(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)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_unique__quotient__lemma__neg,axiom,
% 14.82/14.71 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 14.82/14.71 ( hBOOL(hAPP(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)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zdiv__mono2__lemma,axiom,
% 14.82/14.71 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 14.82/14.71 ( 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)
% 14.82/14.71 => ( hBOOL(hAPP(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)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_unique__quotient__lemma,axiom,
% 14.82/14.71 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 14.82/14.71 ( hBOOL(hAPP(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)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_q__neg__lemma,axiom,
% 14.82/14.71 ! [V_r_H,V_q_H,V_b_H] :
% 14.82/14.71 ( hBOOL(hAPP(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)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__is__id,axiom,
% 14.82/14.71 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__0__neq__1,axiom,
% 14.82/14.71 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_q__pos__lemma,axiom,
% 14.82/14.71 ! [V_r_H,V_q_H,V_b_H] :
% 14.82/14.71 ( hBOOL(hAPP(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)))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 14.82/14.71 ! [V_y,V_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 14.82/14.71 hBOOL(hAPP(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))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 14.82/14.71 ! [V_y,V_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Suc__nat__number__of__add,axiom,
% 14.82/14.71 ! [V_n,V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 14.82/14.71 hBOOL(hAPP(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))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Suc__nat__number__of,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__number__of__lemma,axiom,
% 14.82/14.71 ! [V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__eq__iff,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2,T_b] :
% 14.82/14.71 ( class_Nat_Osemiring__char__0(T_b)
% 14.82/14.71 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
% 14.82/14.71 <=> V_m_2 = V_n_2 ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_not__neg__int,axiom,
% 14.82/14.71 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 14.82/14.71 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 14.82/14.71 ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 14.82/14.71 ! [V_Pa_2] :
% 14.82/14.71 ( ? [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 14.82/14.71 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.82/14.71 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 14.82/14.71 ! [V_Pa_2] :
% 14.82/14.71 ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 14.82/14.71 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.82/14.71 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 14.82/14.71 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_not__neg__0,axiom,
% 14.82/14.71 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 14.82/14.71 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 14.82/14.71 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_not__neg__1,axiom,
% 14.82/14.71 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__nat__number__of,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__0,axiom,
% 14.82/14.71 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__eq__0__conv,axiom,
% 14.82/14.71 ! [V_n_2] :
% 14.82/14.71 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.71 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zero__zle__int,axiom,
% 14.82/14.71 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__less__0__conv,axiom,
% 14.82/14.71 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zless__int,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__int,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__int__left,axiom,
% 14.82/14.71 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zadd__int,axiom,
% 14.82/14.71 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zle__iff__zadd,axiom,
% 14.82/14.71 ! [V_z_2,V_w_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 14.82/14.71 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__0__le__iff,axiom,
% 14.82/14.71 ! [V_n,T_a] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zero__le__imp__of__nat,axiom,
% 14.82/14.71 ! [V_m,T_a] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__less__0__iff,axiom,
% 14.82/14.71 ! [V_m,T_a] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.71 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__number__of__eq,axiom,
% 14.82/14.71 ! [V_v,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__int,axiom,
% 14.82/14.71 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__mult,axiom,
% 14.82/14.71 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__0,axiom,
% 14.82/14.71 ! [T_a] :
% 14.82/14.71 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__less__imp__less,axiom,
% 14.82/14.71 ! [V_n,V_m,T_a] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__imp__of__nat__less,axiom,
% 14.82/14.71 ! [V_n,V_m,T_a] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__less__iff,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2,T_b] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__1,axiom,
% 14.82/14.71 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__le__iff,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2,T_b] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__add,axiom,
% 14.82/14.71 ! [V_n,V_m,T_a] :
% 14.82/14.71 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__mult,axiom,
% 14.82/14.71 ! [V_n,V_m,T_a] :
% 14.82/14.71 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__1,axiom,
% 14.82/14.71 ! [T_a] :
% 14.82/14.71 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Ints__of__nat,axiom,
% 14.82/14.71 ! [V_n_2,T_b] :
% 14.82/14.71 ( class_Rings_Oring__1(T_b)
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_not__neg__eq__ge__0,axiom,
% 14.82/14.71 ! [V_x_2] :
% 14.82/14.71 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__def,axiom,
% 14.82/14.71 ! [V_Z_2] :
% 14.82/14.71 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__le__0__conv,axiom,
% 14.82/14.71 ! [V_n_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.71 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__Suc0__eq__1,axiom,
% 14.82/14.71 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zless__iff__Suc__zadd,axiom,
% 14.82/14.71 ! [V_z_2,V_w_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 14.82/14.71 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__Suc,axiom,
% 14.82/14.71 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zdiff__int,axiom,
% 14.82/14.71 ! [V_m,V_n] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__Suc,axiom,
% 14.82/14.71 ! [V_m,T_a] :
% 14.82/14.71 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__diff,axiom,
% 14.82/14.71 ! [V_m,V_n,T_a] :
% 14.82/14.71 ( class_Rings_Oring__1(T_a)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.82/14.71 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__imp__number__of__eq__0,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zero__less__int__conv,axiom,
% 14.82/14.71 ! [V_n_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zmult__zless__mono2__lemma,axiom,
% 14.82/14.71 ! [V_k,V_j,V_i] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_of__nat__0__less__iff,axiom,
% 14.82/14.71 ! [V_n_2,T_b] :
% 14.82/14.71 ( class_Rings_Olinordered__semidom(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__nat__number__of,axiom,
% 14.82/14.71 ! [V_v_H_2,V_v_2] :
% 14.82/14.71 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
% 14.82/14.71 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 14.82/14.71 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 14.82/14.71 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nat__number__of__add__left,axiom,
% 14.82/14.71 ! [V_k,V_v_H,V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.71 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zdiff__int__split,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2,V_Pa_2] :
% 14.82/14.71 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 14.82/14.71 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 14.82/14.71 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 14.82/14.71 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_setsum__bounded,axiom,
% 14.82/14.71 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.71 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 14.82/14.71 & class_Rings_Osemiring__1(T_c) )
% 14.82/14.71 => ( ! [B_i] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_tsub__def,axiom,
% 14.82/14.71 ! [V_x,V_y] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 14.82/14.71 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 14.82/14.71 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nat__1__add__number__of,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nat__number__of__add__1,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_neg__number__of__pred__iff__0,axiom,
% 14.82/14.71 ! [V_v_2] :
% 14.82/14.71 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 14.82/14.71 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__nat__number__of,axiom,
% 14.82/14.71 ! [V_v_H,V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_int__int__eq,axiom,
% 14.82/14.71 ! [V_n_2,V_m_2] :
% 14.82/14.71 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
% 14.82/14.71 <=> V_m_2 = V_n_2 ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 14.82/14.71 ! [V_y_2,V_x_2] :
% 14.82/14.71 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
% 14.82/14.71 <=> V_x_2 = V_y_2 ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Pls__def,axiom,
% 14.82/14.71 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_rel__simps_I19_J,axiom,
% 14.82/14.71 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_rel__simps_I2_J,axiom,
% 14.82/14.71 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__Pls__right,axiom,
% 14.82/14.71 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__Pls,axiom,
% 14.82/14.71 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 14.82/14.71
% 14.82/14.71 fof(fact_mult__Pls,axiom,
% 14.82/14.71 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 14.82/14.71
% 14.82/14.71 fof(fact_diff__bin__simps_I1_J,axiom,
% 14.82/14.71 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 14.82/14.71
% 14.82/14.71 fof(fact_succ__pred,axiom,
% 14.82/14.71 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 14.82/14.71
% 14.82/14.71 fof(fact_semiring__norm_I112_J,axiom,
% 14.82/14.71 ! [T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of__Pls,axiom,
% 14.82/14.71 ! [T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__numeral__0,axiom,
% 14.82/14.71 ! [V_a,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__numeral__0__right,axiom,
% 14.82/14.71 ! [V_a,T_a] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_a)
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_number__of2,axiom,
% 14.82/14.71 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_bin__less__0__simps_I1_J,axiom,
% 14.82/14.71 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nat__number__of__Pls,axiom,
% 14.82/14.71 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_semiring__norm_I113_J,axiom,
% 14.82/14.71 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_zero__is__num__zero,axiom,
% 14.82/14.71 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Suc__diff__number__of,axiom,
% 14.82/14.71 ! [V_m,V_v] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_not__neg__number__of__Pls,axiom,
% 14.82/14.71 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__iff__pred__less,axiom,
% 14.82/14.71 ! [V_l_2,V_k_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_pred__def,axiom,
% 14.82/14.71 ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 14.82/14.71 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nat__number__of__diff__1,axiom,
% 14.82/14.71 ! [V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_divide__Numeral0,axiom,
% 14.82/14.71 ! [V_x,T_a] :
% 14.82/14.71 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.71 & class_Int_Onumber__ring(T_a) )
% 14.82/14.71 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__number__of__0,axiom,
% 14.82/14.71 ! [V_v_2] :
% 14.82/14.71 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_eq__0__number__of,axiom,
% 14.82/14.71 ! [V_v_2] :
% 14.82/14.71 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__nat__number__of,axiom,
% 14.82/14.71 ! [V_v_H_2,V_v_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 14.82/14.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 14.82/14.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__nat__number__of,axiom,
% 14.82/14.71 ! [V_v_H_2,V_v_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
% 14.82/14.71 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__special_I3_J,axiom,
% 14.82/14.71 ! [V_x_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_le__special_I1_J,axiom,
% 14.82/14.71 ! [V_y_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__special_I1_J,axiom,
% 14.82/14.71 ! [V_y_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__special_I3_J,axiom,
% 14.82/14.71 ! [V_x_2,T_b] :
% 14.82/14.71 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_less__0__number__of,axiom,
% 14.82/14.71 ! [V_v_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 14.82/14.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_add__nat__number__of,axiom,
% 14.82/14.71 ! [V_v_H,V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) ) ) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 14.82/14.71 ! [V_y,V_x] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.71 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_tsub__eq,axiom,
% 14.82/14.71 ! [V_x,V_y] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 14.82/14.71 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_nat__number__of__mult__left,axiom,
% 14.82/14.71 ! [V_k,V_v_H,V_v] :
% 14.82/14.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 14.82/14.71 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_Nats__number__of,axiom,
% 14.82/14.71 ! [V_w_2,T_b] :
% 14.82/14.71 ( class_Int_Onumber__ring(T_b)
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 14.82/14.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ).
% 14.82/14.71
% 14.82/14.71 fof(fact_decr__mult__lemma,axiom,
% 14.82/14.71 ! [V_k_2,V_Pa_2,V_d_2] :
% 14.82/14.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 14.82/14.71 => ( ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.71 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 14.82/14.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 14.82/14.71 => ! [B_x] :
% 14.82/14.71 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_incr__mult__lemma,axiom,
% 14.82/14.72 ! [V_k_2,V_Pa_2,V_d_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 14.82/14.72 => ( ! [B_x] :
% 14.82/14.72 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 14.82/14.72 => ! [B_x] :
% 14.82/14.72 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zero__less__imp__eq__int,axiom,
% 14.82/14.72 ! [V_k] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 14.82/14.72 => ? [B_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 14.82/14.72 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_incr__lemma,axiom,
% 14.82/14.72 ! [V_x,V_z,V_d] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 14.82/14.72 => hBOOL(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_decr__lemma,axiom,
% 14.82/14.72 ! [V_z,V_x,V_d] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__idempotent,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__le__D1,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__ge__self,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__zero,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__eq__0,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.72 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__add__abs,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__mult__self,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__mult,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.72 => hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__minus__commute,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__one,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__of__nat,axiom,
% 14.82/14.72 ! [V_n,T_a] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__divide,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__int__eq,axiom,
% 14.82/14.72 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__ge__zero,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__le__zero__iff,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__of__nonneg,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__not__less__zero,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zero__less__abs__iff,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
% 14.82/14.72 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__of__pos,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__triangle__ineq,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__mult__less,axiom,
% 14.82/14.72 ! [V_d,V_b,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__triangle__ineq2__sym,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__triangle__ineq2,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__triangle__ineq3,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nonzero__abs__divide,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Fields_Olinordered__field(T_a)
% 14.82/14.72 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__zmult__eq__1,axiom,
% 14.82/14.72 ! [V_n,V_m] :
% 14.82/14.72 ( hAPP(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)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__mult__pos,axiom,
% 14.82/14.72 ! [V_y,V_x,T_a] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__eq__mult,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Oordered__ring__abs(T_a)
% 14.82/14.72 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.72 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 14.82/14.72 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.82/14.72 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 14.82/14.72 => hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__diff__triangle__ineq,axiom,
% 14.82/14.72 ! [V_d,V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__triangle__ineq4,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__div__pos,axiom,
% 14.82/14.72 ! [V_x,V_y,T_a] :
% 14.82/14.72 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zabs__less__one__iff,axiom,
% 14.82/14.72 ! [V_z_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 14.82/14.72 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Nats__0,axiom,
% 14.82/14.72 ! [T_b] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Nats__add,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Nats__mult,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Nats__1,axiom,
% 14.82/14.72 ! [T_b] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_of__nat__in__Nats,axiom,
% 14.82/14.72 ! [V_n_2,T_b] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_int__val__lemma,axiom,
% 14.82/14.72 ! [V_k_2,V_f_2,V_n_2] :
% 14.82/14.72 ( ! [B_i] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 14.82/14.72 => ? [B_i] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 14.82/14.72 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat0__intermed__int__val,axiom,
% 14.82/14.72 ! [V_k_2,V_f_2,V_n_2] :
% 14.82/14.72 ( ! [B_i] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 14.82/14.72 => ? [B_i] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 14.82/14.72 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__intermed__int__val,axiom,
% 14.82/14.72 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 14.82/14.72 ( ! [B_i] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 14.82/14.72 => ? [B_i] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 14.82/14.72 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 14.82/14.72 ! [V_m,V_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_divmod__int__rel__mod__eq,axiom,
% 14.82/14.72 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 14.82/14.72 ( 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_q_1)),V_y)
% 14.82/14.72 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 14.82/14.72 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmult2__lemma__aux2,axiom,
% 14.82/14.72 ! [V_q,V_r,V_b,V_c] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hBOOL(hAPP(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),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I51_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 14.82/14.72 <=> V_k_2 = V_l_2 ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mod__trivial,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__0,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__by__0,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__self,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__add__self2,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__add__self1,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__add__right__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__add__left__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__add__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__simps_I2_J,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__simps_I1_J,axiom,
% 14.82/14.72 ! [V_b,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__add__cong,axiom,
% 14.82/14.72 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__cong,axiom,
% 14.82/14.72 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__simps_I4_J,axiom,
% 14.82/14.72 ! [V_b,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__mult2,axiom,
% 14.82/14.72 ! [V_b,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__mult1,axiom,
% 14.82/14.72 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__left__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__right__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__diff__right__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Oring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__diff__left__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Oring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__diff__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Oring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__diff__cong,axiom,
% 14.82/14.72 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Oring__div(T_a)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zero,axiom,
% 14.82/14.72 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__self,axiom,
% 14.82/14.72 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__eq__int__code_I16_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I34_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I17_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__int__code_I16_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I46_J,axiom,
% 14.82/14.72 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I39_J,axiom,
% 14.82/14.72 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__simps_I3_J,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zmult1__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiff__zmod__right,axiom,
% 14.82/14.72 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiff__zmod__left,axiom,
% 14.82/14.72 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__self2__is__0,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__self1__is__0,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__self1,axiom,
% 14.82/14.72 ! [V_b,V_c,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(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) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__self2,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(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) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__by__1,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 14.82/14.72 ! [V_y,V_x] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__le__nonneg__dividend,axiom,
% 14.82/14.72 ! [V_k,V_m] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__mod__bound,axiom,
% 14.82/14.72 ! [V_a,V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__mod__bound,axiom,
% 14.82/14.72 ! [V_a,V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_bin__less__0__simps_I4_J,axiom,
% 14.82/14.72 ! [V_w_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__eq__0__iff,axiom,
% 14.82/14.72 ! [V_d_2,V_m_2] :
% 14.82/14.72 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I22_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I12_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Bit1__def,axiom,
% 14.82/14.72 ! [V_k] : c_Int_OBit1(V_k) = 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_k)),V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__number__of__Bit1,axiom,
% 14.82/14.72 ! [V_w_2] :
% 14.82/14.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 14.82/14.72 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_succ__Pls,axiom,
% 14.82/14.72 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_number__of__Bit1,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__numeral__1,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__numeral__1__right,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__neg__neg__trivial,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__mod__conj,axiom,
% 14.82/14.72 ! [V_a,V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__mod__sign,axiom,
% 14.82/14.72 ! [V_a,V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__pos__pos__trivial,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__mod__conj,axiom,
% 14.82/14.72 ! [V_a,V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__mod__sign,axiom,
% 14.82/14.72 ! [V_a,V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_semiring__norm_I110_J,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_numeral__1__eq__1,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I5_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I29_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_divide__numeral__1,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( ( class_Fields_Ofield(T_a)
% 14.82/14.72 & class_Int_Onumber__ring(T_a) )
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_divide__Numeral1,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( ( class_Fields_Ofield(T_a)
% 14.82/14.72 & class_Int_Onumber__ring(T_a) )
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_one__is__num__one,axiom,
% 14.82/14.72 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__numeral__1__eq__1,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Numeral1__eq1__nat,axiom,
% 14.82/14.72 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__pos__neg__trivial,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_numeral__1__eq__Suc__0,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_numeral__3__eq__3,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 14.82/14.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Suc3__eq__add__3,axiom,
% 14.82/14.72 ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_le__special_I4_J,axiom,
% 14.82/14.72 ! [V_x_2,T_b] :
% 14.82/14.72 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.72 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_le__special_I2_J,axiom,
% 14.82/14.72 ! [V_y_2,T_b] :
% 14.82/14.72 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.72 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__special_I2_J,axiom,
% 14.82/14.72 ! [V_y_2,T_b] :
% 14.82/14.72 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.72 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__special_I4_J,axiom,
% 14.82/14.72 ! [V_x_2,T_b] :
% 14.82/14.72 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.72 & class_Rings_Olinordered__idom(T_b) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__special_I3_J,axiom,
% 14.82/14.72 ! [V_v,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__special_I2_J,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_split__zmod,axiom,
% 14.82/14.72 ! [V_k_2,V_n_2,V_Pa_2] :
% 14.82/14.72 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 14.82/14.72 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 14.82/14.72 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 14.82/14.72 => ! [B_i,B_j] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 14.82/14.72 & 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) )
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 14.82/14.72 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => ! [B_i,B_j] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 & 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) )
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmult2__lemma__aux3,axiom,
% 14.82/14.72 ! [V_q,V_b,V_r,V_c] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 14.82/14.72 => hBOOL(hAPP(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),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmult2__lemma__aux4,axiom,
% 14.82/14.72 ! [V_q,V_b,V_r,V_c] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 14.82/14.72 => hBOOL(hAPP(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),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmult2__lemma__aux1,axiom,
% 14.82/14.72 ! [V_q,V_r,V_b,V_c] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__zmod__mult__2,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__number__of__Bit1,axiom,
% 14.82/14.72 ! [V_v,V_w] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__zmod__mult__2,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_one__code__numeral__code,axiom,
% 14.82/14.72 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__minus1,axiom,
% 14.82/14.72 ! [V_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__special_I2_J,axiom,
% 14.82/14.72 ! [V_v,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_negative__zle,axiom,
% 14.82/14.72 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_negative__zless,axiom,
% 14.82/14.72 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__minus1,axiom,
% 14.82/14.72 ! [V_z,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__minus1__right,axiom,
% 14.82/14.72 ! [V_z,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__number__of__mult,axiom,
% 14.82/14.72 ! [V_z,V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pred__Min,axiom,
% 14.82/14.72 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_number__of__minus,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_arith__simps_I30_J,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_code__numeral__zero__minus__one,axiom,
% 14.82/14.72 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Int_OMin__def,axiom,
% 14.82/14.72 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zminus__zminus,axiom,
% 14.82/14.72 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__Bit0,axiom,
% 14.82/14.72 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I42_J,axiom,
% 14.82/14.72 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I45_J,axiom,
% 14.82/14.72 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I48_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 14.82/14.72 <=> V_k_2 = V_l_2 ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__minus,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_equation__minus__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_b)
% 14.82/14.72 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 14.82/14.72 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__equation__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_b)
% 14.82/14.72 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 14.82/14.72 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__equal__iff__equal,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_b)
% 14.82/14.72 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 14.82/14.72 <=> V_a_2 = V_b_2 ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_double__compl,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_uminus__apply,axiom,
% 14.82/14.72 ! [V_x_2,V_A_2,T_c,T_b] :
% 14.82/14.72 ( class_Groups_Ouminus(T_b)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_compl__eq__compl__iff,axiom,
% 14.82/14.72 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_b)
% 14.82/14.72 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 14.82/14.72 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I28_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__Min,axiom,
% 14.82/14.72 ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I8_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_arith__simps_I31_J,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_number__of__Min,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I11_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I25_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_divide__minus1,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.72 & class_Int_Onumber__ring(T_a) )
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__Min,axiom,
% 14.82/14.72 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I5_J,axiom,
% 14.82/14.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I6_J,axiom,
% 14.82/14.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_compl__mono,axiom,
% 14.82/14.72 ! [V_y,V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_compl__le__compl__iff,axiom,
% 14.82/14.72 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_le__imp__neg__le,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__le__iff__le,axiom,
% 14.82/14.72 ! [V_a_2,V_b_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__le__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_le__minus__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__zero,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__0__equal__iff__equal,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_b)
% 14.82/14.72 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 14.82/14.72 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_equal__neg__zero,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.72 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 14.82/14.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__equal__0__iff__equal,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_b)
% 14.82/14.72 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__equal__zero,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.72 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 14.82/14.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__minus__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__less__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__less__iff__less,axiom,
% 14.82/14.72 ! [V_a_2,V_b_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__add__distrib,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oab__group__add(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__add,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__minus__cancel,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__add__cancel,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_square__eq__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Rings_Oidom(T_b)
% 14.82/14.72 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
% 14.82/14.72 <=> ( V_a_2 = V_b_2
% 14.82/14.72 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__mult__minus,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Oring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__mult__commute,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Oring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__mult__left,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Oring(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__mult__right,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Oring(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__diff__eq,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oab__group__add(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 14.82/14.72 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__less,axiom,
% 14.82/14.72 ! [V_n,V_m] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__minus__eq,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Oring__div(T_a)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__minus__cong,axiom,
% 14.82/14.72 ! [V_a_H,V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Oring__div(T_a)
% 14.82/14.72 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__less__eq__dividend,axiom,
% 14.82/14.72 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I31_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__eq__int__code_I13_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__int__code_I13_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I14_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zminus__0,axiom,
% 14.82/14.72 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Bit0__Pls,axiom,
% 14.82/14.72 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I38_J,axiom,
% 14.82/14.72 ! [V_l_2] :
% 14.82/14.72 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 14.82/14.72 <=> c_Int_OPls = V_l_2 ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I44_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 14.82/14.72 <=> V_k_2 = c_Int_OPls ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I49_J,axiom,
% 14.82/14.72 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I50_J,axiom,
% 14.82/14.72 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__distrib2,axiom,
% 14.82/14.72 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__distrib,axiom,
% 14.82/14.72 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Bit0__def,axiom,
% 14.82/14.72 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__Bit0__Bit0,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I24_J,axiom,
% 14.82/14.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I7_J,axiom,
% 14.82/14.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__divide__left,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__divide__right,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__divide__divide,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__Bit0,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__minus__cancel,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I40_J,axiom,
% 14.82/14.72 c_Int_OMin != c_Int_OPls ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I37_J,axiom,
% 14.82/14.72 c_Int_OPls != c_Int_OMin ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Bit1__Min,axiom,
% 14.82/14.72 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I43_J,axiom,
% 14.82/14.72 ! [V_l_2] :
% 14.82/14.72 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 14.82/14.72 <=> c_Int_OMin = V_l_2 ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I47_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 14.82/14.72 <=> V_k_2 = c_Int_OMin ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__Pls,axiom,
% 14.82/14.72 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zminus__zadd__distrib,axiom,
% 14.82/14.72 ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__numeral__code_I5_J,axiom,
% 14.82/14.72 ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I7_J,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmult__zminus,axiom,
% 14.82/14.72 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zminus2,axiom,
% 14.82/14.72 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zminus__zminus,axiom,
% 14.82/14.72 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zminus__zmod,axiom,
% 14.82/14.72 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus1__divide,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.72 & class_Int_Onumber__ring(T_a) )
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod2__Suc__Suc,axiom,
% 14.82/14.72 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__0__le__iff__le,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_le__minus__self__iff,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__le__0__iff__le,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__le__self__iff,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__minus__self__iff,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__0__less__iff__less,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__less__0__iff__less,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__less__nonneg,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_right__minus,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_b)
% 14.82/14.72 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 14.82/14.72 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_left__minus,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_ab__left__minus,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oab__group__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__unique,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__0,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 14.82/14.72 ! [V_y,V_x,T_a] :
% 14.82/14.72 ( class_Rings_Ocomm__ring__1(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__def,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_ab__diff__minus,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oab__group__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__minus__eq__add,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Ogroup__add(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( class_Rings_Ocomm__ring__1(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_square__eq__1__iff,axiom,
% 14.82/14.72 ! [V_x_2,T_b] :
% 14.82/14.72 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 14.82/14.72 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.72 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.72 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_compl__inf__bot,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_inf__compl__bot,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__eq,axiom,
% 14.82/14.72 ! [V_y,V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__Suc,axiom,
% 14.82/14.72 ! [V_n,V_m] :
% 14.82/14.72 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.72 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__1,axiom,
% 14.82/14.72 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__less__divisor,axiom,
% 14.82/14.72 ! [V_m,V_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_compl__inf,axiom,
% 14.82/14.72 ! [V_y,V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_compl__sup,axiom,
% 14.82/14.72 ! [V_y,V_x,T_a] :
% 14.82/14.72 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nonzero__minus__divide__right,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.72 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nonzero__minus__divide__divide,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Rings_Odivision__ring(T_a)
% 14.82/14.72 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__le__D2,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__leI,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__le__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 14.82/14.72 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__ge__minus__self,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__less__iff,axiom,
% 14.82/14.72 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.72 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 14.82/14.72 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__eq__0__iff,axiom,
% 14.82/14.72 ! [V_d_2,V_m_2] :
% 14.82/14.72 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_bin__less__0__simps_I3_J,axiom,
% 14.82/14.72 ! [V_w_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__if,axiom,
% 14.82/14.72 ! [V_n,V_m] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__geq,axiom,
% 14.82/14.72 ! [V_n,V_m] :
% 14.82/14.72 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__self3,axiom,
% 14.82/14.72 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I27_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I21_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__eq__int__code_I14_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I32_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_le__mod__geq,axiom,
% 14.82/14.72 ! [V_m,V_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I4_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I10_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I16_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__int__code_I15_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__Bit1__Bit0,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__Bit0__Bit1,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_bin__less__0__simps_I2_J,axiom,
% 14.82/14.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zadd__zminus__inverse2,axiom,
% 14.82/14.72 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_negative__eq__positive,axiom,
% 14.82/14.72 ! [V_m_2,V_n_2] :
% 14.82/14.72 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
% 14.82/14.72 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I20_J,axiom,
% 14.82/14.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I23_J,axiom,
% 14.82/14.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I30_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I26_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I6_J,axiom,
% 14.82/14.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I3_J,axiom,
% 14.82/14.72 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I9_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I13_J,axiom,
% 14.82/14.72 ! [V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I3_J,axiom,
% 14.82/14.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I9_J,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I10_J,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__int,axiom,
% 14.82/14.72 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 14.82/14.72 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_eq__number__of__Pls__Min,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_not__int__zless__negative,axiom,
% 14.82/14.72 ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zminus2__not__zero,axiom,
% 14.82/14.72 ! [V_l,V_k] :
% 14.82/14.72 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zminus1__not__zero,axiom,
% 14.82/14.72 ! [V_l,V_k] :
% 14.82/14.72 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__int__def,axiom,
% 14.82/14.72 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__int__def__symmetric,axiom,
% 14.82/14.72 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Ints__minus,axiom,
% 14.82/14.72 ! [V_a_2,T_b] :
% 14.82/14.72 ( class_Rings_Oring__1(T_b)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__number__of__Bit0,axiom,
% 14.82/14.72 ! [V_w_2] :
% 14.82/14.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 14.82/14.72 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pred__Bit0,axiom,
% 14.82/14.72 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pred__Bit1,axiom,
% 14.82/14.72 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__number__of__Min,axiom,
% 14.82/14.72 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pred__Pls,axiom,
% 14.82/14.72 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__Bit1,axiom,
% 14.82/14.72 ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__Min__right,axiom,
% 14.82/14.72 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__Min,axiom,
% 14.82/14.72 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_succ__Bit1,axiom,
% 14.82/14.72 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_succ__Bit0,axiom,
% 14.82/14.72 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_succ__Min,axiom,
% 14.82/14.72 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I2_J,axiom,
% 14.82/14.72 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod2__gr__0,axiom,
% 14.82/14.72 ! [V_m_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 14.82/14.72 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_number__of__Bit0,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__of__nonpos,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__minus__le__zero,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__if,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oabs__if(T_a)
% 14.82/14.72 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__of__neg,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__le__divisor,axiom,
% 14.82/14.72 ! [V_m,V_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__mult__self4,axiom,
% 14.82/14.72 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__eq__int__code_I15_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I33_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__int__code_I14_J,axiom,
% 14.82/14.72 ! [V_k2_2,V_k1_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_rel__simps_I15_J,axiom,
% 14.82/14.72 ! [V_l_2,V_k_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__number__of__eq,axiom,
% 14.82/14.72 ! [V_w,V_v,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__Bit1,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__minus__one,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 & class_Rings_Olinordered__idom(T_a) )
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_int__zle__neg,axiom,
% 14.82/14.72 ! [V_m_2,V_n_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
% 14.82/14.72 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_negative__zle__0,axiom,
% 14.82/14.72 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__minus1__right,axiom,
% 14.82/14.72 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I4_J,axiom,
% 14.82/14.72 ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 14.82/14.72 ! [V_n,V_m] :
% 14.82/14.72 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 14.82/14.72 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 14.82/14.72 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmult__eq__1__iff,axiom,
% 14.82/14.72 ! [V_n_2,V_m_2] :
% 14.82/14.72 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 14.82/14.72 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 14.82/14.72 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 14.82/14.72 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 14.82/14.72 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_minus__numeral__code_I6_J,axiom,
% 14.82/14.72 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zminus1__eq__if,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.72 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zminus2__eq__if,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.72 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zabs__def,axiom,
% 14.82/14.72 ! [V_i] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__zminus__int,axiom,
% 14.82/14.72 ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__bin__simps_I8_J,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__Bit1__Bit1,axiom,
% 14.82/14.72 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zero__code__numeral__code,axiom,
% 14.82/14.72 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_double__number__of__Bit0,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => 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))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_abs__number__of,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 & class_Rings_Olinordered__idom(T_a) )
% 14.82/14.72 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.72 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_split__mod,axiom,
% 14.82/14.72 ! [V_k_2,V_n_2,V_Pa_2] :
% 14.82/14.72 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 14.82/14.72 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 14.82/14.72 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 => ! [B_i,B_j] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 14.82/14.72 => ( 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)
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__lemma,axiom,
% 14.82/14.72 ! [V_q,V_b,V_r,V_c] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 14.82/14.72 => hBOOL(hAPP(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_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__number__of__diff2,axiom,
% 14.82/14.72 ! [V_w,V_c,V_v,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_number__of1,axiom,
% 14.82/14.72 ! [V_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n))))
% 14.82/14.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Suc__times__mod__eq,axiom,
% 14.82/14.72 ! [V_m,V_k] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 14.82/14.72 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_number__of__pred,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_not__zle__0__negative,axiom,
% 14.82/14.72 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_negative__zless__0,axiom,
% 14.82/14.72 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__2__right,axiom,
% 14.82/14.72 ! [V_z,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mult__2,axiom,
% 14.82/14.72 ! [V_z,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_one__add__one__is__two,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 14.82/14.72 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 14.82/14.72 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 14.82/14.72 ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_numeral__2__eq__2,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_semiring__norm_I115_J,axiom,
% 14.82/14.72 hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 14.82/14.72 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__2__eq__Suc,axiom,
% 14.82/14.72 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_add__2__eq__Suc_H,axiom,
% 14.82/14.72 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__mult__2__right,axiom,
% 14.82/14.72 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__mult__2,axiom,
% 14.82/14.72 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 14.82/14.72 hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__1__add__1,axiom,
% 14.82/14.72 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__number__of__Bit0,axiom,
% 14.82/14.72 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_half__gt__zero,axiom,
% 14.82/14.72 ! [V_r,T_a] :
% 14.82/14.72 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 14.82/14.72 & class_Int_Onumber__ring(T_a) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_half__gt__zero__iff,axiom,
% 14.82/14.72 ! [V_r_2,T_b] :
% 14.82/14.72 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 14.82/14.72 & class_Int_Onumber__ring(T_b) )
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_less__2__cases,axiom,
% 14.82/14.72 ! [V_n] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 14.82/14.72 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_diff__special_I1_J,axiom,
% 14.82/14.72 ! [V_w,T_a] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_eq__special_I4_J,axiom,
% 14.82/14.72 ! [V_x_2,T_b] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_b)
% 14.82/14.72 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_eq__special_I2_J,axiom,
% 14.82/14.72 ! [V_y_2,T_b] :
% 14.82/14.72 ( class_Int_Onumber__ring(T_b)
% 14.82/14.72 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 14.82/14.72 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_z3mod__def,axiom,
% 14.82/14.72 ! [V_k,V_l] :
% 14.82/14.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 14.82/14.72 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 14.82/14.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 14.82/14.72 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__zdiv__mult__2,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__zdiv__mult__2,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_of__nat__double,axiom,
% 14.82/14.72 ! [V_x,T_a] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.72 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_ComplI,axiom,
% 14.82/14.72 ! [V_A_2,V_ca_2,T_b] :
% 14.82/14.72 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_ComplE,axiom,
% 14.82/14.72 ! [V_A_2,V_ca_2,T_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 14.82/14.72 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_ComplD,axiom,
% 14.82/14.72 ! [V_A_2,V_ca_2,T_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 14.82/14.72 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__iff,axiom,
% 14.82/14.72 ! [V_A_2,V_ca_2,T_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 14.82/14.72 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__zero,axiom,
% 14.82/14.72 ! [V_b] : hAPP(hAPP(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) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__anti__mono,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__subset__Compl__iff,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__int,axiom,
% 14.82/14.72 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__zminus__zminus,axiom,
% 14.82/14.72 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__zminus2,axiom,
% 14.82/14.72 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__0,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__by__0,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_vimage__Compl,axiom,
% 14.82/14.72 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__by__1,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_iszero__0,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.72 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_iszero__def,axiom,
% 14.82/14.72 ! [V_z_2,T_b] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.72 => ( c_Int_Oiszero(T_b,V_z_2)
% 14.82/14.72 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__0,axiom,
% 14.82/14.72 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 14.82/14.72 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 14.82/14.72 ! [V_y,V_x] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_not__iszero__1,axiom,
% 14.82/14.72 ! [T_a] :
% 14.82/14.72 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.72 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 14.82/14.72 ! [V_a_2,V_b_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 14.82/14.72 ! [V_a_2,V_b_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__neg__pos__less0,axiom,
% 14.82/14.72 ! [V_b,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_eq__nat__nat__iff,axiom,
% 14.82/14.72 ! [V_z_H_2,V_z_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 14.82/14.72 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 14.82/14.72 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 14.82/14.72 ! [V_y_2,V_x_2] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 14.82/14.72 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 14.82/14.72 <=> V_x_2 = V_y_2 ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_all__nat,axiom,
% 14.82/14.72 ! [V_Pa_2] :
% 14.82/14.72 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 14.82/14.72 <=> ! [B_x] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 14.82/14.72 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_ex__nat,axiom,
% 14.82/14.72 ! [V_Pa_2] :
% 14.82/14.72 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 14.82/14.72 <=> ? [B_x] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 14.82/14.72 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__self,axiom,
% 14.82/14.72 ! [V_a] :
% 14.82/14.72 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_subset__Compl__self__eq,axiom,
% 14.82/14.72 ! [V_A_2,T_b] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 14.82/14.72 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__disjoint,axiom,
% 14.82/14.72 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__disjoint2,axiom,
% 14.82/14.72 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__number__of__Bit0,axiom,
% 14.82/14.72 ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zmod__zdiv__trivial,axiom,
% 14.82/14.72 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_DIVISION__BY__ZERO,axiom,
% 14.82/14.72 ! [V_a] :
% 14.82/14.72 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.72 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__number__of__def,axiom,
% 14.82/14.72 ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__number__of,axiom,
% 14.82/14.72 ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__Un,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__Int,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__zadd1__eq,axiom,
% 14.82/14.72 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Compl__Diff__eq,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Diff__Compl,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_Diff__eq,axiom,
% 14.82/14.72 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 14.82/14.72 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_neg__nat,axiom,
% 14.82/14.72 ! [V_z] :
% 14.82/14.72 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 14.82/14.72 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_not__neg__nat,axiom,
% 14.82/14.72 ! [V_z] :
% 14.82/14.72 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 14.82/14.72 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__mult__mult1__if,axiom,
% 14.82/14.72 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(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) )
% 14.82/14.72 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__mult__self2__is__id,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__mult__self1__is__id,axiom,
% 14.82/14.72 ! [V_a,V_b,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__mult__mult2,axiom,
% 14.82/14.72 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__mult__mult1,axiom,
% 14.82/14.72 ! [V_b,V_a,V_c,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__self,axiom,
% 14.82/14.72 ! [V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_mod__div__trivial,axiom,
% 14.82/14.72 ! [V_b,V_a,T_a] :
% 14.82/14.72 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.72 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__le__0,axiom,
% 14.82/14.72 ! [V_z] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_nat__0__iff,axiom,
% 14.82/14.72 ! [V_i_2] :
% 14.82/14.72 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__mono1__neg,axiom,
% 14.82/14.72 ! [V_b,V_a_H,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_zdiv__mono1,axiom,
% 14.82/14.72 ! [V_b,V_a_H,V_a] :
% 14.82/14.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 14.82/14.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ).
% 14.82/14.72
% 14.82/14.72 fof(fact_div__neg__neg__trivial,axiom,
% 14.82/14.73 ! [V_b,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__mono2__neg,axiom,
% 14.82/14.73 ! [V_b,V_b_H,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__nonpos__pos__le0,axiom,
% 14.82/14.73 ! [V_b,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 14.82/14.73 ! [V_a_2,V_b_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__pos__pos__trivial,axiom,
% 14.82/14.73 ! [V_b,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__nonneg__neg__le0,axiom,
% 14.82/14.73 ! [V_b,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__mono2,axiom,
% 14.82/14.73 ! [V_b,V_b_H,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 14.82/14.73 ! [V_b_2,V_a_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 14.82/14.73 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 14.82/14.73 ! [V_i_2,V_k_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 14.82/14.73 ! [V_a_2,V_b_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__eq__0__iff,axiom,
% 14.82/14.73 ! [V_k_2,V_i_2] :
% 14.82/14.73 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 14.82/14.73 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zless__nat__conj,axiom,
% 14.82/14.73 ! [V_z_2,V_w_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mono__iff,axiom,
% 14.82/14.73 ! [V_w_2,V_z_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__1,axiom,
% 14.82/14.73 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__div__less__self,axiom,
% 14.82/14.73 ! [V_k,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__zmult2__eq,axiom,
% 14.82/14.73 ! [V_b,V_a,V_c] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__0__le,axiom,
% 14.82/14.73 ! [V_z] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__eq__iff,axiom,
% 14.82/14.73 ! [V_z_2,V_m_2] :
% 14.82/14.73 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 14.82/14.73 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__nat__eq,axiom,
% 14.82/14.73 ! [V_z] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zless__nat__eq__int__zless,axiom,
% 14.82/14.73 ! [V_z_2,V_m_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_disjoint__eq__subset__Compl,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mod__distrib,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.73 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__zminus__int,axiom,
% 14.82/14.73 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__zmod__equality2,axiom,
% 14.82/14.73 ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__zmod__equality,axiom,
% 14.82/14.73 ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__zmult1__eq,axiom,
% 14.82/14.73 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zmod__zdiv__equality,axiom,
% 14.82/14.73 ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__minus1__right,axiom,
% 14.82/14.73 ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zmod__zdiv__equality_H,axiom,
% 14.82/14.73 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zmult__div__cancel,axiom,
% 14.82/14.73 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__abs__mult__distrib,axiom,
% 14.82/14.73 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mult__self1,axiom,
% 14.82/14.73 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => hAPP(hAPP(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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mult__self2,axiom,
% 14.82/14.73 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => hAPP(hAPP(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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__add__self2,axiom,
% 14.82/14.73 ! [V_a,V_b,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => hAPP(hAPP(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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__add__self1,axiom,
% 14.82/14.73 ! [V_a,V_b,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => hAPP(hAPP(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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mod__equality,axiom,
% 14.82/14.73 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => 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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mod__equality2,axiom,
% 14.82/14.73 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => 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),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mod__div__equality,axiom,
% 14.82/14.73 ! [V_b,V_a,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mod__div__equality2,axiom,
% 14.82/14.73 ! [V_a,V_b,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 14.82/14.73 ! [V_b,V_a,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_iszero__Numeral0,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_iszero__number__of__Bit1,axiom,
% 14.82/14.73 ! [V_w,T_a] :
% 14.82/14.73 ( ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 & class_Int_Oring__char__0(T_a) )
% 14.82/14.73 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_iszero__number__of__Bit0,axiom,
% 14.82/14.73 ! [V_w_2,T_b] :
% 14.82/14.73 ( ( class_Int_Onumber__ring(T_b)
% 14.82/14.73 & class_Int_Oring__char__0(T_b) )
% 14.82/14.73 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 14.82/14.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nonzero__number__of__Min,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__less__nat__eq,axiom,
% 14.82/14.73 ! [V_z_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__less__eq__zless,axiom,
% 14.82/14.73 ! [V_z_2,V_w_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__eq__iff2,axiom,
% 14.82/14.73 ! [V_w_2,V_m_2] :
% 14.82/14.73 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 14.82/14.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__eq__iff,axiom,
% 14.82/14.73 ! [V_m_2,V_w_2] :
% 14.82/14.73 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 14.82/14.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__le__eq__zle,axiom,
% 14.82/14.73 ! [V_z_2,V_w_2] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__nat,axiom,
% 14.82/14.73 ! [V_i_2,V_Pa_2] :
% 14.82/14.73 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 14.82/14.73 <=> ( ! [B_n] :
% 14.82/14.73 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 14.82/14.73 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__add__distrib,axiom,
% 14.82/14.73 ! [V_z_H,V_z] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 14.82/14.73 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.73 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__eq__iff__number__of,axiom,
% 14.82/14.73 ! [V_v_2,V_m_2] :
% 14.82/14.73 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
% 14.82/14.73 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mult__distrib,axiom,
% 14.82/14.73 ! [V_z_H,V_z] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__eq__minus1,axiom,
% 14.82/14.73 ! [V_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__diff__distrib,axiom,
% 14.82/14.73 ! [V_z,V_z_H] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 14.82/14.73 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 14.82/14.73 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.73 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_one__less__nat__eq,axiom,
% 14.82/14.73 ! [V_z_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__zdiv,axiom,
% 14.82/14.73 ! [V_k_2,V_n_2,V_Pa_2] :
% 14.82/14.73 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 14.82/14.73 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.73 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 14.82/14.73 => ! [B_i] :
% 14.82/14.73 ( ? [B_j] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 14.82/14.73 & 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) )
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 14.82/14.73 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ! [B_i] :
% 14.82/14.73 ( ? [B_j] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 & 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) )
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_divmod__int__rel__div__eq,axiom,
% 14.82/14.73 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 14.82/14.73 ( 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)
% 14.82/14.73 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 14.82/14.73 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__less__iff,axiom,
% 14.82/14.73 ! [V_m_2,V_w_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 14.82/14.73 ! [V_z] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zmod__zmult2__eq,axiom,
% 14.82/14.73 ! [V_b,V_a,V_c] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 14.82/14.73 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mult__distrib__neg,axiom,
% 14.82/14.73 ! [V_z_H,V_z] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__zminus2__eq__if,axiom,
% 14.82/14.73 ! [V_a,V_b] :
% 14.82/14.73 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 14.82/14.73 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__zminus1__eq__if,axiom,
% 14.82/14.73 ! [V_a,V_b] :
% 14.82/14.73 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) )
% 14.82/14.73 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mod__nat__number__of,axiom,
% 14.82/14.73 ! [V_v_H,V_v] :
% 14.82/14.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_not__iszero__Numeral1,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_eq__number__of__eq,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_b)
% 14.82/14.73 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 14.82/14.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__2,axiom,
% 14.82/14.73 hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__pos__neg__trivial,axiom,
% 14.82/14.73 ! [V_b,V_a] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__pos__lemma,axiom,
% 14.82/14.73 ! [V_n_2,V_Pa_2,V_k_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 14.82/14.73 <=> ! [B_i,B_j] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 14.82/14.73 & 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) )
% 14.82/14.73 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__neg__lemma,axiom,
% 14.82/14.73 ! [V_n_2,V_Pa_2,V_k_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 14.82/14.73 <=> ! [B_i,B_j] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 & 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) )
% 14.82/14.73 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__number__of__Bit1,axiom,
% 14.82/14.73 ! [V_v,V_w] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_one__mod__nat__number__of,axiom,
% 14.82/14.73 ! [V_v_H] :
% 14.82/14.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 14.82/14.73 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_eq__special_I3_J,axiom,
% 14.82/14.73 ! [V_x_2,T_b] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_b)
% 14.82/14.73 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_eq__special_I1_J,axiom,
% 14.82/14.73 ! [V_y_2,T_b] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_b)
% 14.82/14.73 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 14.82/14.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_z3div__def,axiom,
% 14.82/14.73 ! [V_k,V_l] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 14.82/14.73 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 14.82/14.73 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__aux__def,axiom,
% 14.82/14.73 ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__of__aux__code,axiom,
% 14.82/14.73 ! [V_n,V_i] :
% 14.82/14.73 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 14.82/14.73 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 14.82/14.73 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 14.82/14.73 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_transfer__morphism__nat__int,axiom,
% 14.82/14.73 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__m1__odd,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_double__complement,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Compl__eq__Compl__iff,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
% 14.82/14.73 <=> V_A_2 = V_B_2 ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 14.82/14.73 ! [V_q,V_y,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => 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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__le__mono,axiom,
% 14.82/14.73 ! [V_k,V_n,V_m] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__le__dividend,axiom,
% 14.82/14.73 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__power,axiom,
% 14.82/14.73 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zpower__int,axiom,
% 14.82/14.73 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 14.82/14.73 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mult2__eq,axiom,
% 14.82/14.73 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 14.82/14.73 ! [V_q,V_p,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => 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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zpower__zpower,axiom,
% 14.82/14.73 ! [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)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zpower__zmod,axiom,
% 14.82/14.73 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__power__eq,axiom,
% 14.82/14.73 ! [V_n,V_z] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 14.82/14.73 ! [V_n,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__1,axiom,
% 14.82/14.73 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__less,axiom,
% 14.82/14.73 ! [V_n,V_m] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mult__div__cancel__disj,axiom,
% 14.82/14.73 ! [V_n,V_m,V_k] :
% 14.82/14.73 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => hAPP(hAPP(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) )
% 14.82/14.73 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => hAPP(hAPP(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 14.82/14.73 ! [V_q,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 14.82/14.73 ! [V_q,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => 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),hAPP(c_Nat_OSuc,V_q)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 14.82/14.73 ! [V_q,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => 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),hAPP(c_Nat_OSuc,V_q)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => 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) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 14.82/14.73 ! [V_q,V_p,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => 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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 14.82/14.73 ! [V_n,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__add1__eq,axiom,
% 14.82/14.73 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zdiv__int,axiom,
% 14.82/14.73 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 14.82/14.73 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zpower__zadd__distrib,axiom,
% 14.82/14.73 ! [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)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Ints__power,axiom,
% 14.82/14.73 ! [V_n_2,V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Oring__1(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__nat__number__of__number__of,axiom,
% 14.82/14.73 ! [V_w,V_v] :
% 14.82/14.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__nat__number__of,axiom,
% 14.82/14.73 ! [V_n,V_v] :
% 14.82/14.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__le__mono2,axiom,
% 14.82/14.73 ! [V_k,V_n,V_m] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mult__div__cancel1,axiom,
% 14.82/14.73 ! [V_n,V_m,V_k] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 14.82/14.73 => hAPP(hAPP(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)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mult__self1__is__m,axiom,
% 14.82/14.73 ! [V_m,V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => hAPP(hAPP(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 ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mult__self__is__m,axiom,
% 14.82/14.73 ! [V_m,V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => hAPP(hAPP(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 ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__less__dividend,axiom,
% 14.82/14.73 ! [V_m,V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mod__mult2__eq,axiom,
% 14.82/14.73 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mult1__eq,axiom,
% 14.82/14.73 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__mod__equality_H,axiom,
% 14.82/14.73 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mult__div__cancel,axiom,
% 14.82/14.73 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Divides_Omod__div__equality_H,axiom,
% 14.82/14.73 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__le__zpower__abs,axiom,
% 14.82/14.73 ! [V_n,V_x] : hBOOL(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__if,axiom,
% 14.82/14.73 ! [V_m,V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__geq,axiom,
% 14.82/14.73 ! [V_m,V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__div,axiom,
% 14.82/14.73 ! [V_k_2,V_n_2,V_Pa_2] :
% 14.82/14.73 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 14.82/14.73 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 14.82/14.73 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => ! [B_i,B_j] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 14.82/14.73 => ( 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)
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__div__distrib,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 14.82/14.73 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power3__eq__cube,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_abs__power__minus__one,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 & class_Rings_Olinordered__idom(T_a) )
% 14.82/14.73 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__eq__if,axiom,
% 14.82/14.73 ! [V_p,V_m] :
% 14.82/14.73 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 14.82/14.73 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__less__zpower__abs__iff,axiom,
% 14.82/14.73 ! [V_n_2,V_x_2] :
% 14.82/14.73 ( hBOOL(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
% 14.82/14.73 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_le__div__geq,axiom,
% 14.82/14.73 ! [V_m,V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__div__lemma,axiom,
% 14.82/14.73 ! [V_m_2,V_q_2,V_n_2] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 14.82/14.73 => ( ( hBOOL(hAPP(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))
% 14.82/14.73 & hBOOL(hAPP(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),hAPP(c_Nat_OSuc,V_q_2)))) )
% 14.82/14.73 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_split__div_H,axiom,
% 14.82/14.73 ! [V_n_2,V_m_2,V_Pa_2] :
% 14.82/14.73 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 14.82/14.73 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 14.82/14.73 | ? [B_q] :
% 14.82/14.73 ( hBOOL(hAPP(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))
% 14.82/14.73 & hBOOL(hAPP(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),hAPP(c_Nat_OSuc,B_q))))
% 14.82/14.73 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__Suc__eq__div__add3,axiom,
% 14.82/14.73 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Suc__div__eq__add3__div,axiom,
% 14.82/14.73 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 14.82/14.73 ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div2__Suc__Suc,axiom,
% 14.82/14.73 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_add__self__div__2,axiom,
% 14.82/14.73 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__power2,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__eq__power2,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 14.82/14.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__eq__square,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_one__power2,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__minus,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__even__eq,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_abs__power2,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__abs,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__eq__imp__eq,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.73 => V_x = V_y ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__le__imp__le,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__le__power2,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hBOOL(hAPP(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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__less__0,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__less__power2,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 14.82/14.73 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sum__power2__eq__zero__iff,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__eq__square__number__of,axiom,
% 14.82/14.73 ! [V_w,T_b] :
% 14.82/14.73 ( ( class_Groups_Omonoid__mult(T_b)
% 14.82/14.73 & class_Int_Onumber(T_b) )
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__eq__1__iff,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 14.82/14.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.73 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.73 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__nat__number__of,axiom,
% 14.82/14.73 ! [V_v_H,V_v] :
% 14.82/14.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.73 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 14.82/14.73 ! [V_n,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__minus__even,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_div__2__gt__zero,axiom,
% 14.82/14.73 ! [V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__less__imp__less,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_one__div__nat__number__of,axiom,
% 14.82/14.73 ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sum__power2__le__zero__iff,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.73 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sum__power2__ge__zero,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hBOOL(hAPP(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_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sum__power2__gt__zero__iff,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 14.82/14.73 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_not__sum__power2__lt__zero,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__sum,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__le__even__power_H,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 14.82/14.73 ! [V_n,V_x,T_a] :
% 14.82/14.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__odd__eq,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__minus1__even,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__power__div__base,axiom,
% 14.82/14.73 ! [V_k,V_m] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 14.82/14.73 => hAPP(hAPP(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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 14.82/14.73 ! [V_n] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power2__diff,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(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),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_odd__power__less__zero,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__minus1__odd,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__m1__even,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__of__code,axiom,
% 14.82/14.73 ! [V_k] :
% 14.82/14.73 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 14.82/14.73 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.73 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 14.82/14.73 => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 14.82/14.73 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) )
% 14.82/14.73 & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 14.82/14.73 => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__strict__mono,axiom,
% 14.82/14.73 ! [V_n,V_b,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__diff,axiom,
% 14.82/14.73 ! [V_m,V_n,V_a,T_a] :
% 14.82/14.73 ( class_Fields_Ofield(T_a)
% 14.82/14.73 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_one__less__power,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__increasing__iff,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_field__power__not__zero,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 14.82/14.73 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__Suc__0,axiom,
% 14.82/14.73 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 14.82/14.73 ! [V_m_2,V_x_2] :
% 14.82/14.73 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.82/14.73 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__zero__less__power__iff,axiom,
% 14.82/14.73 ! [V_n_2,V_x_2] :
% 14.82/14.73 ( hBOOL(hAPP(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)))
% 14.82/14.73 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 14.82/14.73 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__power__less__imp__less,axiom,
% 14.82/14.73 ! [V_n,V_m,V_i] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 14.82/14.73 => ( hBOOL(hAPP(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)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__mult__distrib,axiom,
% 14.82/14.73 ! [V_n,V_b,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Ocomm__monoid__mult(T_a)
% 14.82/14.73 => 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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__commutes,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => 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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__one,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => 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) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__nat__power,axiom,
% 14.82/14.73 ! [V_n,V_m,T_a] :
% 14.82/14.73 ( class_Rings_Osemiring__1(T_a)
% 14.82/14.73 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__mult,axiom,
% 14.82/14.73 ! [V_n,V_m,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => 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) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__divide,axiom,
% 14.82/14.73 ! [V_n,V_b,V_a,T_a] :
% 14.82/14.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__abs,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__one__right,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__le__power,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__mono,axiom,
% 14.82/14.73 ! [V_n,V_b,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__less__power,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__eq__0__iff,axiom,
% 14.82/14.73 ! [V_n_2,V_a_2,T_b] :
% 14.82/14.73 ( ( class_Power_Opower(T_b)
% 14.82/14.73 & class_Rings_Omult__zero(T_b)
% 14.82/14.73 & class_Rings_Ono__zero__divisors(T_b)
% 14.82/14.73 & class_Rings_Ozero__neq__one(T_b) )
% 14.82/14.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_one__le__power,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__0__Suc,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( ( class_Power_Opower(T_a)
% 14.82/14.73 & class_Rings_Osemiring__0(T_a) )
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__inject__exp,axiom,
% 14.82/14.73 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 14.82/14.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
% 14.82/14.73 <=> V_m_2 = V_n_2 ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__Suc,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Power_Opower(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__Suc2,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(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) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__one__le__power,axiom,
% 14.82/14.73 ! [V_n,V_i] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(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))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__0,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Power_Opower(T_a)
% 14.82/14.73 => 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) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__add,axiom,
% 14.82/14.73 ! [V_n,V_m,V_a,T_a] :
% 14.82/14.73 ( class_Groups_Omonoid__mult(T_a)
% 14.82/14.73 => 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)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nonzero__power__divide,axiom,
% 14.82/14.73 ! [V_n,V_a,V_b,T_a] :
% 14.82/14.73 ( class_Fields_Ofield(T_a)
% 14.82/14.73 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(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)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__one__over,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Fields_Ofield__inverse__zero(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_abs__power__minus,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__less__imp__less__base,axiom,
% 14.82/14.73 ! [V_b,V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(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)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__inject__base,axiom,
% 14.82/14.73 ! [V_b,V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.82/14.73 => V_a = V_b ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__le__imp__le__base,axiom,
% 14.82/14.73 ! [V_b,V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__gt1__lemma,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__less__power__Suc,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__0__left,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( ( class_Power_Opower(T_a)
% 14.82/14.73 & class_Rings_Osemiring__0(T_a) )
% 14.82/14.73 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => 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) )
% 14.82/14.73 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => 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) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__gt1,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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),hAPP(c_Nat_OSuc,V_n)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__strict__increasing__iff,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__less__imp__less__exp,axiom,
% 14.82/14.73 ! [V_n,V_m,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(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)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__strict__increasing,axiom,
% 14.82/14.73 ! [V_a,V_N,V_n,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zero__le__power__abs,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hBOOL(hAPP(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),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__increasing,axiom,
% 14.82/14.73 ! [V_a,V_N,V_n,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__minus,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__Suc__less,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__eq__imp__eq__base,axiom,
% 14.82/14.73 ! [V_b,V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( 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)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.73 => V_a = V_b ) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__Suc__less__one,axiom,
% 14.82/14.73 ! [V_n,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__strict__decreasing,axiom,
% 14.82/14.73 ! [V_a,V_N,V_n,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__decreasing,axiom,
% 14.82/14.73 ! [V_a,V_N,V_n,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 14.82/14.73 => hBOOL(hAPP(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))) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__le__imp__le__exp,axiom,
% 14.82/14.73 ! [V_n,V_m,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__semidom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 14.82/14.73 => ( hBOOL(hAPP(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)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_card__Pow,axiom,
% 14.82/14.73 ! [V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.73 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power__power__power,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( class_Power_Opower(T_b)
% 14.82/14.73 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osize_I1_J,axiom,
% 14.82/14.73 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__of__nat,axiom,
% 14.82/14.73 ! [V_k,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 14.82/14.73 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_PowI,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__eq__iff,axiom,
% 14.82/14.73 ! [V_z_2,V_w_2,T_b] :
% 14.82/14.73 ( class_Int_Oring__char__0(T_b)
% 14.82/14.73 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 14.82/14.73 <=> V_w_2 = V_z_2 ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_number__of__eq,axiom,
% 14.82/14.73 ! [V_k,T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_int__number__of__def,axiom,
% 14.82/14.73 ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__int__eq,axiom,
% 14.82/14.73 ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__top,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Union__Pow__eq,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__not__empty,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__0,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__0__eq__iff,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Int_Oring__char__0(T_b)
% 14.82/14.73 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 14.82/14.73 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__eq__0__iff,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Int_Oring__char__0(T_b)
% 14.82/14.73 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__le__iff,axiom,
% 14.82/14.73 ! [V_z_2,V_w_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__less__iff,axiom,
% 14.82/14.73 ! [V_z_2,V_w_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__add,axiom,
% 14.82/14.73 ! [V_z,V_w,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__number__of__eq,axiom,
% 14.82/14.73 ! [V_v,T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__mult,axiom,
% 14.82/14.73 ! [V_z,V_w,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__1,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__diff,axiom,
% 14.82/14.73 ! [V_z,V_w,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__of__nat__eq,axiom,
% 14.82/14.73 ! [V_n,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__minus,axiom,
% 14.82/14.73 ! [V_z,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__bottom,axiom,
% 14.82/14.73 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__iff,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_PowD,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Ints__of__int,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Rings_Oring__1(T_b)
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__power,axiom,
% 14.82/14.73 ! [V_n,V_z,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__mono,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__Pow__iff,axiom,
% 14.82/14.73 ! [V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 14.82/14.73 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_subset__Pow__Union,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power_Opower_Opower__0,axiom,
% 14.82/14.73 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 14.82/14.73
% 14.82/14.73 fof(fact_power_Opower_Opower__Suc,axiom,
% 14.82/14.73 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__Int__eq,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__m1,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Int_Onumber__ring(T_a)
% 14.82/14.73 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__empty,axiom,
% 14.82/14.73 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__le__0__iff,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__0__le__iff,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__0__less__iff,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__int__less__0__iff,axiom,
% 14.82/14.73 ! [V_z_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_of__nat__nat,axiom,
% 14.82/14.73 ! [V_z,T_a] :
% 14.82/14.73 ( class_Rings_Oring__1(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 14.82/14.73 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Un__Pow__subset,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 14.82/14.73 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osize_I2_J,axiom,
% 14.82/14.73 ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_negD,axiom,
% 14.82/14.73 ! [V_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.73 => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osize_I3_J,axiom,
% 14.82/14.73 hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__if,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Groups_Osgn__if(T_a)
% 14.82/14.73 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 14.82/14.73 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 14.82/14.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Oinject,axiom,
% 14.82/14.73 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 14.82/14.73 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 14.82/14.73 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__sgn,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__0__0,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.73 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn0,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Groups_Osgn__if(T_a)
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__times,axiom,
% 14.82/14.73 ! [V_b,V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(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_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 14.82/14.73 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 14.82/14.73 ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__less,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__greater,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osize_I4_J,axiom,
% 14.82/14.73 ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mult__sgn__abs,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_abs__sgn,axiom,
% 14.82/14.73 ! [V_k,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Suc__code__numeral__minus__one,axiom,
% 14.82/14.73 ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__1__pos,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__pos,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__gcd_Osimps,axiom,
% 14.82/14.73 ! [V_x,V_y] :
% 14.82/14.73 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 14.82/14.73 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.73 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_zsgn__def,axiom,
% 14.82/14.73 ! [V_i] :
% 14.82/14.73 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.73 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__neg,axiom,
% 14.82/14.73 ! [V_a,T_a] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_a)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 14.82/14.73 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sgn__1__neg,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Rings_Olinordered__idom(T_b)
% 14.82/14.73 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 14.82/14.73 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 14.82/14.73 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_compl__unique,axiom,
% 14.82/14.73 ! [V_y,V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.73 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 14.82/14.73 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 14.82/14.73 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 14.82/14.73 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 14.82/14.73 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 14.82/14.73
% 14.82/14.73 fof(fact_UNIV__I,axiom,
% 14.82/14.73 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__fun__UNIVD2,axiom,
% 14.82/14.73 ! [T_c,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 14.82/14.73 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_UNIV__not__empty,axiom,
% 14.82/14.73 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__UNIV,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( class_Finite__Set_Ofinite(T_b)
% 14.82/14.73 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_subset__UNIV,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_UNIV__Plus__UNIV,axiom,
% 14.82/14.73 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__option__UNIV,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
% 14.82/14.73 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__Prod__UNIV,axiom,
% 14.82/14.73 ! [T_c,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 14.82/14.73 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Union__UNIV,axiom,
% 14.82/14.73 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_top__apply,axiom,
% 14.82/14.73 ! [V_x_2,T_c,T_b] :
% 14.82/14.73 ( class_Orderings_Otop(T_b)
% 14.82/14.73 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Sup__UNIV,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Int__UNIV__right,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Int__UNIV__left,axiom,
% 14.82/14.73 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Un__UNIV__right,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Un__UNIV__left,axiom,
% 14.82/14.73 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Pow__UNIV,axiom,
% 14.82/14.73 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_card__UNIV__unit,axiom,
% 14.82/14.73 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__Plus__UNIV__iff,axiom,
% 14.82/14.73 ! [T_c,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
% 14.82/14.73 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.73 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_vimage__UNIV,axiom,
% 14.82/14.73 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 14.82/14.73 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 14.82/14.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 14.82/14.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 14.82/14.73 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 14.82/14.73 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 14.82/14.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 14.82/14.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 14.82/14.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 14.82/14.73 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 14.82/14.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 14.82/14.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_top__greatest,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Orderings_Otop(T_a)
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sup__top__right,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Obounded__lattice__top(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sup__top__left,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Obounded__lattice__top(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_inf__top__left,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Obounded__lattice__top(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_inf__top__right,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Obounded__lattice__top(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_inf__eq__top__iff,axiom,
% 14.82/14.73 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.73 ( class_Lattices_Obounded__lattice__top(T_b)
% 14.82/14.73 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 14.82/14.73 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 14.82/14.73 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 14.82/14.73 ! [V_n,V_x] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 14.82/14.73 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Diff__UNIV,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 14.82/14.73 ! [V_y,V_x] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x)
% 14.82/14.73 => ( c_Nat__Transfer_Ois__nat(V_y)
% 14.82/14.73 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 14.82/14.73 ! [V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.73 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.73 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Compl__empty__eq,axiom,
% 14.82/14.73 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Compl__UNIV__eq,axiom,
% 14.82/14.73 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__compl,axiom,
% 14.82/14.73 ! [V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 14.82/14.73 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Compl__partition2,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Compl__partition,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 14.82/14.73 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_is__nat__def,axiom,
% 14.82/14.73 ! [V_x_2] :
% 14.82/14.73 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 14.82/14.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_compl__bot__eq,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.73 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_compl__top__eq,axiom,
% 14.82/14.73 ! [T_a] :
% 14.82/14.73 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.73 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_sup__compl__top,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_compl__sup__top,axiom,
% 14.82/14.73 ! [V_x,T_a] :
% 14.82/14.73 ( class_Lattices_Oboolean__algebra(T_a)
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 14.82/14.73 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__UNIV__card__ge__0,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_card__UNIV__bool,axiom,
% 14.82/14.73 hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__fun__UNIVD1,axiom,
% 14.82/14.73 ! [T_c,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 14.82/14.73 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 14.82/14.73 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__fold__inf,axiom,
% 14.82/14.73 ! [V_A_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.73 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_nat__mod__eq__lemma,axiom,
% 14.82/14.73 ! [V_y,V_n,V_x] :
% 14.82/14.73 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 14.82/14.73 => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mod__induct__0,axiom,
% 14.82/14.73 ! [V_i_2,V_Pa_2,V_p_2] :
% 14.82/14.73 ( ! [B_i] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 14.82/14.73 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 14.82/14.73 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 14.82/14.73 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_log_Osimps,axiom,
% 14.82/14.73 ! [V_i,V_b] :
% 14.82/14.73 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 14.82/14.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 14.82/14.73 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 14.82/14.73 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
% 14.82/14.73 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 14.82/14.73 => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_finite__Inter,axiom,
% 14.82/14.73 ! [V_M_2,T_b] :
% 14.82/14.73 ( ? [B_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 14.82/14.73 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 14.82/14.73 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_top1I,axiom,
% 14.82/14.73 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_InterD,axiom,
% 14.82/14.73 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_InterE,axiom,
% 14.82/14.73 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__UNIV,axiom,
% 14.82/14.73 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__empty,axiom,
% 14.82/14.73 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_le__Inf__iff,axiom,
% 14.82/14.73 ! [V_A_2,V_b_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 14.82/14.73 <=> ! [B_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__less__iff,axiom,
% 14.82/14.73 ! [V_a_2,V_S_2,T_b] :
% 14.82/14.73 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 & class_Orderings_Olinorder(T_b) )
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 14.82/14.73 <=> ? [B_x] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 14.82/14.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__UNIV,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__lower,axiom,
% 14.82/14.73 ! [V_A_2,V_B_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__anti__mono,axiom,
% 14.82/14.73 ! [V_A_2,V_B_2,T_b] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__insert,axiom,
% 14.82/14.73 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__lower,axiom,
% 14.82/14.73 ! [V_A_2,V_x_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__Un__distrib,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__singleton,axiom,
% 14.82/14.73 ! [V_a_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__empty,axiom,
% 14.82/14.73 ! [T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__insert,axiom,
% 14.82/14.73 ! [V_A_2,V_a_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Int__eq__Inter,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__Un__subset,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__binary,axiom,
% 14.82/14.73 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_inf__Inf__fold__inf,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.73 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inf__fin__Inf,axiom,
% 14.82/14.73 ! [V_A_2,T_b] :
% 14.82/14.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.73 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.73 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_minus__shift__def,axiom,
% 14.82/14.73 ! [V_r,V_l,V_k] :
% 14.82/14.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 14.82/14.73 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) )
% 14.82/14.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 14.82/14.73 => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_inc__shift__def,axiom,
% 14.82/14.73 ! [V_k,V_v] :
% 14.82/14.73 ( ( V_v = V_k
% 14.82/14.73 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 14.82/14.73 & ( V_v != V_k
% 14.82/14.73 => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_iso__tuple__UNIV__I,axiom,
% 14.82/14.73 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_mod__div__decomp,axiom,
% 14.82/14.73 ! [V_b,V_a,T_a] :
% 14.82/14.73 ( class_Divides_Osemiring__div(T_a)
% 14.82/14.73 => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_Inter__subset,axiom,
% 14.82/14.73 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.73 ( ! [B_X] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 14.82/14.73 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_InterI,axiom,
% 14.82/14.73 ! [V_A_2,V_C_2,T_b] :
% 14.82/14.73 ( ! [B_X] :
% 14.82/14.73 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 14.82/14.73 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osize_I14_J,axiom,
% 14.82/14.73 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osize_I6_J,axiom,
% 14.82/14.73 ! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I5_J,axiom,
% 14.82/14.73 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 14.82/14.73 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 14.82/14.73 <=> ( V_fun_2 = V_fun_H_2
% 14.82/14.73 & V_com_2 = V_com_H_2 ) ) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I52_J,axiom,
% 14.82/14.73 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I53_J,axiom,
% 14.82/14.73 ! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I46_J,axiom,
% 14.82/14.73 ! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I47_J,axiom,
% 14.82/14.73 ! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I38_J,axiom,
% 14.82/14.73 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 14.82/14.73
% 14.82/14.73 fof(fact_com_Osimps_I39_J,axiom,
% 14.82/14.74 ! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_com_Osimps_I16_J,axiom,
% 14.82/14.74 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_com_Osimps_I17_J,axiom,
% 14.82/14.74 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 14.82/14.74
% 14.82/14.74 fof(fact_minus__code__numeral__code,axiom,
% 14.82/14.74 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_subtract__code__numeral__def,axiom,
% 14.82/14.74 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__box_Osize_I1_J,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 14.82/14.74 ! [V_w] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.74 => ( ( hBOOL(hAPP(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),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
% 14.82/14.74 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(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),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
% 14.82/14.74 => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__box_Oinject,axiom,
% 14.82/14.74 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.74 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 14.82/14.74 <=> ( V_a_2 = V_a_H_2
% 14.82/14.74 & V_b_2 = V_b_H_2 ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg__div__mod,axiom,
% 14.82/14.74 ! [V_l,V_k] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 14.82/14.74 => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg__minus1,axiom,
% 14.82/14.74 ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg_Osimps,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( ( ( hBOOL(hAPP(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_a),V_b)))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 14.82/14.74 & ( ~ ( hBOOL(hAPP(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_a),V_b)))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg__eqn,axiom,
% 14.82/14.74 ! [V_a,V_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => ( ( hBOOL(hAPP(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_a),V_b)))
% 14.82/14.74 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(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_a),V_b)))
% 14.82/14.74 => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg__eqn__number__of,axiom,
% 14.82/14.74 ! [V_w,V_v] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.74 => ( ( hBOOL(hAPP(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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 14.82/14.74 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 14.82/14.74 => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 14.82/14.74 ! [V_w] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.74 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.74 => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg_Osimps,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) )
% 14.82/14.74 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_in__rel__def,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg__eqn__number__of,axiom,
% 14.82/14.74 ! [V_w,V_v] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.74 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 14.82/14.74 => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg__0,axiom,
% 14.82/14.74 ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg__div__mod,axiom,
% 14.82/14.74 ! [V_l,V_k] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 14.82/14.74 => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg__eqn,axiom,
% 14.82/14.74 ! [V_a,V_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 14.82/14.74 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 14.82/14.74 => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__mod__code__numeral__def,axiom,
% 14.82/14.74 ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Nitpick_Orefl_H__def,axiom,
% 14.82/14.74 ! [V_r_2,T_b] :
% 14.82/14.74 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 14.82/14.74 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__step,axiom,
% 14.82/14.74 ! [V_m,V_n] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 14.82/14.74 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__box_Osize_I2_J,axiom,
% 14.82/14.74 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__zero,axiom,
% 14.82/14.74 ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__base,axiom,
% 14.82/14.74 ! [V_n,V_m] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 14.82/14.74 => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__div__mod,axiom,
% 14.82/14.74 ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 14.82/14.74 ! [V_a,V_r,V_q,V_c,V_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 14.82/14.74 ! [V_c,V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__box_Orecs,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__box_Osimps_I2_J,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel__unique,axiom,
% 14.82/14.74 ! [V_qr_H,V_qr,V_n,V_m] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 14.82/14.74 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 14.82/14.74 => V_qr = V_qr_H ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__eq,axiom,
% 14.82/14.74 ! [V_qr,V_n,V_m] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 14.82/14.74 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 14.82/14.74 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__eq,axiom,
% 14.82/14.74 ! [V_r,V_q,V_n,V_m] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__eq,axiom,
% 14.82/14.74 ! [V_r,V_q,V_n,V_m] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel,axiom,
% 14.82/14.74 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 14.82/14.74 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
% 14.82/14.74 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg_Opsimps,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 14.82/14.74 => ( ( ( hBOOL(hAPP(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_a_2),V_b_2)))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) )
% 14.82/14.74 & ( ~ ( hBOOL(hAPP(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_a_2),V_b_2)))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pdivmod__posDivAlg,axiom,
% 14.82/14.74 ! [V_k,V_l] :
% 14.82/14.74 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) )
% 14.82/14.74 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pdivmod__def,axiom,
% 14.82/14.74 ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_zmult2__lemma,axiom,
% 14.82/14.74 ! [V_c,V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_unique__remainder,axiom,
% 14.82/14.74 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
% 14.82/14.74 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => V_r = V_r_H ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_unique__quotient,axiom,
% 14.82/14.74 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
% 14.82/14.74 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => V_q = V_q_H ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_self__remainder,axiom,
% 14.82/14.74 ! [V_r,V_q,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__rel__0,axiom,
% 14.82/14.74 ! [V_b] :
% 14.82/14.74 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_self__quotient,axiom,
% 14.82/14.74 ! [V_r,V_q,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__rel__mod,axiom,
% 14.82/14.74 ! [V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__rel__div,axiom,
% 14.82/14.74 ! [V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg__correct,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__rel__div__mod,axiom,
% 14.82/14.74 ! [V_a,V_b] :
% 14.82/14.74 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg__correct,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_zadd1__lemma,axiom,
% 14.82/14.74 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
% 14.82/14.74 => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
% 14.82/14.74 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_zminus1__lemma,axiom,
% 14.82/14.74 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__relI,axiom,
% 14.82/14.74 ! [V_r,V_q,V_b,V_a] :
% 14.82/14.74 ( V_a = 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)
% 14.82/14.74 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_zmult1__lemma,axiom,
% 14.82/14.74 ! [V_a,V_r,V_q,V_c,V_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
% 14.82/14.74 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg_Opsimps,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 14.82/14.74 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) )
% 14.82/14.74 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negDivAlg_Opinduct,axiom,
% 14.82/14.74 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 14.82/14.74 => ( ! [B_a,B_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 14.82/14.74 => ( ( ~ ( hBOOL(hAPP(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),B_a),B_b)))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_posDivAlg_Opinduct,axiom,
% 14.82/14.74 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 14.82/14.74 => ( ! [B_a,B_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 14.82/14.74 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_accp__subset,axiom,
% 14.82/14.74 ! [V_R2_2,V_R1_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_predicate2D,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_rev__predicate2D,axiom,
% 14.82/14.74 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_accp_Osimps,axiom,
% 14.82/14.74 ! [V_a_2,V_r_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 14.82/14.74 <=> ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 14.82/14.74 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_accp_Oequations,axiom,
% 14.82/14.74 ! [V_a_2,V_r_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 14.82/14.74 <=> ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 14.82/14.74 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_accp__downward,axiom,
% 14.82/14.74 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 14.82/14.74 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__gcd_Opsimps,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
% 14.82/14.74 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 14.82/14.74 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat_Osize_I2_J,axiom,
% 14.82/14.74 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_in__measure,axiom,
% 14.82/14.74 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mlex__leq,axiom,
% 14.82/14.74 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat_Osize_I1_J,axiom,
% 14.82/14.74 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mlex__less,axiom,
% 14.82/14.74 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__gcd_Opinduct,axiom,
% 14.82/14.74 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
% 14.82/14.74 => ( ! [B_x,B_y] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
% 14.82/14.74 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat_Osize_I4_J,axiom,
% 14.82/14.74 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__def,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 14.82/14.74 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__pos__pos__1__number__of,axiom,
% 14.82/14.74 ! [V_w] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__int__def,axiom,
% 14.82/14.74 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__size,axiom,
% 14.82/14.74 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat_Osize_I3_J,axiom,
% 14.82/14.74 hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__pos__neg,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negateSnd__eq,axiom,
% 14.82/14.74 ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__neg__neg,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__rel__neg,axiom,
% 14.82/14.74 ! [V_qr,V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__neg__pos,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__correct,axiom,
% 14.82/14.74 ! [V_a,V_b] :
% 14.82/14.74 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__pos__neg__1__number__of,axiom,
% 14.82/14.74 ! [V_w] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__pos__pos,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__mod__div,axiom,
% 14.82/14.74 ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__pos__neg__1__number__of,axiom,
% 14.82/14.74 ! [V_w] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__neg__neg,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_snd__eqD,axiom,
% 14.82/14.74 ! [V_a,V_y,V_x,T_a,T_b] :
% 14.82/14.74 ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
% 14.82/14.74 => V_y = V_a ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_snd__conv,axiom,
% 14.82/14.74 ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Pair__fst__snd__eq,axiom,
% 14.82/14.74 ! [T_c,T_b,V_t_2,V_s_2] :
% 14.82/14.74 ( V_s_2 = V_t_2
% 14.82/14.74 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 14.82/14.74 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_prod__eqI,axiom,
% 14.82/14.74 ! [V_q,V_p,T_b,T_a] :
% 14.82/14.74 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 14.82/14.74 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 14.82/14.74 => V_p = V_q ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fst__conv,axiom,
% 14.82/14.74 ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fst__eqD,axiom,
% 14.82/14.74 ! [V_a,V_y,V_x,T_b,T_a] :
% 14.82/14.74 ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
% 14.82/14.74 => V_x = V_a ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_surjective__pairing,axiom,
% 14.82/14.74 ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__collapse,axiom,
% 14.82/14.74 ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__int__def,axiom,
% 14.82/14.74 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mod__nat__def,axiom,
% 14.82/14.74 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Pair__inject,axiom,
% 14.82/14.74 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 14.82/14.74 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
% 14.82/14.74 => ~ ( V_a = V_a_H
% 14.82/14.74 => V_b != V_b_H ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Pair__eq,axiom,
% 14.82/14.74 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.74 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 14.82/14.74 <=> ( V_a_2 = V_a_H_2
% 14.82/14.74 & V_b_2 = V_b_H_2 ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__paired__All,axiom,
% 14.82/14.74 ! [T_c,T_b,V_Pa_2] :
% 14.82/14.74 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 14.82/14.74 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__neg__pos,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__pos__pos,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__pos__pos__1__number__of,axiom,
% 14.82/14.74 ! [V_w] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__pos__neg,axiom,
% 14.82/14.74 ! [V_b,V_a] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_prod__size__simp,axiom,
% 14.82/14.74 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_conjI__realizer,axiom,
% 14.82/14.74 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] :
% 14.82/14.74 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 14.82/14.74 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 14.82/14.74 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 14.82/14.74 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_exI__realizer,axiom,
% 14.82/14.74 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_prod_Orecs,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_div__nat__def,axiom,
% 14.82/14.74 ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__rel__def,axiom,
% 14.82/14.74 ! [V_qr_2,V_n_2,V_m_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 14.82/14.74 <=> ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))
% 14.82/14.74 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.74 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)) ) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_range,axiom,
% 14.82/14.74 ! [V_s,V_k] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_in__lex__prod,axiom,
% 14.82/14.74 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 14.82/14.74 | ( V_a_2 = V_a_H_2
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_in__finite__psubset,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.74 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__lessI2,axiom,
% 14.82/14.74 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__lessI1,axiom,
% 14.82/14.74 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_same__fstI,axiom,
% 14.82/14.74 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 14.82/14.74 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__leqI2,axiom,
% 14.82/14.74 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_smax__insertI,axiom,
% 14.82/14.74 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_smin__insertI,axiom,
% 14.82/14.74 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_smin__emptyI,axiom,
% 14.82/14.74 ! [V_X_2] :
% 14.82/14.74 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_smax__emptyI,axiom,
% 14.82/14.74 ! [V_Y_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 14.82/14.74 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__leqI1,axiom,
% 14.82/14.74 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_wmin__insertI,axiom,
% 14.82/14.74 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_wmax__insertI,axiom,
% 14.82/14.74 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_wmin__emptyI,axiom,
% 14.82/14.74 ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_wmax__emptyI,axiom,
% 14.82/14.74 ! [V_X_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__by__empty,axiom,
% 14.82/14.74 ! [V_B_2,T_b,V_A_2] :
% 14.82/14.74 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__weak__def,axiom,
% 14.82/14.74 c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__weak__def,axiom,
% 14.82/14.74 c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__rpair__set,axiom,
% 14.82/14.74 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__rpair__set,axiom,
% 14.82/14.74 c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__strict__def,axiom,
% 14.82/14.74 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__ext__additive,axiom,
% 14.82/14.74 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__strict__def,axiom,
% 14.82/14.74 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__than__iff,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_intrel__iff,axiom,
% 14.82/14.74 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
% 14.82/14.74 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_rp__inv__image__rp,axiom,
% 14.82/14.74 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 14.82/14.74 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 14.82/14.74 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__ext_Ointros,axiom,
% 14.82/14.74 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 14.82/14.74 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 14.82/14.74 => ? [B_xa] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pair__less__def,axiom,
% 14.82/14.74 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_equiv__intrel__iff,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2] :
% 14.82/14.74 ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 14.82/14.74 ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_measure__def,axiom,
% 14.82/14.74 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_adjust__eq,axiom,
% 14.82/14.74 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__abs,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__abs__ge__zero,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod_Odistrib,axiom,
% 14.82/14.74 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum_Odistrib,axiom,
% 14.82/14.74 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__dividef,axiom,
% 14.82/14.74 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.74 ( class_Fields_Ofield__inverse__zero(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__number__of__Bit0,axiom,
% 14.82/14.74 ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__negf,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Oab__group__add(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fun__Compl__def,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ouminus(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_int__setprod,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__1,axiom,
% 14.82/14.74 ! [V_A_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_abs__setsum__abs,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 14.82/14.74 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_abs__setprod,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Fields_Olinordered__field(T_b)
% 14.82/14.74 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__right__distrib,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__0(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__left__distrib,axiom,
% 14.82/14.74 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__0(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__product,axiom,
% 14.82/14.74 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__0(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf__fun__def,axiom,
% 14.82/14.74 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Lattices_Olattice(T_b)
% 14.82/14.74 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__timesf,axiom,
% 14.82/14.74 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 14.82/14.74 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 14.82/14.74 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.82/14.74 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__commute,axiom,
% 14.82/14.74 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 14.82/14.74 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 14.82/14.74 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 14.82/14.74 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__divide__distrib,axiom,
% 14.82/14.74 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Fields_Ofield(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fold__image__def,axiom,
% 14.82/14.74 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_int__setsum,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__0,axiom,
% 14.82/14.74 ! [V_A_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fun__diff__def,axiom,
% 14.82/14.74 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ominus(T_b)
% 14.82/14.74 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__subtractf,axiom,
% 14.82/14.74 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Oab__group__add(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__int__setprod,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.82/14.74 & class_Rings_Oring__1(T_b) )
% 14.82/14.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__int__setsum,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Rings_Oring__1(T_b)
% 14.82/14.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__addf,axiom,
% 14.82/14.74 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf__Int__eq,axiom,
% 14.82/14.74 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pred__equals__eq,axiom,
% 14.82/14.74 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.74 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
% 14.82/14.74 <=> V_R_2 = V_S_2 ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pred__subset__eq,axiom,
% 14.82/14.74 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup__Un__eq,axiom,
% 14.82/14.74 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup__Un__eq2,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf__Int__eq2,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pred__equals__eq2,axiom,
% 14.82/14.74 ! [V_S_2,V_R_2,T_c,T_b] :
% 14.82/14.74 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
% 14.82/14.74 <=> V_R_2 = V_S_2 ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__eq__Suc__le__raw,axiom,
% 14.82/14.74 ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup__fun__def,axiom,
% 14.82/14.74 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Lattices_Olattice(T_b)
% 14.82/14.74 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_bot__fun__def,axiom,
% 14.82/14.74 ! [V_x_2,T_c,T_b] :
% 14.82/14.74 ( class_Orderings_Obot(T_b)
% 14.82/14.74 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_bot__empty__eq2,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_bot__empty__eq,axiom,
% 14.82/14.74 ! [V_x_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__nat__setsum,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.74 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_card__eq__setsum,axiom,
% 14.82/14.74 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__nat__setprod,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.82/14.74 & class_Rings_Osemiring__1(T_b) )
% 14.82/14.74 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 14.82/14.74 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__delta_H,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__delta,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__delta_H,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__delta,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_vimage__const,axiom,
% 14.82/14.74 ! [T_c,V_A_2,V_ca_2,T_b] :
% 14.82/14.74 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.82/14.74 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.82/14.74 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__constant,axiom,
% 14.82/14.74 ! [V_A_2,V_y_2,T_c,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_power__number__of__even,axiom,
% 14.82/14.74 ! [V_w_2,V_z_2,T_b] :
% 14.82/14.74 ( class_Int_Onumber__ring(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fold__image__distrib,axiom,
% 14.82/14.74 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__constant,axiom,
% 14.82/14.74 ! [V_y_2,V_A_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_zpower__number__of__even,axiom,
% 14.82/14.74 ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_pred__subset__eq2,axiom,
% 14.82/14.74 ! [V_S_2,V_R_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_falseE,axiom,
% 14.82/14.74 ! [V_Q_2,V_ca_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Powp__Pow__eq,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__restrict__set,axiom,
% 14.82/14.74 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_power__number__of__even__number__of,axiom,
% 14.82/14.74 ! [V_w_2,V_v_2,T_b] :
% 14.82/14.74 ( class_Int_Onumber__ring(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_card_Oeq__fold__g,axiom,
% 14.82/14.74 ! [V_A_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_card__def,axiom,
% 14.82/14.74 ! [V_A_2,T_b] :
% 14.82/14.74 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fun__left__comm__idem__remove,axiom,
% 14.82/14.74 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_vimage__if,axiom,
% 14.82/14.74 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 14.82/14.74 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 14.82/14.74 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 14.82/14.74 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 14.82/14.74 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 14.82/14.74 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_diff__nat__eq__if,axiom,
% 14.82/14.74 ! [V_z_2,V_z_H_2] :
% 14.82/14.74 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_LoopF,axiom,
% 14.82/14.74 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_minus__fold__remove,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_eq__number__of__Suc,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2] :
% 14.82/14.74 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Suc__eq__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_n_2] :
% 14.82/14.74 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__number__of__Bit1,axiom,
% 14.82/14.74 ! [V_w_2] :
% 14.82/14.74 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__Suc__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_n_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__number__of__Suc,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_le__number__of__Suc,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_le__Suc__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_n_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_power__number__of__odd,axiom,
% 14.82/14.74 ! [V_z_2,V_w_2,T_b] :
% 14.82/14.74 ( class_Int_Onumber__ring(T_b)
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setprod__gen__delta,axiom,
% 14.82/14.74 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_zpower__number__of__odd,axiom,
% 14.82/14.74 ! [V_z_2,V_w_2] :
% 14.82/14.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__number__of__Suc,axiom,
% 14.82/14.74 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__Suc__number__of,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_power__number__of__odd__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_w_2,T_b] :
% 14.82/14.74 ( class_Int_Onumber__ring(T_b)
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 14.82/14.74 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_diff__nat__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_v_H_2] :
% 14.82/14.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Nitpick_Oone__frac__def,axiom,
% 14.82/14.74 ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 14.82/14.74 ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Image__singleton__iff,axiom,
% 14.82/14.74 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_norm__frac_Osimps,axiom,
% 14.82/14.74 ! [V_a_2,V_b_2] :
% 14.82/14.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 14.82/14.74 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup2CI,axiom,
% 14.82/14.74 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 14.82/14.74 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup2E,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 14.82/14.74 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf2I,axiom,
% 14.82/14.74 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf2E,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 14.82/14.74 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 14.82/14.74 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_bot2E,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup2I2,axiom,
% 14.82/14.74 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup2I1,axiom,
% 14.82/14.74 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf2D1,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_inf2D2,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Image__empty,axiom,
% 14.82/14.74 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Image__Un,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Image__Int__subset,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Image__mono,axiom,
% 14.82/14.74 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Un__Image,axiom,
% 14.82/14.74 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_in__inv__image,axiom,
% 14.82/14.74 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Image__iff,axiom,
% 14.82/14.74 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 14.82/14.74 <=> ? [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_rev__ImageI,axiom,
% 14.82/14.74 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_norm__frac_Opsimps,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 14.82/14.74 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 14.82/14.74 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__int__num,axiom,
% 14.82/14.74 ! [V_k_2,T_b] :
% 14.82/14.74 ( class_Rings_Oring__1(T_b)
% 14.82/14.74 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 14.82/14.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__extp__max__ext__eq,axiom,
% 14.82/14.74 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 14.82/14.74 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__case__add__eq__if,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__weak__cong,axiom,
% 14.82/14.74 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 14.82/14.74 ( V_p_2 = V_q_2
% 14.82/14.74 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_prod_Osimps_I2_J,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__conv,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__twice,axiom,
% 14.82/14.74 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__eta,axiom,
% 14.82/14.74 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fst__def,axiom,
% 14.82/14.74 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_snd__def,axiom,
% 14.82/14.74 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__case__0,axiom,
% 14.82/14.74 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__case__Suc,axiom,
% 14.82/14.74 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_prod__case__beta,axiom,
% 14.82/14.74 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__comp__eq,axiom,
% 14.82/14.74 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__beta,axiom,
% 14.82/14.74 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_split__def,axiom,
% 14.82/14.74 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 14.82/14.74 ! [V_n_2,V_m_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 14.82/14.74 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_diff__Suc,axiom,
% 14.82/14.74 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__Suc1,axiom,
% 14.82/14.74 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__Suc2,axiom,
% 14.82/14.74 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__rel__def,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mlex__prod__def,axiom,
% 14.82/14.74 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__case__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_adjust__def,axiom,
% 14.82/14.74 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Nitpick_OFrac__def,axiom,
% 14.82/14.74 c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__pdivmod,axiom,
% 14.82/14.74 ! [V_l_2,V_k_2] :
% 14.82/14.74 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 14.82/14.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 14.82/14.74 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__int__code,axiom,
% 14.82/14.74 ! [V_l_2,V_k_2] :
% 14.82/14.74 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 14.82/14.74 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) )
% 14.82/14.74 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 14.82/14.74 => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__int,axiom,
% 14.82/14.74 ! [V_j_2,V_i_2,T_b] :
% 14.82/14.74 ( class_Rings_Oring__1(T_b)
% 14.82/14.74 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mem__splitI,axiom,
% 14.82/14.74 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_prod__caseI,axiom,
% 14.82/14.74 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_splitI,axiom,
% 14.82/14.74 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_splitD_H,axiom,
% 14.82/14.74 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_ca_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_splitD,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_apsnd__conv,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_fst__apsnd,axiom,
% 14.82/14.74 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_snd__apsnd,axiom,
% 14.82/14.74 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_apsnd__eq__conv,axiom,
% 14.82/14.74 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 14.82/14.74 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
% 14.82/14.74 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_negateSnd__def,axiom,
% 14.82/14.74 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_rp__inv__image__def,axiom,
% 14.82/14.74 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_divmod__nat__if,axiom,
% 14.82/14.74 ! [V_m_2,V_n_2] :
% 14.82/14.74 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 14.82/14.74 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
% 14.82/14.74 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 14.82/14.74 => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_minus,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Zero__int__def,axiom,
% 14.82/14.74 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_int__def,axiom,
% 14.82/14.74 ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_add,axiom,
% 14.82/14.74 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less,axiom,
% 14.82/14.74 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_le,axiom,
% 14.82/14.74 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mult,axiom,
% 14.82/14.74 ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_One__int__def,axiom,
% 14.82/14.74 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__rec__add__eq__if,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 14.82/14.74 ! [V_n_2,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.74 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__rec__number__of,axiom,
% 14.82/14.74 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_dual__max,axiom,
% 14.82/14.74 ! [T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__rec__0,axiom,
% 14.82/14.74 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__rec__Suc,axiom,
% 14.82/14.74 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 14.82/14.74 ! [V_i_2,V_inc_2,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.74 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 14.82/14.74 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 14.82/14.74 ( class_Rings_Osemiring__1(T_b)
% 14.82/14.74 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 14.82/14.74 ! [V_f_2,V_A_2,T_b] :
% 14.82/14.74 ( ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.74 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_irrefl__def,axiom,
% 14.82/14.74 ! [V_r_2,T_b] :
% 14.82/14.74 ( c_Relation_Oirrefl(T_b,V_r_2)
% 14.82/14.74 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 14.82/14.74 ! [V_f_2,V_A_2,T_b] :
% 14.82/14.74 ( ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.74 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_norm__frac_Opinduct,axiom,
% 14.82/14.74 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 14.82/14.74 => ( ! [B_a,B_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 14.82/14.74 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Nitpick_Ofrac__def,axiom,
% 14.82/14.74 ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_eq__Abs__Integ,axiom,
% 14.82/14.74 ! [V_z_2] :
% 14.82/14.74 ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_arith__series__int,axiom,
% 14.82/14.74 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Field__insert,axiom,
% 14.82/14.74 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_finite__lessThan,axiom,
% 14.82/14.74 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_lessThan__0,axiom,
% 14.82/14.74 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_lessThan__eq__iff,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 14.82/14.74 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_card__lessThan,axiom,
% 14.82/14.74 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ).
% 14.82/14.74
% 14.82/14.74 fof(fact_lessThan__Suc,axiom,
% 14.82/14.74 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_lessThan__iff,axiom,
% 14.82/14.74 ! [V_k_2,V_i_2,T_b] :
% 14.82/14.74 ( class_Orderings_Oord(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_lessThan__subset__iff,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__lessThan__Suc,axiom,
% 14.82/14.74 ! [V_n_2,V_f_2,T_b] :
% 14.82/14.74 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_lessThan__strict__subset__iff,axiom,
% 14.82/14.74 ! [V_n_2,V_m_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_single__Diff__lessThan,axiom,
% 14.82/14.74 ! [V_k_2,T_b] :
% 14.82/14.74 ( class_Orderings_Oorder(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_finite__nat__set__iff__bounded,axiom,
% 14.82/14.74 ! [V_N_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 14.82/14.74 <=> ? [B_m] :
% 14.82/14.74 ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Field__empty,axiom,
% 14.82/14.74 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_mono__Field,axiom,
% 14.82/14.74 ! [V_s_2,V_r_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 14.82/14.74 ! [V_N_2] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 14.82/14.74 <=> ? [B_m] :
% 14.82/14.74 ! [B_x] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Field__Un,axiom,
% 14.82/14.74 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_finite__Field,axiom,
% 14.82/14.74 ! [V_r_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 14.82/14.74 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_arith__series__general,axiom,
% 14.82/14.74 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 14.82/14.74 ( class_Rings_Ocomm__semiring__1(T_b)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_arith__series__nat,axiom,
% 14.82/14.74 ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OatMost__iff,axiom,
% 14.82/14.74 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OatLeast__iff,axiom,
% 14.82/14.74 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OlessThan__iff,axiom,
% 14.82/14.74 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OgreaterThan__iff,axiom,
% 14.82/14.74 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 14.82/14.74 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_infinite__UNIV__nat,axiom,
% 14.82/14.74 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 14.82/14.74 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 14.82/14.74 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 14.82/14.74 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 14.82/14.74 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__nonneg__0,axiom,
% 14.82/14.74 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Oordered__ab__group__add(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 14.82/14.74 => ( ! [B_i] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 14.82/14.74 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 14.82/14.74 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_setsum__nonneg__leq__bound,axiom,
% 14.82/14.74 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 14.82/14.74 ( class_Groups_Oordered__ab__group__add(T_c)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 14.82/14.74 => ( ! [B_i] :
% 14.82/14.74 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 14.82/14.74 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__number__of__Suc,axiom,
% 14.82/14.74 ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__Suc__number__of,axiom,
% 14.82/14.74 ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_le__max__iff__disj,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ole__supE,axiom,
% 14.82/14.74 ! [V_x,V_b,V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
% 14.82/14.74 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 14.82/14.74 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__mono,axiom,
% 14.82/14.74 ! [V_d,V_b,V_c,V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__least,axiom,
% 14.82/14.74 ! [V_z,V_x,V_y,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ole__supI,axiom,
% 14.82/14.74 ! [V_b,V_x,V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__absorb1,axiom,
% 14.82/14.74 ! [V_x,V_y,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__absorb2,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ole__supI2,axiom,
% 14.82/14.74 ! [V_a,V_b,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ole__supI1,axiom,
% 14.82/14.74 ! [V_b,V_a,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ole__sup__iff,axiom,
% 14.82/14.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ole__iff__sup,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 14.82/14.74 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_le__maxI2,axiom,
% 14.82/14.74 ! [V_x,V_y,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_le__maxI1,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 14.82/14.74 ! [T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__add__distrib__left,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Oless__supI1,axiom,
% 14.82/14.74 ! [V_b,V_a,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Oless__supI2,axiom,
% 14.82/14.74 ! [V_a,V_b,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_less__max__iff__disj,axiom,
% 14.82/14.74 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 14.82/14.74 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__less__iff__conj,axiom,
% 14.82/14.74 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 14.82/14.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 14.82/14.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__diff__distrib__left,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Groups_Oordered__ab__group__add(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup_Oidem,axiom,
% 14.82/14.74 ! [V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup_Ocommute,axiom,
% 14.82/14.74 ! [V_b,V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__commute,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 14.82/14.74 ! [V_b,V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__left__idem,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 14.82/14.74 ! [V_c,V_a,V_b,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__left__commute,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup_Oassoc,axiom,
% 14.82/14.74 ! [V_c,V_b,V_a,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__assoc,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Oidem,axiom,
% 14.82/14.74 ! [V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 14.82/14.74 ! [V_x,V_z,V_y,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 14.82/14.74 ! [V_x,V_z,V_y,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__inf__absorb,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__Suc__Suc,axiom,
% 14.82/14.74 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__0L,axiom,
% 14.82/14.74 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__0R,axiom,
% 14.82/14.74 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup__nat__def,axiom,
% 14.82/14.74 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sup__max,axiom,
% 14.82/14.74 ! [T_b] :
% 14.82/14.74 ( ( class_Lattices_Osemilattice__sup(T_b)
% 14.82/14.74 & class_Orderings_Olinorder(T_b) )
% 14.82/14.74 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__number__of,axiom,
% 14.82/14.74 ! [V_v,V_u,T_b] :
% 14.82/14.74 ( ( class_Int_Onumber(T_b)
% 14.82/14.74 & class_Orderings_Oord(T_b) )
% 14.82/14.74 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) )
% 14.82/14.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Odistrib__sup__le,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Odistrib__inf__le,axiom,
% 14.82/14.74 ! [V_z,V_y,V_x,T_a] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_a)
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_minus__max__eq__min,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Groups_Olinordered__ab__group__add(T_a)
% 14.82/14.74 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_minus__min__eq__max,axiom,
% 14.82/14.74 ! [V_y,V_x,T_a] :
% 14.82/14.74 ( class_Groups_Olinordered__ab__group__add(T_a)
% 14.82/14.74 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_nat__minus__add__max,axiom,
% 14.82/14.74 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__Suc1,axiom,
% 14.82/14.74 ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__Suc2,axiom,
% 14.82/14.74 ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_max__ord__max,axiom,
% 14.82/14.74 ! [T_b] :
% 14.82/14.74 ( class_Orderings_Oord(T_b)
% 14.82/14.74 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Ofold__sup__insert,axiom,
% 14.82/14.74 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_dual__min,axiom,
% 14.82/14.74 ! [T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 14.82/14.74 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 14.82/14.74 ! [V_a_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Oremove,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 14.82/14.74 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OInf__le__Sup,axiom,
% 14.82/14.74 ! [V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 14.82/14.74 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_sum__diff__distrib,axiom,
% 14.82/14.74 ! [V_n_2,V_Pa_2,V_Q_2] :
% 14.82/14.74 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_Pa_2,B_x)))
% 14.82/14.74 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Osingleton,axiom,
% 14.82/14.74 ! [V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max__ge,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 14.82/14.74 ! [V_x_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max__in,axiom,
% 14.82/14.74 ! [V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Oin__idem,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 14.82/14.74 ! [V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_OF__eq,axiom,
% 14.82/14.74 ! [V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 14.82/14.74 ! [V_a_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.74 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max__mono,axiom,
% 14.82/14.74 ! [V_N_2,V_M_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 14.82/14.74 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 14.82/14.74 ! [V_a_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max__insert,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Osubset__idem,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max__Un,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.74 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 14.82/14.74 ! [V_a_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.82/14.74 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.74 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 14.82/14.74 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.74 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.74 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.74 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.74 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.74 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 14.82/14.74
% 14.82/14.74 fof(fact_Max_Oinsert,axiom,
% 14.82/14.74 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.74 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Max_Oinsert__remove,axiom,
% 14.82/14.75 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 14.82/14.75 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Max_Ounion__disjoint,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.75 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Max_Ounion__inter,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.75 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Max_Oeq__fold_H,axiom,
% 14.82/14.75 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 14.82/14.75 ! [V_A_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Max_Oclosed,axiom,
% 14.82/14.75 ! [V_A_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_apfst__apsnd,axiom,
% 14.82/14.75 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_apsnd__apfst,axiom,
% 14.82/14.75 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_apfst__conv,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_apfst__eq__conv,axiom,
% 14.82/14.75 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 14.82/14.75 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
% 14.82/14.75 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fst__apfst,axiom,
% 14.82/14.75 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_snd__apfst,axiom,
% 14.82/14.75 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_apsnd__apfst__commute,axiom,
% 14.82/14.75 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__natinterval__difff,axiom,
% 14.82/14.75 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Oab__group__add(T_b)
% 14.82/14.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_gauss__sum,axiom,
% 14.82/14.75 ! [V_n_2,T_b] :
% 14.82/14.75 ( class_Rings_Ocomm__semiring__1(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INFI__fold__inf,axiom,
% 14.82/14.75 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUPR__fold__sup,axiom,
% 14.82/14.75 ! [V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP1__I,axiom,
% 14.82/14.75 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__I,axiom,
% 14.82/14.75 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF1__E,axiom,
% 14.82/14.75 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 14.82/14.75 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 14.82/14.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF1__D,axiom,
% 14.82/14.75 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__D,axiom,
% 14.82/14.75 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__E,axiom,
% 14.82/14.75 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 14.82/14.75 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP2__I,axiom,
% 14.82/14.75 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF2__D,axiom,
% 14.82/14.75 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF2__E,axiom,
% 14.82/14.75 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 14.82/14.75 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 14.82/14.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__INT,axiom,
% 14.82/14.75 ! [V_A_2,T_c,V_I_2,T_b] :
% 14.82/14.75 ( ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 14.82/14.75 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I5_J,axiom,
% 14.82/14.75 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I5_J,axiom,
% 14.82/14.75 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__UN,axiom,
% 14.82/14.75 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UNION__empty__conv_I2_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__constant,axiom,
% 14.82/14.75 ! [V_ca_2,T_c,T_b,V_A_2] :
% 14.82/14.75 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__empty2,axiom,
% 14.82/14.75 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UNION__empty__conv_I1_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I4_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Union__def,axiom,
% 14.82/14.75 ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Pow__INT__eq,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Compl__INT,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Compl__UN,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUPR__apply,axiom,
% 14.82/14.75 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INFI__apply,axiom,
% 14.82/14.75 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP__commute,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__commute,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I8_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I8_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I8_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I8_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I7_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I6_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I7_J,axiom,
% 14.82/14.75 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I6_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__iff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__iff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__subset__iff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__subset__iff,axiom,
% 14.82/14.75 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__Pow__subset,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__UN,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__INT,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Image__UN,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I5_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I4_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__Int__distrib,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I5_J,axiom,
% 14.82/14.75 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__UN__distrib,axiom,
% 14.82/14.75 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I4_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__UN__distrib2,axiom,
% 14.82/14.75 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Inter__def,axiom,
% 14.82/14.75 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I4_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Un__INT__distrib2,axiom,
% 14.82/14.75 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I6_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__Un,axiom,
% 14.82/14.75 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Un__INT__distrib,axiom,
% 14.82/14.75 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I7_J,axiom,
% 14.82/14.75 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__Un__distrib,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I6_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I7_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__INT__eq2,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP__UN__eq2,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP__le__iff,axiom,
% 14.82/14.75 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_le__INF__iff,axiom,
% 14.82/14.75 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_less__SUP__iff,axiom,
% 14.82/14.75 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 14.82/14.75 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 & class_Orderings_Olinorder(T_b) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__less__iff,axiom,
% 14.82/14.75 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.75 & class_Orderings_Olinorder(T_b) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__insert__distrib,axiom,
% 14.82/14.75 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__lower,axiom,
% 14.82/14.75 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__INT__eq,axiom,
% 14.82/14.75 ! [V_x_2,V_r_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__absorb,axiom,
% 14.82/14.75 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP__const,axiom,
% 14.82/14.75 ! [V_M_2,T_b,V_A_2,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__const,axiom,
% 14.82/14.75 ! [V_M_2,T_b,V_A_2,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__insert__distrib,axiom,
% 14.82/14.75 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__constant,axiom,
% 14.82/14.75 ! [V_ca_2,T_c,T_b,V_A_2] :
% 14.82/14.75 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__empty,axiom,
% 14.82/14.75 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I2_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I1_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__upper,axiom,
% 14.82/14.75 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP__UN__eq,axiom,
% 14.82/14.75 ! [V_x_2,V_r_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__absorb,axiom,
% 14.82/14.75 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__insert,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I1_J,axiom,
% 14.82/14.75 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__singleton,axiom,
% 14.82/14.75 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I1_J,axiom,
% 14.82/14.75 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__Un,axiom,
% 14.82/14.75 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I2_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I3_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I2_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I3_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__insert,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Image__INT__subset,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__Union,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__Union2,axiom,
% 14.82/14.75 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Un__Inter,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastatMost__empty__iff2,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
% 14.82/14.75 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastatMost__empty__iff,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastatMost__empty,axiom,
% 14.82/14.75 ! [V_a_2,V_b_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastatMost__subset__iff,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 14.82/14.75 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 14.82/14.75 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastAtMost__singleton,axiom,
% 14.82/14.75 ! [V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 14.82/14.75 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 <=> ( V_a_2 = V_b_2
% 14.82/14.75 & V_b_2 = V_ca_2 ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastAtMost__singleton_H,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( V_a_2 = V_b_2
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__Union,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 14.82/14.75 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 14.82/14.75 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,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))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__lessThan__UNIV,axiom,
% 14.82/14.75 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__subset,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP__subset,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I2_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I1_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I3_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I3_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 14.82/14.75 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) )
% 14.82/14.75 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Image__eq__UN,axiom,
% 14.82/14.75 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__eq__UN,axiom,
% 14.82/14.75 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastAtMostSuc__conv,axiom,
% 14.82/14.75 ! [V_n_2,V_m_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF__leI,axiom,
% 14.82/14.75 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_le__SUPI,axiom,
% 14.82/14.75 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 14.82/14.75 ! [V_k_2,V_f_2] :
% 14.82/14.75 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastatMost__psubset__iff,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 14.82/14.75 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 14.82/14.75 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 14.82/14.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 14.82/14.75 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I4_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__head__Suc,axiom,
% 14.82/14.75 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__cl__ivl__Suc,axiom,
% 14.82/14.75 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_sup__SUPR__fold__sup,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inf__INFI__fold__inf,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 14.82/14.75 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__ub__add__nat,axiom,
% 14.82/14.75 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_minus__int__def,axiom,
% 14.82/14.75 ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ex__nat__less,axiom,
% 14.82/14.75 ! [V_Pa_2,V_n_2] :
% 14.82/14.75 ( ? [B_m] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 14.82/14.75 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
% 14.82/14.75 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_all__nat__less,axiom,
% 14.82/14.75 ! [V_Pa_2,V_n_2] :
% 14.82/14.75 ( ! [B_m] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 14.82/14.75 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
% 14.82/14.75 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_nat__def,axiom,
% 14.82/14.75 ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP2__iff,axiom,
% 14.82/14.75 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF2__iff,axiom,
% 14.82/14.75 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SUP1__iff,axiom,
% 14.82/14.75 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INF1__iff,axiom,
% 14.82/14.75 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__UN__flatten,axiom,
% 14.82/14.75 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I9_J,axiom,
% 14.82/14.75 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I9_J,axiom,
% 14.82/14.75 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I9_J,axiom,
% 14.82/14.75 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I9_J,axiom,
% 14.82/14.75 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ball__UN,axiom,
% 14.82/14.75 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.75 ( ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 14.82/14.75 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 => ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 14.82/14.75 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Rep__Integ__inject,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2] :
% 14.82/14.75 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Rep__Integ__inverse,axiom,
% 14.82/14.75 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 14.82/14.75
% 14.82/14.75 fof(fact_simp__from__to,axiom,
% 14.82/14.75 ! [V_i_2,V_j_2] :
% 14.82/14.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__atLeastAtMost__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_aset_I6_J,axiom,
% 14.82/14.75 ! [V_A_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_bset_I8_J,axiom,
% 14.82/14.75 ! [V_B_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_aset_I8_J,axiom,
% 14.82/14.75 ! [V_t_2,V_A_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__atLeastAtMost__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_aset_I4_J,axiom,
% 14.82/14.75 ! [V_A_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( B_x != V_t_2
% 14.82/14.75 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_bset_I4_J,axiom,
% 14.82/14.75 ! [V_B_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( B_x != V_t_2
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_bset_I7_J,axiom,
% 14.82/14.75 ! [V_B_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_infinite__UNIV__int,axiom,
% 14.82/14.75 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_bset_I3_J,axiom,
% 14.82/14.75 ! [V_B_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 14.82/14.75 => ( ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 14.82/14.75 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_aset_I3_J,axiom,
% 14.82/14.75 ! [V_A_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 14.82/14.75 => ( ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 14.82/14.75 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 14.82/14.75 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_aset_I5_J,axiom,
% 14.82/14.75 ! [V_A_2,V_t_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_bset_I6_J,axiom,
% 14.82/14.75 ! [V_t_2,V_B_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_periodic__finite__ex,axiom,
% 14.82/14.75 ! [V_Pa_2,V_d_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 14.82/14.75 => ( ! [B_x,B_k] :
% 14.82/14.75 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.75 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 14.82/14.75 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2)))
% 14.82/14.75 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_aset_I7_J,axiom,
% 14.82/14.75 ! [V_t_2,V_A_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_bset_I5_J,axiom,
% 14.82/14.75 ! [V_t_2,V_B_2,V_D_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 14.82/14.75 => ! [B_x] :
% 14.82/14.75 ( ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 14.82/14.75 => ! [B_xb] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 14.82/14.75 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__greaterThanLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Id__on__def,axiom,
% 14.82/14.75 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__greaterThanLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Id__on__def_H,axiom,
% 14.82/14.75 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_greaterThanLessThan__empty,axiom,
% 14.82/14.75 ! [V_k_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 14.82/14.75 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Id__on__empty,axiom,
% 14.82/14.75 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Image__Id__on,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I13_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I12_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__greaterThanLessThan,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Id__on__iff,axiom,
% 14.82/14.75 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
% 14.82/14.75 <=> ( V_x_2 = V_y_2
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Id__on__eqI,axiom,
% 14.82/14.75 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 14.82/14.75 ( V_a_2 = V_b_2
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__le__eq__Un0,axiom,
% 14.82/14.75 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I19_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I4_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__greaterThanAtMost,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__greaterThanLessThan,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__greaterThanAtMost__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__atMost,axiom,
% 14.82/14.75 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I3_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I9_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atMost__eq__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_greaterThanAtMost__empty,axiom,
% 14.82/14.75 ! [V_k_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 14.82/14.75 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 14.82/14.75 ! [V_l_2,V_k_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
% 14.82/14.75 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 14.82/14.75 ! [V_l_2,V_k_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast0AtMost,axiom,
% 14.82/14.75 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I20_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I14_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_lessThan__Suc__atMost,axiom,
% 14.82/14.75 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__atMost,axiom,
% 14.82/14.75 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atMost__Suc,axiom,
% 14.82/14.75 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atMost__iff,axiom,
% 14.82/14.75 ! [V_k_2,V_i_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oord(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atMost__subset__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__greaterThanAtMost,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I22_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I16_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__atMost__UNIV,axiom,
% 14.82/14.75 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__greaterThanAtMost,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__atMost__Suc,axiom,
% 14.82/14.75 ! [V_n_2,V_f_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atMost__0,axiom,
% 14.82/14.75 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I10_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__greaterThanLessThan,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__atLeastAtMostR1,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__atLeastAtMostL1,axiom,
% 14.82/14.75 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__greaterThanAtMost__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__le__add__shift,axiom,
% 14.82/14.75 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I1_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I16_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__head,axiom,
% 14.82/14.75 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I2_J,axiom,
% 14.82/14.75 ! [V_u_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I10_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I7_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I5_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__def,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Id__onE,axiom,
% 14.82/14.75 ! [V_A_2,V_ca_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 14.82/14.75 => ~ ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ImageE,axiom,
% 14.82/14.75 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 14.82/14.75 => ~ ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
% 14.82/14.75 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__is__empty,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 14.82/14.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__is__empty2,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
% 14.82/14.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__empty,axiom,
% 14.82/14.75 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotientI,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_singleton__quotient,axiom,
% 14.82/14.75 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equiv__class__nondisjoint,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_subset__equiv__class,axiom,
% 14.82/14.75 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotientE,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ~ ! [B_x] :
% 14.82/14.75 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.75 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equiv__intrel,axiom,
% 14.82/14.75 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Union__quotient,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equiv__class__self,axiom,
% 14.82/14.75 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__disj,axiom,
% 14.82/14.75 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( V_X_2 = V_Y_2
% 14.82/14.75 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equiv__class__eq,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 14.82/14.75 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__eq__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 14.82/14.75 => ( V_X_2 = V_Y_2
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__eqI,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 14.82/14.75 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equiv__class__eq__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 14.82/14.75 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_eq__equiv__class__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 14.82/14.75 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_eq__equiv__class,axiom,
% 14.82/14.75 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 14.82/14.75 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.75 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equiv__class__subset,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_eq__equiv__class__iff2,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 14.82/14.75 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__equiv__class2,axiom,
% 14.82/14.75 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 14.82/14.75 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__equiv__class,axiom,
% 14.82/14.75 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equivp__equiv,axiom,
% 14.82/14.75 ! [V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 14.82/14.75 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equivp__transp,axiom,
% 14.82/14.75 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equivp__symp,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equivp__reflp,axiom,
% 14.82/14.75 ! [V_x_2,V_R_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 14.82/14.75 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_equivp__def,axiom,
% 14.82/14.75 ! [V_R_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 14.82/14.75 <=> ! [B_x,B_y] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 14.82/14.75 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_identity__equivp,axiom,
% 14.82/14.75 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_congruent2__implies__congruent,axiom,
% 14.82/14.75 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_congruent2D,axiom,
% 14.82/14.75 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
% 14.82/14.75 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_congruentD,axiom,
% 14.82/14.75 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
% 14.82/14.75 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_congruent2__implies__congruent__UN,axiom,
% 14.82/14.75 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 14.82/14.75 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 14.82/14.75 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__equiv__class__inject,axiom,
% 14.82/14.75 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 14.82/14.75 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => ! [B_y] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 14.82/14.75 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 14.82/14.75 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__equiv__class__type2,axiom,
% 14.82/14.75 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 14.82/14.75 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
% 14.82/14.75 => ( ! [B_x1] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 14.82/14.75 => ! [B_x2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__equiv__class__type,axiom,
% 14.82/14.75 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.75 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.75 => ( ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Integ__def,axiom,
% 14.82/14.75 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__quotient__disjoint,axiom,
% 14.82/14.75 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 14.82/14.75 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_geometric__sum,axiom,
% 14.82/14.75 ! [V_n_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Fields_Ofield(T_b)
% 14.82/14.75 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__atLeastLessThan,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__eq__iff,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 14.82/14.75 <=> ( V_a_2 = V_ca_2
% 14.82/14.75 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 14.82/14.75 => V_a_2 = V_ca_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 14.82/14.75 => V_b_2 = V_d_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ex__nat__less__eq,axiom,
% 14.82/14.75 ! [V_Pa_2,V_n_2] :
% 14.82/14.75 ( ? [B_m] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 14.82/14.75 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 14.82/14.75 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_all__nat__less__eq,axiom,
% 14.82/14.75 ! [V_Pa_2,V_n_2] :
% 14.82/14.75 ( ! [B_m] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 14.82/14.75 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 14.82/14.75 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__add__Un,axiom,
% 14.82/14.75 ! [V_k_2,V_j_2,V_i_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 14.82/14.75 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan0,axiom,
% 14.82/14.75 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast0LessThan,axiom,
% 14.82/14.75 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_subset__card__intvl__is__intvl,axiom,
% 14.82/14.75 ! [V_k_2,V_A_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
% 14.82/14.75 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__atLeastLessThan,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__empty,axiom,
% 14.82/14.75 ! [V_a_2,V_b_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 14.82/14.75 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
% 14.82/14.75 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__empty__iff,axiom,
% 14.82/14.75 ! [V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__subset__iff,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 14.82/14.75 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 14.82/14.75 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I17_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 14.82/14.75 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,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))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__diff,axiom,
% 14.82/14.75 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I11_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__vimageI,axiom,
% 14.82/14.75 ! [V_h_2,T_c,V_F_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__add__nat__ivl,axiom,
% 14.82/14.75 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__diff__nat__ivl,axiom,
% 14.82/14.75 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Oab__group__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 14.82/14.75 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThan__singleton,axiom,
% 14.82/14.75 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Rep__Integ,axiom,
% 14.82/14.75 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__UN__finite__eq,axiom,
% 14.82/14.75 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I21_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I15_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__atLeastLessThan,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I8_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I2_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I9_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 14.82/14.75 ! [V_k_2,V_f_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__head__upt__Suc,axiom,
% 14.82/14.75 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThanSuc,axiom,
% 14.82/14.75 ! [V_n_2,V_m_2] :
% 14.82/14.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 14.82/14.75 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_setsum__op__ivl__Suc,axiom,
% 14.82/14.75 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 14.82/14.75 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I15_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_quotient__diff1,axiom,
% 14.82/14.75 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I6_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I3_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I18_J,axiom,
% 14.82/14.75 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__uminus,axiom,
% 14.82/14.75 ! [V_A_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__empty,axiom,
% 14.82/14.75 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__singleton,axiom,
% 14.82/14.75 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__atLeastLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__add__nat,axiom,
% 14.82/14.75 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__Suc,axiom,
% 14.82/14.75 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__of__nat,axiom,
% 14.82/14.75 ! [T_b] :
% 14.82/14.75 ( class_Nat_Osemiring__char__0(T_b)
% 14.82/14.75 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__int,axiom,
% 14.82/14.75 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_swap__inj__on,axiom,
% 14.82/14.75 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__def,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 <=> ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.75 => ! [B_xa] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 14.82/14.75 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 14.82/14.75 => B_x = B_xa ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__atLeastLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__id2,axiom,
% 14.82/14.75 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__ident,axiom,
% 14.82/14.75 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__onD,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 14.82/14.75 => V_x_2 = V_y_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 14.82/14.75 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__contraD,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => ( V_x_2 != V_y_2
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 14.82/14.75 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_subset__inj__on,axiom,
% 14.82/14.75 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__eq,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_injD,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 14.82/14.75 => V_x_2 = V_y_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__Int,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__diff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__fun,axiom,
% 14.82/14.75 ! [T_d,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__vimage__singleton,axiom,
% 14.82/14.75 ! [V_a_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__finite2__subset,axiom,
% 14.82/14.75 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 14.82/14.75 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__finite2__eq,axiom,
% 14.82/14.75 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 14.82/14.75 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
% 14.82/14.75 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_The__split__eq,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_split__paired__The,axiom,
% 14.82/14.75 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fold__def,axiom,
% 14.82/14.75 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_divmod__nat__def,axiom,
% 14.82/14.75 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fold1__def,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_The__split,axiom,
% 14.82/14.75 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_the__elem__def,axiom,
% 14.82/14.75 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_flat__lub__def,axiom,
% 14.82/14.75 ! [V_b_2,V_A_2,T_b] :
% 14.82/14.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 14.82/14.75 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 14.82/14.75 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__finite__subset,axiom,
% 14.82/14.75 ! [V_C_2,V_A_2,T_b] :
% 14.82/14.75 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition__Integ,axiom,
% 14.82/14.75 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_OAbs__inject,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 14.82/14.75 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_OAbs__inverse,axiom,
% 14.82/14.75 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 14.82/14.75 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_ORep,axiom,
% 14.82/14.75 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_ORep__inverse,axiom,
% 14.82/14.75 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_ORep__inject,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 14.82/14.75 ! [V_x_2,V_y_2,V_ca_2] :
% 14.82/14.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 14.82/14.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 14.82/14.75 ! [V_u_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 14.82/14.75 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atMost__Int__atLeast,axiom,
% 14.82/14.75 ! [V_n_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__eqI,axiom,
% 14.82/14.75 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 14.82/14.75 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__imageI,axiom,
% 14.82/14.75 ! [V_h_2,T_c,V_F_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_range__composition,axiom,
% 14.82/14.75 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__uminus__atLeast,axiom,
% 14.82/14.75 ! [V_x_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__uminus__atMost,axiom,
% 14.82/14.75 ! [V_x_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__insert,axiom,
% 14.82/14.75 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_empty__is__image,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
% 14.82/14.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__empty,axiom,
% 14.82/14.75 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__is__empty,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast__eq__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 14.82/14.75 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2] :
% 14.82/14.75 ( V_A_2 = V_B_2
% 14.82/14.75 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Pow__surj,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 14.82/14.75 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__image,axiom,
% 14.82/14.75 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__extend__simps_I10_J,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_INT__simps_I10_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__simps_I10_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__UN,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__extend__simps_I10_J,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__ident,axiom,
% 14.82/14.75 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__mono,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_subset__image__iff,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 14.82/14.75 <=> ? [B_AA] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 14.82/14.75 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Pow__mono,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Un,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__iff,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 14.82/14.75 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_imageI,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_rev__image__eqI,axiom,
% 14.82/14.75 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_insert__image,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_range__eqI,axiom,
% 14.82/14.75 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 14.82/14.75 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_rangeI,axiom,
% 14.82/14.75 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__surj,axiom,
% 14.82/14.75 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Int__subset,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__imageD,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__diff__subset,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__image__eq__iff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 14.82/14.75 <=> V_A_2 = V_B_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 14.82/14.75 <=> V_A_2 = V_B_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__uminus__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__image,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__vimage__subset,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_surj__image__vimage__eq,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Suc__atLeastLessThan,axiom,
% 14.82/14.75 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_OAbs__image,axiom,
% 14.82/14.75 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_type__definition_ORep__range,axiom,
% 14.82/14.75 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 14.82/14.75 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Suc__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__strict__subset,axiom,
% 14.82/14.75 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__constant__conv,axiom,
% 14.82/14.75 ! [V_ca_2,T_c,T_b,V_A_2] :
% 14.82/14.75 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.75 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__range__imageI,axiom,
% 14.82/14.75 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 14.82/14.75 ! [V_A_2,V_x_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b] :
% 14.82/14.75 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 & class_Groups_Ocomm__monoid__mult(T_b) )
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__add__atLeastLessThan,axiom,
% 14.82/14.75 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__add__atLeastAtMost,axiom,
% 14.82/14.75 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Union,axiom,
% 14.82/14.75 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_range__ex1__eq,axiom,
% 14.82/14.75 ! [V_b_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 14.82/14.75 <=> ? [B_x] :
% 14.82/14.75 ( V_b_2 = hAPP(V_f_2,B_x)
% 14.82/14.75 & ! [B_y] :
% 14.82/14.75 ( V_b_2 = hAPP(V_f_2,B_y)
% 14.82/14.75 => B_y = B_x ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__image__mem__iff,axiom,
% 14.82/14.75 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__iff__surj,axiom,
% 14.82/14.75 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 14.82/14.75 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => ( ? [B_f] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) )
% 14.82/14.75 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__surj__inj,axiom,
% 14.82/14.75 ! [V_f_2,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_endo__inj__surj,axiom,
% 14.82/14.75 ! [V_f_2,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__UNIV__surj__inj,axiom,
% 14.82/14.75 ! [V_f_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.75 => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__UNIV__inj__surj,axiom,
% 14.82/14.75 ! [V_f_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__image__le,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__image__subset__iff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__image__Int,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__Int,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_eq__card__imp__inj__on,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
% 14.82/14.75 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__iff__eq__card,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__image__set__diff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__set__diff,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_pigeonhole,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
% 14.82/14.75 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_finite__vimageD,axiom,
% 14.82/14.75 ! [V_F_2,V_h_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 14.82/14.75 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 14.82/14.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast__iff,axiom,
% 14.82/14.75 ! [V_k_2,V_i_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oord(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_surj__Compl__image__subset,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__subsetD,axiom,
% 14.82/14.75 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 14.82/14.75 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__vimage__eq,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__vimage__image__eq,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast__subset__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast__0,axiom,
% 14.82/14.75 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__uminus__atLeastLessThan,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__constant,axiom,
% 14.82/14.75 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__eq__UN,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_b] :
% 14.82/14.75 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.75 & class_Groups_Ocomm__monoid__mult(T_b) )
% 14.82/14.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Compl__atLeast,axiom,
% 14.82/14.75 ! [V_k_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Compl__lessThan,axiom,
% 14.82/14.75 ! [V_k_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 14.82/14.75 ! [V_A_2] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 14.82/14.75 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 14.82/14.75 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 14.82/14.75 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__bij__eq,axiom,
% 14.82/14.75 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 14.82/14.75 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.82/14.75 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__image__Compl__subset,axiom,
% 14.82/14.75 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_vimage__subsetI,axiom,
% 14.82/14.75 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__eq__fold__image,axiom,
% 14.82/14.75 ! [V_f_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 14.82/14.75 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I14_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I8_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__atLeastAtMostL2,axiom,
% 14.82/14.75 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Int__atLeastAtMostR2,axiom,
% 14.82/14.75 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__insert,axiom,
% 14.82/14.75 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 14.82/14.75 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_UN__atLeast__UNIV,axiom,
% 14.82/14.75 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__Un,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.75 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.75 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__int_I6_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Oorder(T_b)
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_card__inj__on__le,axiom,
% 14.82/14.75 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_inj__on__iff__card__le,axiom,
% 14.82/14.75 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.82/14.75 => ( ? [B_f] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 14.82/14.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) )
% 14.82/14.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast__Suc,axiom,
% 14.82/14.75 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_minus__Min__eq__Max,axiom,
% 14.82/14.75 ! [V_S_2,T_b] :
% 14.82/14.75 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.75 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_minus__Max__eq__Min,axiom,
% 14.82/14.75 ! [V_S_2,T_b] :
% 14.82/14.75 ( class_Groups_Olinordered__ab__group__add(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.75 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.75 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 14.82/14.75 ! [V_n_2,V_m_2] :
% 14.82/14.75 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 14.82/14.75 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 14.82/14.75 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_image__INT,axiom,
% 14.82/14.75 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 14.82/14.75 => ( ! [B_x] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_ivl__disj__un_I12_J,axiom,
% 14.82/14.75 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 14.82/14.75 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__image,axiom,
% 14.82/14.75 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 14.82/14.75 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
% 14.82/14.75 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.75 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__triv,axiom,
% 14.82/14.75 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 14.82/14.75
% 14.82/14.75 fof(fact_pair__imageI,axiom,
% 14.82/14.75 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.75 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 14.82/14.75 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_atLeast__Suc__greaterThan,axiom,
% 14.82/14.75 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_Cantors__paradox,axiom,
% 14.82/14.75 ! [V_A_2,T_b] :
% 14.82/14.75 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__idem,axiom,
% 14.82/14.75 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 14.82/14.75 ( hAPP(V_f_2,V_x_2) = V_y_2
% 14.82/14.75 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__other,axiom,
% 14.82/14.75 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 14.82/14.75 ( V_z_2 != V_x_2
% 14.82/14.75 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__twist,axiom,
% 14.82/14.75 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 14.82/14.75 ( V_a_2 != V_ca_2
% 14.82/14.75 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__apply,axiom,
% 14.82/14.75 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 14.82/14.75 ( ( V_z_2 = V_x_2
% 14.82/14.75 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 14.82/14.75 & ( V_z_2 != V_x_2
% 14.82/14.75 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__same,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__upd,axiom,
% 14.82/14.75 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__idem__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 14.82/14.75 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 14.82/14.75 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_fun__upd__def,axiom,
% 14.82/14.75 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 14.82/14.75 ( ( V_x_2 = V_a_2
% 14.82/14.75 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 14.82/14.75 & ( V_x_2 != V_a_2
% 14.82/14.75 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 14.82/14.75
% 14.82/14.75 fof(fact_greaterThan__eq__iff,axiom,
% 14.82/14.75 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.75 ( class_Orderings_Olinorder(T_b)
% 14.82/14.75 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 14.82/14.76 <=> V_x_2 = V_y_2 ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Field__Union,axiom,
% 14.82/14.76 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_UNION__eq__Union__image,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Union__image__eq,axiom,
% 14.82/14.76 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Inter__image__eq,axiom,
% 14.82/14.76 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_INTER__eq__Inter__image,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 14.82/14.76 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_greaterThan__iff,axiom,
% 14.82/14.76 ! [V_k_2,V_i_2,T_b] :
% 14.82/14.76 ( class_Orderings_Oord(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_greaterThan__subset__iff,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Un__Union__image,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Int__Inter__image,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Pow__insert,axiom,
% 14.82/14.76 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Compl__atMost,axiom,
% 14.82/14.76 ! [V_k_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Compl__greaterThan,axiom,
% 14.82/14.76 ! [V_k_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 14.82/14.76 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_INT__greaterThan__UNIV,axiom,
% 14.82/14.76 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__fun__updI,axiom,
% 14.82/14.76 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.76 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 14.82/14.76 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_image__add__int__atLeastLessThan,axiom,
% 14.82/14.76 ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_ivl__disj__int_I7_J,axiom,
% 14.82/14.76 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.76 ( class_Orderings_Oorder(T_b)
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_ivl__disj__un_I11_J,axiom,
% 14.82/14.76 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_image__uminus__greaterThan,axiom,
% 14.82/14.76 ! [V_x_2,T_b] :
% 14.82/14.76 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.76 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_image__uminus__lessThan,axiom,
% 14.82/14.76 ! [V_x_2,T_b] :
% 14.82/14.76 ( class_Groups_Oordered__ab__group__add(T_b)
% 14.82/14.76 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_ivl__disj__int_I5_J,axiom,
% 14.82/14.76 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.76 ( class_Orderings_Oorder(T_b)
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_greaterThan__Suc,axiom,
% 14.82/14.76 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 14.82/14.76 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_ivl__disj__un_I1_J,axiom,
% 14.82/14.76 ! [V_l_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_greaterThan__0,axiom,
% 14.82/14.76 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_ivl__disj__un_I13_J,axiom,
% 14.82/14.76 ! [V_u_2,V_l_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 14.82/14.76 ! [V_f_2,V_A_2,T_b] :
% 14.82/14.76 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.76 & class_Groups_Ocomm__monoid__mult(T_b) )
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__pointwise,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 14.82/14.76 => ( ! [B_p] :
% 14.82/14.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
% 14.82/14.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
% 14.82/14.76 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2))
% 14.82/14.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_Pa_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__inv__into__into,axiom,
% 14.82/14.76 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => ( V_A_2 = V_B_2
% 14.82/14.76 <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 14.82/14.76 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_nat__set__def,axiom,
% 14.82/14.76 ! [V_S_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_S_2)
% 14.82/14.76 <=> ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 14.82/14.76 ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2] :
% 14.82/14.76 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 14.82/14.76 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 14.82/14.76 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__inv__into__f__eq,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.76 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__inv__into__f__f,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.76 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__the__inv__into,axiom,
% 14.82/14.76 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__inv__into__onto,axiom,
% 14.82/14.76 ! [V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__inv__f__f,axiom,
% 14.82/14.76 ! [V_x_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.76 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 14.82/14.76 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__inv__into__def,axiom,
% 14.82/14.76 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 14.82/14.76 ! [V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 14.82/14.76 ! [V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 14.82/14.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 14.82/14.76 ! [V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_f__the__inv__into__f,axiom,
% 14.82/14.76 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.76 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 14.82/14.76 ! [V_A_2,V_x_2] :
% 14.82/14.76 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 14.82/14.76 ! [V_f_2,V_A_2,T_b] :
% 14.82/14.76 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.76 & class_Groups_Ocomm__monoid__mult(T_b) )
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2] :
% 14.82/14.76 ( c_Nat__Transfer_Onat__set(V_A_2)
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Max_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Min_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Inf__fin_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Lattices_Olattice(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sup__fin_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Lattices_Olattice(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_hom__fold1__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,T_b] :
% 14.82/14.76 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_escape,axiom,
% 14.82/14.76 ! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] :
% 14.82/14.76 ( ! [B_Z,B_s] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 14.82/14.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 14.82/14.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 14.82/14.76 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.76 & class_Groups_Ocomm__monoid__mult(T_b) )
% 14.82/14.76 => ( V_A_2 = V_B_2
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 14.82/14.76 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 14.82/14.76 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.76 & class_Groups_Ocomm__monoid__mult(T_b) )
% 14.82/14.76 => ( V_A_2 = V_B_2
% 14.82/14.76 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 14.82/14.76 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_accp__acc__eq,axiom,
% 14.82/14.76 ! [V_x_2,V_r_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_max__extp_Oequations,axiom,
% 14.82/14.76 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 14.82/14.76 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 14.82/14.76 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 14.82/14.76 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 & ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 14.82/14.76 => ? [B_xa] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 14.82/14.76 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_acc__subset,axiom,
% 14.82/14.76 ! [V_R2_2,V_R1_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_acc__downward,axiom,
% 14.82/14.76 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_acc_Osimps,axiom,
% 14.82/14.76 ! [V_r_2,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 14.82/14.76 <=> ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__Inter,axiom,
% 14.82/14.76 ! [V_f_2,T_c,T_b,V_S_2] :
% 14.82/14.76 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 14.82/14.76 => ( ! [B_A] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 14.82/14.76 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 14.82/14.76 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_image__split__eq__Sigma,axiom,
% 14.82/14.76 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 14.82/14.76 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 14.82/14.76 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 14.82/14.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SigmaI,axiom,
% 14.82/14.76 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Union,axiom,
% 14.82/14.76 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__empty1,axiom,
% 14.82/14.76 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Diff__distrib2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Times__Diff__distrib1,axiom,
% 14.82/14.76 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Diff__distrib1,axiom,
% 14.82/14.76 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Times__eq__cancel2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 14.82/14.76 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
% 14.82/14.76 <=> V_A_2 = V_B_2 ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_card__cartesian__product,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__cartesian__product,axiom,
% 14.82/14.76 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_b)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Times__empty,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.76 ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
% 14.82/14.76 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__empty2,axiom,
% 14.82/14.76 ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Compl__Times__UNIV1,axiom,
% 14.82/14.76 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Compl__Times__UNIV2,axiom,
% 14.82/14.76 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setprod__cartesian__product,axiom,
% 14.82/14.76 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__mult(T_b)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Un__distrib1,axiom,
% 14.82/14.76 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Times__Un__distrib1,axiom,
% 14.82/14.76 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Un__distrib2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_swap__product,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__cartesian__product,axiom,
% 14.82/14.76 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_equiv__type,axiom,
% 14.82/14.76 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Int__distrib2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Times__Int__distrib1,axiom,
% 14.82/14.76 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__Int__distrib1,axiom,
% 14.82/14.76 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Id__on__subset__Times,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_UNIV__Times__UNIV,axiom,
% 14.82/14.76 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SigmaE2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 14.82/14.76 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SigmaD2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SigmaD1,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_mem__Sigma__iff,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 14.82/14.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.76 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_card__cartesian__product__singleton,axiom,
% 14.82/14.76 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Times__subset__cancel2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Image__subset,axiom,
% 14.82/14.76 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__cartesian__productD2,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__cartesian__productD1,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 14.82/14.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fst__image__times,axiom,
% 14.82/14.76 ! [V_A_2,T_c,T_b,V_B_2] :
% 14.82/14.76 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.76 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_snd__image__times,axiom,
% 14.82/14.76 ! [V_B_2,T_c,T_b,V_A_2] :
% 14.82/14.76 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.76 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_insert__times__insert,axiom,
% 14.82/14.76 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__equiv__class,axiom,
% 14.82/14.76 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_UN__Times__distrib,axiom,
% 14.82/14.76 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sigma__def,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__quotient,axiom,
% 14.82/14.76 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 14.82/14.76 ! [V_A_2,V_I_2,T_c,T_b] :
% 14.82/14.76 ? [B_f] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))
% 14.82/14.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fold__image__Sigma,axiom,
% 14.82/14.76 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__mult(T_d)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 14.82/14.76 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__SigmaI,axiom,
% 14.82/14.76 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( ! [B_a] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setprod__Sigma,axiom,
% 14.82/14.76 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__mult(T_d)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__Sigma,axiom,
% 14.82/14.76 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_d)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_card__SigmaI,axiom,
% 14.82/14.76 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 14.82/14.76 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SigmaE,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 14.82/14.76 => ~ ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => ! [B_y] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 14.82/14.76 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__surj,axiom,
% 14.82/14.76 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 14.82/14.76 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__inj__on,axiom,
% 14.82/14.76 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 14.82/14.76 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__imageI,axiom,
% 14.82/14.76 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fst__map__pair,axiom,
% 14.82/14.76 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__simp,axiom,
% 14.82/14.76 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__ident,axiom,
% 14.82/14.76 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_snd__prod__fun,axiom,
% 14.82/14.76 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__def,axiom,
% 14.82/14.76 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__surj__on,axiom,
% 14.82/14.76 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 14.82/14.76 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 14.82/14.76 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 14.82/14.76 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_prod__fun__imageE,axiom,
% 14.82/14.76 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 14.82/14.76 => ~ ! [B_x,B_y] :
% 14.82/14.76 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__on__def,axiom,
% 14.82/14.76 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 14.82/14.76 & ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Rep__Integ__cases,axiom,
% 14.82/14.76 ! [V_y_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 14.82/14.76 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__on__Id__on,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__on__empty,axiom,
% 14.82/14.76 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__on__Un,axiom,
% 14.82/14.76 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 14.82/14.76 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__on__Int,axiom,
% 14.82/14.76 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 14.82/14.76 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__onD,axiom,
% 14.82/14.76 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__onD1,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__onD2,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__onI,axiom,
% 14.82/14.76 ! [V_A_2,V_r_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 14.82/14.76 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Rep__Integ__induct,axiom,
% 14.82/14.76 ! [V_Pa_2,V_y_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 14.82/14.76 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 14.82/14.76 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__INTER,axiom,
% 14.82/14.76 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 14.82/14.76 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( ! [B_i] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 14.82/14.76 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 14.82/14.76 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_card__less__Suc,axiom,
% 14.82/14.76 ! [V_i_2,V_M_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 14.82/14.76 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_card__less,axiom,
% 14.82/14.76 ! [V_i_2,V_M_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 14.82/14.76 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_card__less__Suc2,axiom,
% 14.82/14.76 ! [V_i_2,V_M_2] :
% 14.82/14.76 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 14.82/14.76 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_CollectI,axiom,
% 14.82/14.76 ! [T_b,V_a_2,V_Pa_2] :
% 14.82/14.76 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__conjI,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_b] :
% 14.82/14.76 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__less__nat,axiom,
% 14.82/14.76 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__le__nat,axiom,
% 14.82/14.76 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__split,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_SetCompr__Sigma__eq,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__neg__eq,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__conj__eq,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__disj__eq,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__disjI,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2))))
% 14.82/14.76 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_vimage__Collect__eq,axiom,
% 14.82/14.76 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__def,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_empty__def,axiom,
% 14.82/14.76 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__empty__eq,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b] :
% 14.82/14.76 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_empty__Collect__eq,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b] :
% 14.82/14.76 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 14.82/14.76 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_insert__Collect,axiom,
% 14.82/14.76 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_UNIV__def,axiom,
% 14.82/14.76 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_CollectE,axiom,
% 14.82/14.76 ! [V_Pa_2,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_CollectD,axiom,
% 14.82/14.76 ! [V_Pa_2,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_mem__Collect__eq,axiom,
% 14.82/14.76 ! [V_Pa_2,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__mem__eq,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_insert__compr,axiom,
% 14.82/14.76 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_insert__compr__raw,axiom,
% 14.82/14.76 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Un__def,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Int__Collect,axiom,
% 14.82/14.76 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 14.82/14.76 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 14.82/14.76 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Int__def,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__conv__if,axiom,
% 14.82/14.76 ! [T_b,V_a_2,V_Pa_2] :
% 14.82/14.76 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 14.82/14.76 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 14.82/14.76 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 14.82/14.76 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__conv__if2,axiom,
% 14.82/14.76 ! [T_b,V_a_2,V_Pa_2] :
% 14.82/14.76 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 14.82/14.76 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 14.82/14.76 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 14.82/14.76 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_singleton__conv,axiom,
% 14.82/14.76 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_singleton__conv2,axiom,
% 14.82/14.76 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_set__diff__eq,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__not,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 14.82/14.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_insert__def,axiom,
% 14.82/14.76 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Compl__eq,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_vimage__def,axiom,
% 14.82/14.76 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__imp__eq,axiom,
% 14.82/14.76 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__M__bounded__by__nat,axiom,
% 14.82/14.76 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__setsum__restrict,axiom,
% 14.82/14.76 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_d)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_if__image__distrib,axiom,
% 14.82/14.76 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_nat__seg__image__imp__finite,axiom,
% 14.82/14.76 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 14.82/14.76 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__restrict__set_H,axiom,
% 14.82/14.76 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__image__gen,axiom,
% 14.82/14.76 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Image__singleton,axiom,
% 14.82/14.76 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__cases,axiom,
% 14.82/14.76 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__multicount,axiom,
% 14.82/14.76 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 14.82/14.76 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__subsets,axiom,
% 14.82/14.76 ! [V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Pow__Compl,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Pow__def,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Collect__bounded__ex,axiom,
% 14.82/14.76 ! [V_Q_2,T_c,V_Pa_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2)))))
% 14.82/14.76 <=> ! [B_y] :
% 14.82/14.76 ( hBOOL(hAPP(V_Pa_2,B_y))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__image__set,axiom,
% 14.82/14.76 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__graph,axiom,
% 14.82/14.76 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 14.82/14.76 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__psubset__def,axiom,
% 14.82/14.76 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inv__image__def,axiom,
% 14.82/14.76 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 14.82/14.76 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 14.82/14.76 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_add__Min__commute,axiom,
% 14.82/14.76 ! [V_k_2,V_N_2,T_b] :
% 14.82/14.76 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_add__Max__commute,axiom,
% 14.82/14.76 ! [V_k_2,V_N_2,T_b] :
% 14.82/14.76 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 14.82/14.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_sup__Inf2__distrib,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Lattices_Odistrib__lattice(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_sup__Inf1__distrib,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Lattices_Odistrib__lattice(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inf__Sup2__distrib,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Lattices_Odistrib__lattice(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inf__Sup1__distrib,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Lattices_Odistrib__lattice(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 14.82/14.76 ! [V_x_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( class_Orderings_Olinorder(T_b)
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 14.82/14.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nitpick_Oprod__def,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_int__ge__less__than__def,axiom,
% 14.82/14.76 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_int__ge__less__than2__def,axiom,
% 14.82/14.76 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_reflp__def,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Predicate_Oreflp(T_b,V_r_2)
% 14.82/14.76 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 14.82/14.76 ( class_Rings_Osemiring__0(T_d)
% 14.82/14.76 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
% 14.82/14.76 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__multicount__gen,axiom,
% 14.82/14.76 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 14.82/14.76 => ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 14.82/14.76 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__id,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_apsnd__id,axiom,
% 14.82/14.76 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_reflpE,axiom,
% 14.82/14.76 ! [V_x_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Predicate_Oreflp(T_b,V_r_2)
% 14.82/14.76 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_apfst__id,axiom,
% 14.82/14.76 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_id__def,axiom,
% 14.82/14.76 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_id__apply,axiom,
% 14.82/14.76 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 14.82/14.76
% 14.82/14.76 fof(fact_vimage__id,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair_Oidentity,axiom,
% 14.82/14.76 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair_Oid,axiom,
% 14.82/14.76 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_image__id,axiom,
% 14.82/14.76 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_of__int__eq__id,axiom,
% 14.82/14.76 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_surj__id,axiom,
% 14.82/14.76 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_apsnd__def,axiom,
% 14.82/14.76 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_apfst__def,axiom,
% 14.82/14.76 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_split__Pair,axiom,
% 14.82/14.76 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__reindex__id,axiom,
% 14.82/14.76 ! [V_B_2,V_f_2,T_b,T_c] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_c)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setprod__reindex__id,axiom,
% 14.82/14.76 ! [V_B_2,V_f_2,T_b,T_c] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__conv__nat__seg__image,axiom,
% 14.82/14.76 ! [V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__def,axiom,
% 14.82/14.76 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__Collect__split,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__compI,axiom,
% 14.82/14.76 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_ca_2)),V_s_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_RangeI,axiom,
% 14.82/14.76 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__UNION__distrib,axiom,
% 14.82/14.76 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__UNION__distrib2,axiom,
% 14.82/14.76 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__distrib,axiom,
% 14.82/14.76 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__distrib2,axiom,
% 14.82/14.76 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_O__assoc,axiom,
% 14.82/14.76 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__empty2,axiom,
% 14.82/14.76 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__empty1,axiom,
% 14.82/14.76 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__Id__on,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__mono,axiom,
% 14.82/14.76 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_union__comp__emptyR,axiom,
% 14.82/14.76 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 14.82/14.76 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_union__comp__emptyL,axiom,
% 14.82/14.76 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 14.82/14.76 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 14.82/14.76 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 14.82/14.76 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__Union,axiom,
% 14.82/14.76 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__empty__iff,axiom,
% 14.82/14.76 ! [V_r_2,T_b,T_c] :
% 14.82/14.76 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__empty,axiom,
% 14.82/14.76 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_rel__comp__subset__Sigma,axiom,
% 14.82/14.76 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__Un__eq,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Range,axiom,
% 14.82/14.76 ! [V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_snd__eq__Range,axiom,
% 14.82/14.76 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__iff,axiom,
% 14.82/14.76 ! [V_r_2,T_c,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 14.82/14.76 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__insert,axiom,
% 14.82/14.76 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__Int__subset,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Range__Diff__subset,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_max__ext__compat,axiom,
% 14.82/14.76 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__ext__compat,axiom,
% 14.82/14.76 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_RangeP__Range__eq,axiom,
% 14.82/14.76 ! [V_x_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_RangeE,axiom,
% 14.82/14.76 ! [V_r_2,T_c,V_b_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 14.82/14.76 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_pred__comp__rel__comp__eq,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_pred__comp_Ointros,axiom,
% 14.82/14.76 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_RangeP_Ointros,axiom,
% 14.82/14.76 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 14.82/14.76 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_RangeP_Oequations,axiom,
% 14.82/14.76 ! [V_a2_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 14.82/14.76 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_pred__comp_Oequations,axiom,
% 14.82/14.76 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 14.82/14.76 <=> ? [B_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 14.82/14.76 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_reduction__pairI,axiom,
% 14.82/14.76 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_R_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 14.82/14.76 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__Collect__split,axiom,
% 14.82/14.76 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__eq__trivial,axiom,
% 14.82/14.76 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__less__than,axiom,
% 14.82/14.76 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__empty,axiom,
% 14.82/14.76 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__inv__image,axiom,
% 14.82/14.76 ! [V_f_2,T_c,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__lex__prod,axiom,
% 14.82/14.76 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 14.82/14.76 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 14.82/14.76 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__measure,axiom,
% 14.82/14.76 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_DomainI,axiom,
% 14.82/14.76 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__comp__self,axiom,
% 14.82/14.76 ! [V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_R_2)
% 14.82/14.76 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__subset,axiom,
% 14.82/14.76 ! [V_p_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
% 14.82/14.76 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_min__ext__wf,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__Int2,axiom,
% 14.82/14.76 ! [V_r_H_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__Int1,axiom,
% 14.82/14.76 ! [V_r_H_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_max__ext__wf,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__pair__less,axiom,
% 14.82/14.76 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__Id__on,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__finite__psubset,axiom,
% 14.82/14.76 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__mlex,axiom,
% 14.82/14.76 ! [V_f_2,V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_R_2)
% 14.82/14.76 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__less,axiom,
% 14.82/14.76 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__not__refl,axiom,
% 14.82/14.76 ! [V_a_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__not__sym,axiom,
% 14.82/14.76 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__asym,axiom,
% 14.82/14.76 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__irrefl,axiom,
% 14.82/14.76 ! [V_a_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__int__ge__less__than2,axiom,
% 14.82/14.76 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__int__ge__less__than,axiom,
% 14.82/14.76 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__Un,axiom,
% 14.82/14.76 ! [V_s_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 14.82/14.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_acc__wfD,axiom,
% 14.82/14.76 ! [V_x_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__acc__iff,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__no__loop,axiom,
% 14.82/14.76 ! [V_R_2,T_b] :
% 14.82/14.76 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 14.82/14.76 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__union__merge,axiom,
% 14.82/14.76 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 14.82/14.76 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__empty__iff,axiom,
% 14.82/14.76 ! [V_r_2,T_c,T_b] :
% 14.82/14.76 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__empty,axiom,
% 14.82/14.76 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__mono,axiom,
% 14.82/14.76 ! [V_s_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__Un__eq,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__Domain,axiom,
% 14.82/14.76 ! [V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fst__eq__Domain,axiom,
% 14.82/14.76 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 <=> ~ ? [B_f] :
% 14.82/14.76 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfE__pf,axiom,
% 14.82/14.76 ! [V_A_2,V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_R_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
% 14.82/14.76 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__union__compatible,axiom,
% 14.82/14.76 ! [V_S_2,V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_R_2)
% 14.82/14.76 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__iff,axiom,
% 14.82/14.76 ! [V_r_2,T_c,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 14.82/14.76 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf,axiom,
% 14.82/14.76 ! [T_b] :
% 14.82/14.76 ( class_Orderings_Owellorder(T_b)
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__insert,axiom,
% 14.82/14.76 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_reduction__pair__def,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b] :
% 14.82/14.76 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 14.82/14.76 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 14.82/14.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_reduction__pair__lemma,axiom,
% 14.82/14.76 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 14.82/14.76 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 14.82/14.76 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__Int__subset,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__Diff__subset,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Field__def,axiom,
% 14.82/14.76 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__map__pair__image,axiom,
% 14.82/14.76 ! [V_f_2,T_c,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.76 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Domain__Union,axiom,
% 14.82/14.76 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_the__sym__eq__trivial,axiom,
% 14.82/14.76 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_DomainP__Domain__eq,axiom,
% 14.82/14.76 ! [V_x_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
% 14.82/14.76 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__lenlex,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_DomainE,axiom,
% 14.82/14.76 ! [V_r_2,T_c,V_a_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 14.82/14.76 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_DomainP_Ointros,axiom,
% 14.82/14.76 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 14.82/14.76 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_DomainP_Oequations,axiom,
% 14.82/14.76 ! [V_a1_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 14.82/14.76 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_pred__nat__def,axiom,
% 14.82/14.76 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__lex,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__lexn,axiom,
% 14.82/14.76 ! [V_n_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_lex__def,axiom,
% 14.82/14.76 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_lexn_Osimps_I1_J,axiom,
% 14.82/14.76 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__pred__nat,axiom,
% 14.82/14.76 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__same__fst,axiom,
% 14.82/14.76 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 14.82/14.76 ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.76 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 14.82/14.76 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__if__measure,axiom,
% 14.82/14.76 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 14.82/14.76 ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(V_Pa_2,B_x))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
% 14.82/14.76 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__def,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 14.82/14.76 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__empty,axiom,
% 14.82/14.76 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_accp__wfPD,axiom,
% 14.82/14.76 ! [V_x_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 14.82/14.76 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__accp__iff,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 14.82/14.76 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__subset,axiom,
% 14.82/14.76 ! [V_p_2,V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
% 14.82/14.76 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__in__rel,axiom,
% 14.82/14.76 ! [V_R_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_R_2)
% 14.82/14.76 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__wf__eq,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
% 14.82/14.76 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__acyclicP,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_pigeonhole__infinite,axiom,
% 14.82/14.76 ! [V_f_2,T_c,V_A_2,T_b] :
% 14.82/14.76 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 14.82/14.76 => ? [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_refl__on__def_H,axiom,
% 14.82/14.76 ! [V_r_2,V_A_2,T_b] :
% 14.82/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 14.82/14.76 <=> ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) )
% 14.82/14.76 & ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_ball__empty,axiom,
% 14.82/14.76 ! [V_Pa_2,T_b,B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 14.82/14.76 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__acyclic,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_acyclic__subset,axiom,
% 14.82/14.76 ! [V_r_2,V_s_2,T_b] :
% 14.82/14.76 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 14.82/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 14.82/14.76 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Powp__def,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 14.82/14.76 <=> ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 14.82/14.76 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_INFI__bool__eq,axiom,
% 14.82/14.76 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Collect__ball__eq,axiom,
% 14.82/14.76 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_congruent__def,axiom,
% 14.82/14.76 ! [V_f_2,V_r_2,T_c,T_b] :
% 14.82/14.76 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 14.82/14.76 <=> ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_INTER__def,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 14.82/14.76 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 14.82/14.76 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__acyclic__wf,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 14.82/14.76 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 14.82/14.76 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Sup__Inf,axiom,
% 14.82/14.76 ! [V_A_2,T_b] :
% 14.82/14.76 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.76 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Inf__Sup,axiom,
% 14.82/14.76 ! [V_A_2,T_b] :
% 14.82/14.76 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 14.82/14.76 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Nitpick_Owf_H__def,axiom,
% 14.82/14.76 ! [V_r_2,T_b] :
% 14.82/14.76 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 14.82/14.76 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 14.82/14.76 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 14.82/14.76 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Abs__Integ__cases,axiom,
% 14.82/14.76 ! [V_x_2] :
% 14.82/14.76 ~ ! [B_y] :
% 14.82/14.76 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Abs__Integ__induct,axiom,
% 14.82/14.76 ! [V_x_2,V_Pa_2] :
% 14.82/14.76 ( ! [B_y] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 14.82/14.76 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 14.82/14.76 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_Inter__eq,axiom,
% 14.82/14.76 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_finite__UN__I,axiom,
% 14.82/14.76 ! [V_B_2,T_c,V_A_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 14.82/14.76 => ( ! [B_a] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 14.82/14.76 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__diff__nat,axiom,
% 14.82/14.76 ! [V_k_2,V_N_2] :
% 14.82/14.76 ( ! [B_x] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 14.82/14.76 => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_wfP__SUP,axiom,
% 14.82/14.76 ! [T_b,V_r_2,T_c] :
% 14.82/14.76 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 14.82/14.76 => ( ! [B_i,B_j] :
% 14.82/14.76 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 14.82/14.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 14.82/14.76 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_mem__splitI2,axiom,
% 14.82/14.76 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 14.82/14.76 ( ! [B_a,B_b] :
% 14.82/14.76 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 14.82/14.76 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_mem__splitE,axiom,
% 14.82/14.76 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 14.82/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2)))
% 14.82/14.76 => ~ ! [B_x,B_y] :
% 14.82/14.76 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 14.82/14.76 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_vimage__Times,axiom,
% 14.82/14.76 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__eq__id__dest,axiom,
% 14.82/14.76 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 14.82/14.76 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2)
% 14.82/14.76 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_id__o,axiom,
% 14.82/14.76 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__id,axiom,
% 14.82/14.76 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fun__upd__comp,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_apsnd__compose,axiom,
% 14.82/14.76 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 14.82/14.76 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 14.82/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_comp__cong,axiom,
% 14.82/14.76 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 14.82/14.76 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
% 14.82/14.76 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 14.82/14.76 ! [V_x_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 14.82/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__eq__dest__lhs,axiom,
% 14.82/14.76 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 14.82/14.76 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
% 14.82/14.76 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_K__record__comp,axiom,
% 14.82/14.76 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ).
% 14.82/14.76
% 14.82/14.76 fof(fact_apfst__compose,axiom,
% 14.82/14.76 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__def,axiom,
% 14.82/14.76 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_vimage__compose,axiom,
% 14.82/14.76 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__assoc,axiom,
% 14.82/14.76 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__apply,axiom,
% 14.82/14.76 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__eq__dest,axiom,
% 14.82/14.76 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 14.82/14.76 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 14.82/14.76 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_o__eq__elim,axiom,
% 14.82/14.76 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 14.82/14.76 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 14.82/14.76 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair_Ocompositionality,axiom,
% 14.82/14.76 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair__compose,axiom,
% 14.82/14.76 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_map__pair_Ocomp,axiom,
% 14.82/14.76 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_image__compose,axiom,
% 14.82/14.76 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_comp__surj,axiom,
% 14.82/14.76 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 14.82/14.76 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 14.82/14.76 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 14.82/14.76 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__imageI2,axiom,
% 14.82/14.76 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
% 14.82/14.76 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__comp,axiom,
% 14.82/14.76 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 14.82/14.76 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 14.82/14.76 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_comp__inj__on__iff,axiom,
% 14.82/14.76 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 14.82/14.76 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_comp__inj__on,axiom,
% 14.82/14.76 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 14.82/14.76 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_inj__on__imageI,axiom,
% 14.82/14.76 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 14.82/14.76 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
% 14.82/14.76 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ).
% 14.82/14.76
% 14.82/14.76 fof(fact_setsum__reindex,axiom,
% 14.82/14.76 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 14.82/14.76 ( class_Groups_Ocomm__monoid__add(T_d)
% 14.82/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 14.82/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setprod__reindex,axiom,
% 15.02/14.76 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__mult(T_d)
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setprod__reindex__cong,axiom,
% 15.02/14.76 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__mult(T_d)
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.76 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 15.02/14.76 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setsum_Oreindex,axiom,
% 15.02/14.76 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__add(T_c)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setprod_Oreindex,axiom,
% 15.02/14.76 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_the__inv__into__comp,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 15.02/14.76 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 15.02/14.76 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_fold__image__reindex,axiom,
% 15.02/14.76 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 15.02/14.76 ( class_Groups_Oab__semigroup__mult(T_d)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 15.02/14.76 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Oremove,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.76 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__image_Oreindex,axiom,
% 15.02/14.76 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 15.02/14.76 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 15.02/14.76 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ounion,axiom,
% 15.02/14.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 15.02/14.76 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.76 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 15.02/14.76 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__comp,axiom,
% 15.02/14.76 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__left__comp,axiom,
% 15.02/14.76 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_fst__comp__map__pair,axiom,
% 15.02/14.76 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_UN__o,axiom,
% 15.02/14.76 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_snd__comp__map__pair,axiom,
% 15.02/14.76 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__image_Odistrib,axiom,
% 15.02/14.76 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 15.02/14.76 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_split__comp,axiom,
% 15.02/14.76 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__comp_H,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 15.02/14.76 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 15.02/14.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 15.02/14.76 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Oempty,axiom,
% 15.02/14.76 ! [V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Oeq__fold,axiom,
% 15.02/14.76 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__image_Oeq__fold,axiom,
% 15.02/14.76 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 15.02/14.76 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Oinsert,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Ounion__inter,axiom,
% 15.02/14.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding_Oinsert__remove,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Loop__sound__lemma,axiom,
% 15.02/14.76 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 15.02/14.76 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 15.02/14.76 => c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_hoare__derivs_OIf,axiom,
% 15.02/14.76 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 15.02/14.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 15.02/14.76 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 15.02/14.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Loop,axiom,
% 15.02/14.76 ! [V_ca_2,V_b_2,V_Pa_2,V_Ga_2,T_b] :
% 15.02/14.76 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 15.02/14.76 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_peek__and__def,axiom,
% 15.02/14.76 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 15.02/14.76 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 15.02/14.76 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setsum__reindex__nonzero,axiom,
% 15.02/14.76 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__add(T_d)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 15.02/14.76 => ( ! [B_x] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 15.02/14.76 => ! [B_y] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 15.02/14.76 => ( B_x != B_y
% 15.02/14.76 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 15.02/14.76 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__idem_Ounion__idem,axiom,
% 15.02/14.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 15.02/14.76 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 15.02/14.76 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 15.02/14.76 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__idem_Oidem__comp,axiom,
% 15.02/14.76 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.76 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_folding__idem_Oinsert__idem,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 15.02/14.76 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_strong__setprod__reindex__cong,axiom,
% 15.02/14.76 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__mult(T_d)
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.76 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 15.02/14.76 => ( ! [B_x] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.76 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Eps__split,axiom,
% 15.02/14.76 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_wfI__pf,axiom,
% 15.02/14.76 ! [V_R_2,T_b] :
% 15.02/14.76 ( ! [B_A] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
% 15.02/14.76 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 15.02/14.76 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_exE__some,axiom,
% 15.02/14.76 ! [T_b,V_ca_2,V_Pa_2] :
% 15.02/14.76 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 15.02/14.76 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 15.02/14.76 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_tfl__some,axiom,
% 15.02/14.76 ! [T_b,B_P] :
% 15.02/14.76 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 15.02/14.76 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_someI,axiom,
% 15.02/14.76 ! [T_b,V_x_2,V_Pa_2] :
% 15.02/14.76 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.76 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_some__sym__eq__trivial,axiom,
% 15.02/14.76 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_some__eq__trivial,axiom,
% 15.02/14.76 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_some__eq__ex,axiom,
% 15.02/14.76 ! [T_b,V_Pa_2] :
% 15.02/14.76 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 15.02/14.76 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_someI__ex,axiom,
% 15.02/14.76 ! [T_b,V_Pa_2] :
% 15.02/14.76 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 15.02/14.76 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_split__paired__Eps,axiom,
% 15.02/14.76 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Eps__split__eq,axiom,
% 15.02/14.76 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Sigma__mono,axiom,
% 15.02/14.76 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 15.02/14.76 => ( ! [B_x] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_acc_OaccI,axiom,
% 15.02/14.76 ! [V_r_2,V_x_2,T_b] :
% 15.02/14.76 ( ! [B_y] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_not__acc__down,axiom,
% 15.02/14.76 ! [V_R_2,V_x_2,T_b] :
% 15.02/14.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 15.02/14.76 => ~ ! [B_z] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_max__ext_Osimps,axiom,
% 15.02/14.76 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 15.02/14.76 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 15.02/14.76 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 15.02/14.76 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.76 & ! [B_x] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 15.02/14.76 => ? [B_xa] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 15.02/14.76 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 15.02/14.76 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 15.02/14.76 ( class_Orderings_Olinorder(T_b)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( ! [B_x] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Max__eqI,axiom,
% 15.02/14.76 ! [V_x_2,V_A_2,T_b] :
% 15.02/14.76 ( class_Orderings_Olinorder(T_b)
% 15.02/14.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.76 => ( ! [B_y] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.76 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_wf__no__infinite__down__chainE,axiom,
% 15.02/14.76 ! [V_f_2,V_r_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 15.02/14.76 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_iterate_Osimps,axiom,
% 15.02/14.76 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 15.02/14.76 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.76 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) )
% 15.02/14.76 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.76 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setsum__reindex__cong,axiom,
% 15.02/14.76 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 15.02/14.76 ( class_Groups_Ocomm__monoid__add(T_d)
% 15.02/14.76 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.76 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 15.02/14.76 => ( ! [B_a] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 15.02/14.76 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Pair__scomp,axiom,
% 15.02/14.76 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_scomp__scomp,axiom,
% 15.02/14.76 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_scomp__Pair,axiom,
% 15.02/14.76 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_scomp__apply,axiom,
% 15.02/14.76 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_scomp__def,axiom,
% 15.02/14.76 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_scomp__unfold,axiom,
% 15.02/14.76 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_setsum__ivl__cong,axiom,
% 15.02/14.76 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
% 15.02/14.76 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 15.02/14.76 & class_Orderings_Oord(T_b) )
% 15.02/14.76 => ( V_a_2 = V_ca_2
% 15.02/14.76 => ( V_b_2 = V_d_2
% 15.02/14.76 => ( ! [B_x] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 15.02/14.76 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 15.02/14.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_less__eq,axiom,
% 15.02/14.76 ! [V_n_2,V_m_2] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 15.02/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_wf__trancl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Owf(T_b,V_r_2)
% 15.02/14.76 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_less__than__def,axiom,
% 15.02/14.76 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_acyclic__def,axiom,
% 15.02/14.76 ! [V_r_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 15.02/14.76 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl_Or__into__trancl,axiom,
% 15.02/14.76 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__subset__Field2,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_r__into__trancl_H,axiom,
% 15.02/14.76 ! [V_r_2,V_p_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__empty,axiom,
% 15.02/14.76 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__domain,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__range,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_finite__trancl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_r__r__into__trancl,axiom,
% 15.02/14.76 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_R_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__into__trancl2,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__trans,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__mono,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__unfold,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__subset__Sigma,axiom,
% 15.02/14.76 ! [V_A_2,V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__Int__subset,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__insert,axiom,
% 15.02/14.76 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_reflcl__set__eq,axiom,
% 15.02/14.76 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 15.02/14.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_r__into__rtrancl,axiom,
% 15.02/14.76 ! [V_r_2,V_p_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 15.02/14.76 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_IdI,axiom,
% 15.02/14.76 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__into__rtrancl,axiom,
% 15.02/14.76 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__unfold__left,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__unfold__right,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_reflcl__trancl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__reflcl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__trancl__absorb,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__rtrancl__absorb,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Domain__rtrancl,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Range__rtrancl,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_refl__rtrancl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__trans,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__idemp,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__r__diff__Id,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_in__rtrancl__UnI,axiom,
% 15.02/14.76 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 15.02/14.76 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.76 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__Un__subset,axiom,
% 15.02/14.76 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__reflcl,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__Un__rtrancl,axiom,
% 15.02/14.76 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__reflcl__absorb,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Image__closed__trancl,axiom,
% 15.02/14.76 ! [V_X_2,V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
% 15.02/14.76 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__mono,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__subset,axiom,
% 15.02/14.76 ! [V_S_2,V_R_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.76 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__subset__rtrancl,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__idemp__self__comp,axiom,
% 15.02/14.76 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_r__comp__rtrancl__eq,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__unfold,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__Int__subset,axiom,
% 15.02/14.76 ! [V_r_2,V_s_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__empty,axiom,
% 15.02/14.76 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_R__O__Id,axiom,
% 15.02/14.76 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Id__O__R,axiom,
% 15.02/14.76 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Image__Id,axiom,
% 15.02/14.76 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_pair__in__Id__conv,axiom,
% 15.02/14.76 ! [V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 15.02/14.76 <=> V_a_2 = V_b_2 ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__eq__or__trancl,axiom,
% 15.02/14.76 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.76 <=> ( V_x_2 = V_y_2
% 15.02/14.76 | ( V_x_2 != V_y_2
% 15.02/14.76 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__into__trancl2,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtranclD,axiom,
% 15.02/14.76 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.76 => ( V_a_2 = V_b_2
% 15.02/14.76 | ( V_a_2 != V_b_2
% 15.02/14.76 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__into__trancl1,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__rtrancl__trancl,axiom,
% 15.02/14.76 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__trancl__trancl,axiom,
% 15.02/14.76 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Domain__Id,axiom,
% 15.02/14.76 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Range__Id,axiom,
% 15.02/14.76 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_refl__Id,axiom,
% 15.02/14.76 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_pair__leq__def,axiom,
% 15.02/14.76 c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Not__Domain__rtrancl,axiom,
% 15.02/14.76 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 15.02/14.76 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.76 <=> V_x_2 = V_y_2 ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_acc__downwards__aux,axiom,
% 15.02/14.76 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_acc__downwards,axiom,
% 15.02/14.76 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_wf__insert,axiom,
% 15.02/14.76 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 15.02/14.76 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 15.02/14.76 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_acyclic__insert,axiom,
% 15.02/14.76 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 15.02/14.76 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 15.02/14.76 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_refl__reflcl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Id__def,axiom,
% 15.02/14.76 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_irrefl__diff__Id,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_pred__nat__trancl__eq__le,axiom,
% 15.02/14.76 ! [V_n_2,V_m_2] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 15.02/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__subset__Sigma__aux,axiom,
% 15.02/14.76 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 15.02/14.76 => ( V_a_2 = V_b_2
% 15.02/14.76 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_irrefl__tranclI,axiom,
% 15.02/14.76 ! [V_x_2,V_r_2,T_b] :
% 15.02/14.76 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 15.02/14.76 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_sequence__trans,axiom,
% 15.02/14.76 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 15.02/14.76 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__Id,axiom,
% 15.02/14.76 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_acyclic__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.76 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_refl__on__converse,axiom,
% 15.02/14.76 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.76 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__Id__on,axiom,
% 15.02/14.76 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Field__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__inv__image,axiom,
% 15.02/14.76 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_finite__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_c,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 15.02/14.76 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__Int,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__Un,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__rel__comp,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converseD,axiom,
% 15.02/14.76 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converseI,axiom,
% 15.02/14.76 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__iff,axiom,
% 15.02/14.76 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 15.02/14.76 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__UNION,axiom,
% 15.02/14.76 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__INTER,axiom,
% 15.02/14.76 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_wf__converse__trancl,axiom,
% 15.02/14.76 ! [V_r_2,T_b] :
% 15.02/14.76 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.76 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_equiv__comp__eq,axiom,
% 15.02/14.76 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.76 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 15.02/14.76 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Range__def,axiom,
% 15.02/14.76 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Domain__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Range__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__converseD,axiom,
% 15.02/14.76 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_rtrancl__converseI,axiom,
% 15.02/14.76 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__converseD,axiom,
% 15.02/14.76 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_trancl__converseI,axiom,
% 15.02/14.76 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Image__subset__eq,axiom,
% 15.02/14.76 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
% 15.02/14.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_refl__on__comp__subset,axiom,
% 15.02/14.76 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.76 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 15.02/14.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_comp__equivI,axiom,
% 15.02/14.76 ! [V_A_2,V_r_2,T_b] :
% 15.02/14.76 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
% 15.02/14.76 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 15.02/14.76 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_finite__acyclic__wf__converse,axiom,
% 15.02/14.76 ! [V_r_2,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 15.02/14.76 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 15.02/14.76 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_converse__def,axiom,
% 15.02/14.76 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_Image__INT__eq,axiom,
% 15.02/14.76 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 15.02/14.76 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 15.02/14.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 15.02/14.76 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_total__on__diff__Id,axiom,
% 15.02/14.76 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.76 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 15.02/14.76 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_single__valued__Id,axiom,
% 15.02/14.76 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_single__valued__rel__comp,axiom,
% 15.02/14.76 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 15.02/14.76 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 15.02/14.76 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 15.02/14.76 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_single__valued__subset,axiom,
% 15.02/14.76 ! [V_s_2,V_r_2,T_c,T_b] :
% 15.02/14.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.76 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 15.02/14.76 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_single__valued__Id__on,axiom,
% 15.02/14.76 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_total__on__empty,axiom,
% 15.02/14.76 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_total__on__converse,axiom,
% 15.02/14.76 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.76 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.76 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 15.02/14.76
% 15.02/14.76 fof(fact_single__valuedD,axiom,
% 15.02/14.76 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 15.02/14.76 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
% 15.02/14.77 => V_y_2 = V_z_2 ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_single__valued__def,axiom,
% 15.02/14.77 ! [V_r_2,T_c,T_b] :
% 15.02/14.77 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 15.02/14.77 <=> ! [B_x,B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
% 15.02/14.77 => ! [B_z] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
% 15.02/14.77 => B_y = B_z ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_total__on__def,axiom,
% 15.02/14.77 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.77 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.77 => ! [B_xa] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 15.02/14.77 => ( B_x != B_xa
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_single__valued__confluent,axiom,
% 15.02/14.77 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 15.02/14.77 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Image__Int__eq,axiom,
% 15.02/14.77 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 15.02/14.77 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 15.02/14.77 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 15.02/14.77 ! [V_R_2,V_p_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_acyclicI,axiom,
% 15.02/14.77 ! [V_r_2,T_b] :
% 15.02/14.77 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 15.02/14.77 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_single__valued__rel__pow,axiom,
% 15.02/14.77 ! [V_n_2,V_R_2,T_b] :
% 15.02/14.77 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 15.02/14.77 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_funpow__swap1,axiom,
% 15.02/14.77 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_funpow__mult,axiom,
% 15.02/14.77 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_wf__exp,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,T_b] :
% 15.02/14.77 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
% 15.02/14.77 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_comp__funpow,axiom,
% 15.02/14.77 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__commute,axiom,
% 15.02/14.77 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__1,axiom,
% 15.02/14.77 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__power,axiom,
% 15.02/14.77 ! [V_R_2,V_p_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.77 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__imp__rtrancl,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_relpow_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__add,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_relpow_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__0__I,axiom,
% 15.02/14.77 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__0__E,axiom,
% 15.02/14.77 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 15.02/14.77 => V_x_2 = V_y_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__Suc__I,axiom,
% 15.02/14.77 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__Suc__I2,axiom,
% 15.02/14.77 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_funpow_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_funpow__add,axiom,
% 15.02/14.77 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_funpow_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_trancl__power,axiom,
% 15.02/14.77 ! [V_R_2,V_p_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 15.02/14.77 <=> ? [B_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 15.02/14.77 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_funpow__code__def,axiom,
% 15.02/14.77 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__E,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 15.02/14.77 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => V_x_2 != V_z_2 )
% 15.02/14.77 => ~ ! [B_y,B_m] :
% 15.02/14.77 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__E2,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 15.02/14.77 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => V_x_2 != V_z_2 )
% 15.02/14.77 => ~ ! [B_y,B_m] :
% 15.02/14.77 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__Un__separatorE,axiom,
% 15.02/14.77 ! [V_Q_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2))))
% 15.02/14.77 => ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 15.02/14.77 => ! [B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
% 15.02/14.77 => B_x = B_y ) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 15.02/14.77 ! [V_Q_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2))))
% 15.02/14.77 => ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 15.02/14.77 => ! [B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
% 15.02/14.77 => B_y = B_x ) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__Suc__D2,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 15.02/14.77 => ? [B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__Suc__E,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 15.02/14.77 => ~ ! [B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__pow__Suc__E2,axiom,
% 15.02/14.77 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 15.02/14.77 => ~ ! [B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tranclD,axiom,
% 15.02/14.77 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 15.02/14.77 => ? [B_z] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tranclD2,axiom,
% 15.02/14.77 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 15.02/14.77 => ? [B_z] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_IdE,axiom,
% 15.02/14.77 ! [V_p_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 15.02/14.77 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_wf__eq__minimal,axiom,
% 15.02/14.77 ! [V_r_2,T_b] :
% 15.02/14.77 ( c_Wellfounded_Owf(T_b,V_r_2)
% 15.02/14.77 <=> ! [B_Q] :
% 15.02/14.77 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 15.02/14.77 => ? [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 15.02/14.77 & ! [B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transfer__nat__int__set__cong,axiom,
% 15.02/14.77 ! [V_P_H_2,V_Pa_2] :
% 15.02/14.77 ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 15.02/14.77 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.77 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 15.02/14.77 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Int__Collect__mono,axiom,
% 15.02/14.77 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 15.02/14.77 => ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.77 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.77 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rel__compE,axiom,
% 15.02/14.77 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 15.02/14.77 => ~ ! [B_x,B_y,B_z] :
% 15.02/14.77 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_converseE,axiom,
% 15.02/14.77 ! [V_r_2,V_yx_2,T_c,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 15.02/14.77 => ~ ! [B_x,B_y] :
% 15.02/14.77 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 15.02/14.77 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_internal__split__def,axiom,
% 15.02/14.77 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_internal__split__conv,axiom,
% 15.02/14.77 ! [V_b_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 15.02/14.77 ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Oof__frac__def,axiom,
% 15.02/14.77 ! [V_q,T_a,T_b] :
% 15.02/14.77 ( ( class_Rings_Oinverse(T_b)
% 15.02/14.77 & class_Rings_Oring__1(T_b) )
% 15.02/14.77 => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 15.02/14.77 ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 15.02/14.77 ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Oless__frac__def,axiom,
% 15.02/14.77 ! [V_r_2,V_q_2,T_b] :
% 15.02/14.77 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 15.02/14.77 ! [V_r_2,V_q_2,T_b] :
% 15.02/14.77 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Odenom__def,axiom,
% 15.02/14.77 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Onum__def,axiom,
% 15.02/14.77 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_bool_Osize_I2_J,axiom,
% 15.02/14.77 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_bool_Osize_I1_J,axiom,
% 15.02/14.77 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_finite__less__ub,axiom,
% 15.02/14.77 ! [V_u_2,V_f_2] :
% 15.02/14.77 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 15.02/14.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lenlex__def,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_neq__if__length__neq,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_a] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
% 15.02/14.77 => V_xs != V_ys ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexn__length,axiom,
% 15.02/14.77 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 15.02/14.77 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 15.02/14.77 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lenlex__conv,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__sublist,axiom,
% 15.02/14.77 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexn_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_impossible__Cons,axiom,
% 15.02/14.77 ! [V_x,V_ys,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 15.02/14.77 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_not__Cons__self,axiom,
% 15.02/14.77 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_not__Cons__self2,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Oinject,axiom,
% 15.02/14.77 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 15.02/14.77 <=> ( V_a_2 = V_a_H_2
% 15.02/14.77 & V_list_2 = V_list_H_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osize_I4_J,axiom,
% 15.02/14.77 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Cons__in__lex,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 15.02/14.77 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 15.02/14.77 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 15.02/14.77 | ( V_x_2 = V_y_2
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__Cons__def,axiom,
% 15.02/14.77 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_pick_Osimps,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_i] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 15.02/14.77 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 15.02/14.77 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select__weight__cons__zero,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__cons__cons,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.77 | ( V_a_2 = V_b_2
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__lex,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osize_I2_J,axiom,
% 15.02/14.77 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Cons__acc__listrel1I,axiom,
% 15.02/14.77 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1__converse,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1__mono,axiom,
% 15.02/14.77 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1I2,axiom,
% 15.02/14.77 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 15.02/14.77 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1__eq__len,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__listrel1__converse,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1I1,axiom,
% 15.02/14.77 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Cons__listrel1__Cons,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 15.02/14.77 & V_xs_2 = V_ys_2 )
% 15.02/14.77 | ( V_x_2 = V_y_2
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__Cons,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__irreflexive,axiom,
% 15.02/14.77 ! [V_y_2,V_r_2,T_b] :
% 15.02/14.77 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__rtrancl__refl,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__mono,axiom,
% 15.02/14.77 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__eq__len,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__rtrancl__trans,axiom,
% 15.02/14.77 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1__subset__listrel,axiom,
% 15.02/14.77 ! [V_r_H_2,V_r_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 15.02/14.77 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel_OCons,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrelp__listrel__eq,axiom,
% 15.02/14.77 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 15.02/14.77 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__Cons2,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => ~ ! [B_x,B_xs] :
% 15.02/14.77 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrelp_OCons,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 15.02/14.77 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 15.02/14.77 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrelp_Oequations_I2_J,axiom,
% 15.02/14.77 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 15.02/14.77 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 15.02/14.77 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__Cons1,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => ~ ! [B_y,B_ys] :
% 15.02/14.77 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__subset,axiom,
% 15.02/14.77 ! [V_A_2,V_r_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__UNIV,axiom,
% 15.02/14.77 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__mono,axiom,
% 15.02/14.77 ! [V_B_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_equiv__listrel,axiom,
% 15.02/14.77 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.77 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 15.02/14.77 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__refl__on,axiom,
% 15.02/14.77 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.77 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 15.02/14.77 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Cons__in__lists__iff,axiom,
% 15.02/14.77 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__accI,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__accD,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__iff__nth,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 15.02/14.77 & ! [B_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__linear,axiom,
% 15.02/14.77 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 15.02/14.77 ( ! [B_a,B_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2))
% 15.02/14.77 | B_a = B_b
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) )
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 | V_x_2 = V_y_2
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_infinite__UNIV__listI,axiom,
% 15.02/14.77 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__eq__iff__nth__eq,axiom,
% 15.02/14.77 ! [T_b,V_ys_2,V_xs_2] :
% 15.02/14.77 ( V_xs_2 = V_ys_2
% 15.02/14.77 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 15.02/14.77 & ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__Cons__0,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__Cons__Suc,axiom,
% 15.02/14.77 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth_Osimps,axiom,
% 15.02/14.77 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__Cons_H,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_n] :
% 15.02/14.77 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 15.02/14.77 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__Cons__number__of,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_v] :
% 15.02/14.77 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x )
% 15.02/14.77 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__take__index__conv,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))
% 15.02/14.77 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 )
% 15.02/14.77 | ? [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))))
% 15.02/14.77 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__sublist,axiom,
% 15.02/14.77 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_finite__set,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__subset__Cons,axiom,
% 15.02/14.77 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__all,axiom,
% 15.02/14.77 ! [V_n,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__take__subset,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__take__subset__set__take,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__sublist__subset,axiom,
% 15.02/14.77 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__take,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_n,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_notin__set__sublistI,axiom,
% 15.02/14.77 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__takeD,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__sublistD,axiom,
% 15.02/14.77 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__ConsD,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 15.02/14.77 => ( V_y_2 = V_x_2
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Suc__Cons,axiom,
% 15.02/14.77 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__take,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__take,axiom,
% 15.02/14.77 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__upt__eq__take,axiom,
% 15.02/14.77 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_card__length,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_all__set__conv__all__nth,axiom,
% 15.02/14.77 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.77 ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.77 <=> ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__size__estimation,axiom,
% 15.02/14.77 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__size__estimation_H,axiom,
% 15.02/14.77 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__lists__conv__set,axiom,
% 15.02/14.77 ! [V_A_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__pos__if__in__set,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__conv__nth,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 <=> ? [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__mem,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__eq__set,axiom,
% 15.02/14.77 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__conv__nth,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_finite__lists__length__eq,axiom,
% 15.02/14.77 ! [V_n_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_finite__lists__length__le,axiom,
% 15.02/14.77 ! [V_n_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__iff__zip,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 15.02/14.77 & ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__zip,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__zip,axiom,
% 15.02/14.77 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__zip,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__Cons__Cons,axiom,
% 15.02/14.77 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__eq__iff__zip__eq,axiom,
% 15.02/14.77 ! [T_b,V_ys_2,V_xs_2] :
% 15.02/14.77 ( V_xs_2 = V_ys_2
% 15.02/14.77 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 15.02/14.77 & ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__same,axiom,
% 15.02/14.77 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 & V_a_2 = V_b_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__zip__leftD,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__zip__rightD,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__zipE,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 15.02/14.77 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__zip,axiom,
% 15.02/14.77 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_greaterThanLessThan__upto,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__setsum__nth,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__upto,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_atLeastAtMost__upto,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 15.02/14.77 ! [V_ns_2] :
% 15.02/14.77 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 15.02/14.77 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_elem__le__listsum__nat,axiom,
% 15.02/14.77 ! [V_ns,V_k] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__simps_I2_J,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_a)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_atLeastLessThan__upto,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_greaterThanAtMost__upto,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__list__def,axiom,
% 15.02/14.77 ! [V_l_2] :
% 15.02/14.77 ( c_List_Onat__list(V_l_2)
% 15.02/14.77 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__size__pointwise,axiom,
% 15.02/14.77 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 15.02/14.77 ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__update__nat,axiom,
% 15.02/14.77 ! [V_n,V_ns,V_k] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast__take,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__beyond,axiom,
% 15.02/14.77 ! [V_x,V_i,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
% 15.02/14.77 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__list__update__neq,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a,V_j,V_i] :
% 15.02/14.77 ( V_i != V_j
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__id,axiom,
% 15.02/14.77 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast__list__update,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a,V_k] :
% 15.02/14.77 ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) )
% 15.02/14.77 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__list__update,axiom,
% 15.02/14.77 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__update,axiom,
% 15.02/14.77 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_update__zip,axiom,
% 15.02/14.77 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__overwrite,axiom,
% 15.02/14.77 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__swap,axiom,
% 15.02/14.77 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 15.02/14.77 ( V_i != V_i_H
% 15.02/14.77 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__code_I2_J,axiom,
% 15.02/14.77 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__code_I3_J,axiom,
% 15.02/14.77 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__butlastD,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__update__subsetI,axiom,
% 15.02/14.77 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__update__subset__insert,axiom,
% 15.02/14.77 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__list__update,axiom,
% 15.02/14.77 ! [V_x,V_j,V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => ( ( V_i = V_j
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x )
% 15.02/14.77 & ( V_i != V_j
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__same__conv,axiom,
% 15.02/14.77 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 15.02/14.77 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__list__update__eq,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__butlast,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__butlast,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__update__memI,axiom,
% 15.02/14.77 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast__conv__take,axiom,
% 15.02/14.77 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1__iff__update,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 <=> ? [B_y,B_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__list__update,axiom,
% 15.02/14.77 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__upto,axiom,
% 15.02/14.77 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__take,axiom,
% 15.02/14.77 ! [V_i,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__sublistI,axiom,
% 15.02/14.77 ! [V_I_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__zipI1,axiom,
% 15.02/14.77 ! [V_ys,T_b,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__zipI2,axiom,
% 15.02/14.77 ! [V_xs,T_b,V_ys,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 15.02/14.77 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__card,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_card__distinct,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__conv__nth,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 <=> ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => ! [B_j] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => ( B_i != B_j
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__eq__iff__index__eq,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
% 15.02/14.77 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Ocard_H__def,axiom,
% 15.02/14.77 ! [V_A_2,T_b] :
% 15.02/14.77 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__take__lemma,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_a,V_k] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 15.02/14.77 => ( ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__remove1__eq,axiom,
% 15.02/14.77 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Cons__number__of,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_v] :
% 15.02/14.77 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 15.02/14.77 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists_ONil,axiom,
% 15.02/14.77 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__Nil1,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__Nil2,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 15.02/14.77 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__butlast,axiom,
% 15.02/14.77 ! [T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__remove1,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_x,T_a,V_xs] :
% 15.02/14.77 ( ( V_xs = c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 15.02/14.77 & ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osimps_I3_J,axiom,
% 15.02/14.77 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_y,V_x] :
% 15.02/14.77 ( ( V_x = V_y
% 15.02/14.77 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 15.02/14.77 & ( V_x != V_y
% 15.02/14.77 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upto__empty,axiom,
% 15.02/14.77 ! [V_i,V_j] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 15.02/14.77 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__eq__Nil,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__0,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Nil,axiom,
% 15.02/14.77 ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__nil,axiom,
% 15.02/14.77 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1__commute,axiom,
% 15.02/14.77 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrelp_Oequations_I1_J,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrelp_ONil,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__Nil,axiom,
% 15.02/14.77 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osize_I1_J,axiom,
% 15.02/14.77 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__simps_I1_J,axiom,
% 15.02/14.77 ! [T_a] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_a)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osize_I3_J,axiom,
% 15.02/14.77 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__0__conv,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__empty,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__empty2,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__code_I1_J,axiom,
% 15.02/14.77 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__nonempty,axiom,
% 15.02/14.77 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1__idem,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_notin__set__remove1,axiom,
% 15.02/14.77 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__remove1,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 15.02/14.77 ( V_a_2 != V_b_2
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__empty,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__remove1__subset,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__greater__0__conv,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__1__Cons,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_not__Nil__listrel1,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_not__listrel1__Nil,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel_ONil,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__Nil__right,axiom,
% 15.02/14.77 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nil__notin__lex,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nil2__notin__lex,axiom,
% 15.02/14.77 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Cons,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upto_Osimps,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 15.02/14.77 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 15.02/14.77 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__singleton,axiom,
% 15.02/14.77 ! [V_x_2,T_b,V_A_2] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 15.02/14.77 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 15.02/14.77 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__empty,axiom,
% 15.02/14.77 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Cons_H,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_n] :
% 15.02/14.77 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 15.02/14.77 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upto__rec__number__of,axiom,
% 15.02/14.77 ! [V_n,V_m] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 15.02/14.77 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 15.02/14.77 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel__Nil,axiom,
% 15.02/14.77 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__Cons__sing__Nil,axiom,
% 15.02/14.77 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__remove1,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upto_Opsimps,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] :
% 15.02/14.77 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
% 15.02/14.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 15.02/14.77 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 15.02/14.77 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select,axiom,
% 15.02/14.77 ! [V_s_2,T_b,V_xs_2] :
% 15.02/14.77 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listset_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__Cons1,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osimps_I5_J,axiom,
% 15.02/14.77 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list_Osimps_I4_J,axiom,
% 15.02/14.77 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listset_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__Cons,axiom,
% 15.02/14.77 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__list__of__set__remove,axiom,
% 15.02/14.77 ! [V_x_2,V_A_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upto_Opinduct,axiom,
% 15.02/14.77 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 15.02/14.77 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 15.02/14.77 => ( ! [B_i,B_j] :
% 15.02/14.77 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
% 15.02/14.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 15.02/14.77 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__list__of__set__empty,axiom,
% 15.02/14.77 ! [T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_anamorph_Osimps,axiom,
% 15.02/14.77 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 15.02/14.77 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.77 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) )
% 15.02/14.77 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.77 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__Cons,axiom,
% 15.02/14.77 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__eq__Cons__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 15.02/14.77 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 15.02/14.77 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 15.02/14.77 | ? [B_ys_H] :
% 15.02/14.77 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 15.02/14.77 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Cons__eq__append__conv,axiom,
% 15.02/14.77 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
% 15.02/14.77 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 15.02/14.77 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 15.02/14.77 | ? [B_ys_H] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 15.02/14.77 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append1__eq__conv,axiom,
% 15.02/14.77 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
% 15.02/14.77 <=> ( V_xs_2 = V_ys_2
% 15.02/14.77 & V_x_2 = V_y_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__Cons,axiom,
% 15.02/14.77 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Cons__eq__appendI,axiom,
% 15.02/14.77 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 15.02/14.77 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 15.02/14.77 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__in__lists__conv,axiom,
% 15.02/14.77 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__eq__appendI,axiom,
% 15.02/14.77 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 15.02/14.77 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 15.02/14.77 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__same__eq,axiom,
% 15.02/14.77 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
% 15.02/14.77 <=> V_ys_2 = V_zs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_same__append__eq,axiom,
% 15.02/14.77 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
% 15.02/14.77 <=> V_ys_2 = V_zs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__eq__append__conv2,axiom,
% 15.02/14.77 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2)
% 15.02/14.77 <=> ? [B_us] :
% 15.02/14.77 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 15.02/14.77 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 15.02/14.77 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 15.02/14.77 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__assoc,axiom,
% 15.02/14.77 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_a] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_a)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__append,axiom,
% 15.02/14.77 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
% 15.02/14.77 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
% 15.02/14.77 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__Nil,axiom,
% 15.02/14.77 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nil__is__append__conv,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 15.02/14.77 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 15.02/14.77 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__Nil2,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_self__append__conv,axiom,
% 15.02/14.77 ! [V_ys_2,T_b,V_xs_2] :
% 15.02/14.77 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 15.02/14.77 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_self__append__conv2,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_ys_2] :
% 15.02/14.77 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__is__Nil__conv,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 15.02/14.77 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__self__conv,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 15.02/14.77 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__self__conv2,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_eq__Nil__appendI,axiom,
% 15.02/14.77 ! [T_a,V_ys,V_xs] :
% 15.02/14.77 ( V_xs = V_ys
% 15.02/14.77 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast__append,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_ys] :
% 15.02/14.77 ( ( V_ys = c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 15.02/14.77 & ( V_ys != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__append__length,axiom,
% 15.02/14.77 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__append__length__plus,axiom,
% 15.02/14.77 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__append1,axiom,
% 15.02/14.77 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__length,axiom,
% 15.02/14.77 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__butlast__appendI,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast__snoc,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__listrel1I,axiom,
% 15.02/14.77 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 & V_us_2 = V_vs_2 )
% 15.02/14.77 | ( V_xs_2 = V_ys_2
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__append__leftI,axiom,
% 15.02/14.77 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 15.02/14.77 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_a,V_n] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__update__append,axiom,
% 15.02/14.77 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__append,axiom,
% 15.02/14.77 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1I,axiom,
% 15.02/14.77 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 15.02/14.77 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
% 15.02/14.77 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__append__left__rightI,axiom,
% 15.02/14.77 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Suc__conv__app__nth,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 & V_x_2 = V_y_2 )
% 15.02/14.77 | ( V_xs_2 = V_ys_2
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listrel1E,axiom,
% 15.02/14.77 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 15.02/14.77 => ~ ! [B_x,B_y] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 15.02/14.77 => ! [B_us,B_vs] :
% 15.02/14.77 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 15.02/14.77 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__append__leftD,axiom,
% 15.02/14.77 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate1__def,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upd__conv__take__nth__drop,axiom,
% 15.02/14.77 ! [V_a,V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__take__drop__id,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__1__Cons,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__Suc__Cons,axiom,
% 15.02/14.77 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__via__drop,axiom,
% 15.02/14.77 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__drop,axiom,
% 15.02/14.77 ! [V_i,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct1__rotate,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 15.02/14.77 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_butlast__drop,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__butlast,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__take,axiom,
% 15.02/14.77 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__drop,axiom,
% 15.02/14.77 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__drop,axiom,
% 15.02/14.77 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__0,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__zip,axiom,
% 15.02/14.77 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__rotate1,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__drop,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__rotate1,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__set__dropD,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__drop__subset,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__Nil,axiom,
% 15.02/14.77 ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate1__is__Nil__conv,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__drop__subset__set__drop,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__all,axiom,
% 15.02/14.77 ! [V_n,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 15.02/14.77 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__eq__Nil,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__eq__conv__conj,axiom,
% 15.02/14.77 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 15.02/14.77 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
% 15.02/14.77 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__Cons,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__Cons_H,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_n] :
% 15.02/14.77 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) )
% 15.02/14.77 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__drop,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_i,V_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__eq__append__conv__if,axiom,
% 15.02/14.77 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 15.02/14.77 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 15.02/14.77 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 15.02/14.77 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 15.02/14.77 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 15.02/14.77 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__drop_H,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__simps,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_b,T_a] :
% 15.02/14.77 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 15.02/14.77 & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__Cons__number__of,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a,V_v] :
% 15.02/14.77 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) )
% 15.02/14.77 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__add,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_j,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate1__length01,axiom,
% 15.02/14.77 ! [V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 15.02/14.77 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__append2,axiom,
% 15.02/14.77 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__append1,axiom,
% 15.02/14.77 ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_id__take__nth__drop,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__hd__drop,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__drop__conv__nth,axiom,
% 15.02/14.77 ! [V_n,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd_Osimps,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__append2,axiom,
% 15.02/14.77 ! [V_ys,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__append,axiom,
% 15.02/14.77 ! [V_ys,T_a,V_xs] :
% 15.02/14.77 ( ( V_xs = c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) )
% 15.02/14.77 & ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__in__set,axiom,
% 15.02/14.77 ! [T_b,V_xs_2] :
% 15.02/14.77 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__conv__nth,axiom,
% 15.02/14.77 ! [T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate1__hd__tl,axiom,
% 15.02/14.77 ! [T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__rotate__conv__nth,axiom,
% 15.02/14.77 ! [V_n,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__tl,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tl__drop,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tl_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__tl,axiom,
% 15.02/14.77 ! [V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__rotate,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 15.02/14.77 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__rotate,axiom,
% 15.02/14.77 ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate0,axiom,
% 15.02/14.77 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__add,axiom,
% 15.02/14.77 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__rotate,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__rotate,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tl_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__is__Nil__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] :
% 15.02/14.77 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__def,axiom,
% 15.02/14.77 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate1__rotate__swap,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tl__append2,axiom,
% 15.02/14.77 ! [V_ys,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__tl,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__conv__mod,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__Suc,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__Suc,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tl__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__id,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_n] :
% 15.02/14.77 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__length01,axiom,
% 15.02/14.77 ! [V_n,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 15.02/14.77 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__tl,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_tl__take,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__Suc,axiom,
% 15.02/14.77 ! [V_n,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__drop__take,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_fold1__set,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 15.02/14.77 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__append__rightI,axiom,
% 15.02/14.77 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 15.02/14.77 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__Nil,axiom,
% 15.02/14.77 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_start__le__sum,axiom,
% 15.02/14.77 ! [V_ns_2,V_n_2,V_m_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__assoc,axiom,
% 15.02/14.77 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Groups_Osemigroup__add(T_b)
% 15.02/14.77 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__absorb0,axiom,
% 15.02/14.77 ! [V_zs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_b)
% 15.02/14.77 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__Cons,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__foldl,axiom,
% 15.02/14.77 ! [T_b] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_b)
% 15.02/14.77 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sum__eq__0__conv,axiom,
% 15.02/14.77 ! [V_ns_2,V_m_2] :
% 15.02/14.77 ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 & ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 15.02/14.77 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 15.02/14.77 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 15.02/14.77 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Sup__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.77 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Inf__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.77 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Sup__fin__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Lattices_Olattice(T_b)
% 15.02/14.77 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Inf__fin__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Lattices_Olattice(T_b)
% 15.02/14.77 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Min__fin__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Max__fin__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_SUPR__set__fold,axiom,
% 15.02/14.77 ! [V_f_2,V_xs_2,T_c,T_b] :
% 15.02/14.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_INFI__set__fold,axiom,
% 15.02/14.77 ! [V_f_2,V_xs_2,T_c,T_b] :
% 15.02/14.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_elem__le__sum,axiom,
% 15.02/14.77 ! [V_ns_2,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__list__of__set__insert,axiom,
% 15.02/14.77 ! [V_x_2,V_A_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lexord__Nil__left,axiom,
% 15.02/14.77 ! [V_r_2,V_y_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.77 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__key_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_x_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__key_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__insort,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__key__left__comm,axiom,
% 15.02/14.77 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__left__comm,axiom,
% 15.02/14.77 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_fun__left__comm__insort,axiom,
% 15.02/14.77 ! [T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__insort,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1__insort,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__not__Nil,axiom,
% 15.02/14.77 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__insort,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
% 15.02/14.77 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__insert__insort__key,axiom,
% 15.02/14.77 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 15.02/14.77 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__insert__insort,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__insort__insert,axiom,
% 15.02/14.77 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__insert__triv,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__insort__insert,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__insert__key__triv,axiom,
% 15.02/14.77 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 15.02/14.77 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__list__update,axiom,
% 15.02/14.77 ! [V_x,V_k,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 15.02/14.77 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__conv__nth,axiom,
% 15.02/14.77 ! [T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last_Osimps,axiom,
% 15.02/14.77 ! [V_x,T_a,V_xs] :
% 15.02/14.77 ( ( V_xs = c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 15.02/14.77 & ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__ConsR,axiom,
% 15.02/14.77 ! [V_x,T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__ConsL,axiom,
% 15.02/14.77 ! [V_x,T_a,V_xs] :
% 15.02/14.77 ( V_xs = c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__append,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_ys] :
% 15.02/14.77 ( ( V_ys = c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 15.02/14.77 & ( V_ys != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__appendR,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_ys] :
% 15.02/14.77 ( V_ys != c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__appendL,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_ys] :
% 15.02/14.77 ( V_ys = c_List_Olist_ONil(T_a)
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__in__set,axiom,
% 15.02/14.77 ! [T_b,V_as_2] :
% 15.02/14.77 ( V_as_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__snoc,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__drop,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_n] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.77 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__butlast__last__id,axiom,
% 15.02/14.77 ! [T_a,V_xs] :
% 15.02/14.77 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.77 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_snoc__eq__iff__butlast,axiom,
% 15.02/14.77 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 15.02/14.77 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 15.02/14.77 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists_Osimps,axiom,
% 15.02/14.77 ! [V_A_2,V_a_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 15.02/14.77 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 15.02/14.77 | ? [B_a,B_l] :
% 15.02/14.77 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 15.02/14.77 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select__weigth__select,axiom,
% 15.02/14.77 ! [T_b,V_xs_2] :
% 15.02/14.77 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_inj__mapI,axiom,
% 15.02/14.77 ! [V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.77 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__map,axiom,
% 15.02/14.77 ! [V_f_2,T_c,T_b,V_xs_2] :
% 15.02/14.77 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_rotate__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__tl,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__map2,axiom,
% 15.02/14.77 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__zip__map2,axiom,
% 15.02/14.77 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__zip__map,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__map1,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__map__map,axiom,
% 15.02/14.77 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__same__conv__map,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__is__Nil__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nil__is__map__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__update,axiom,
% 15.02/14.77 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__eq__conv,axiom,
% 15.02/14.77 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 15.02/14.77 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__eq__imp__length__eq,axiom,
% 15.02/14.77 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__mult__const,axiom,
% 15.02/14.77 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( class_Rings_Osemiring__0(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__const__mult,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 15.02/14.77 ( class_Rings_Osemiring__0(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__0,axiom,
% 15.02/14.77 ! [V_xs_2,T_c,T_b] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__addf,axiom,
% 15.02/14.77 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__subtractf,axiom,
% 15.02/14.77 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( class_Groups_Oab__group__add(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_inj__map__eq__map,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.77 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 15.02/14.77 <=> V_xs_2 = V_ys_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__injective,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 15.02/14.77 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.77 => V_xs_2 = V_ys_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__ident,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__butlast,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__map,axiom,
% 15.02/14.77 ! [V_f_2,T_c,T_b,V_xs_2] :
% 15.02/14.77 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.77 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_List_Omap_Oid,axiom,
% 15.02/14.77 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_List_Omap_Oidentity,axiom,
% 15.02/14.77 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_List_Omap_Ocomp,axiom,
% 15.02/14.77 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__comp__map,axiom,
% 15.02/14.77 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_List_Omap_Ocompositionality,axiom,
% 15.02/14.77 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__size__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__inj__on,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 15.02/14.77 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
% 15.02/14.77 => V_xs_2 = V_ys_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_inj__on__map__eq__map,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 15.02/14.77 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 15.02/14.77 <=> V_xs_2 = V_ys_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__map,axiom,
% 15.02/14.77 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__fun__upd,axiom,
% 15.02/14.77 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 15.02/14.77 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 15.02/14.77 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__abs,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_uminus__listsum__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( class_Groups_Oab__group__add(T_b)
% 15.02/14.77 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_inj__on__mapI,axiom,
% 15.02/14.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
% 15.02/14.77 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_inj__mapD,axiom,
% 15.02/14.77 ! [V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 15.02/14.77 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_inj__map,axiom,
% 15.02/14.77 ! [V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 15.02/14.77 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 15.02/14.77 ! [V_f_2,V_xs_2,T_b,T_c] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__triv,axiom,
% 15.02/14.77 ! [V_xs_2,V_r_2,T_c,T_b] :
% 15.02/14.77 ( class_Rings_Osemiring__1(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__map__remove1,axiom,
% 15.02/14.77 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 15.02/14.77 ! [V_f_2,V_A_2,T_b,T_c] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 15.02/14.77 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.77 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_pick__same,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_l_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zero__code__numeral__def,axiom,
% 15.02/14.77 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_times__code__numeral__code,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 15.02/14.77 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] :
% 15.02/14.77 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 15.02/14.77 <=> V_n_2 = V_m_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_one__code__numeral__def,axiom,
% 15.02/14.77 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_less__code__numeral__code,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 15.02/14.77 ! [V_y_2,V_x_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 15.02/14.77 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 15.02/14.77 <=> V_x_2 = V_y_2 ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__fst__zip,axiom,
% 15.02/14.77 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 15.02/14.77 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__snd__zip,axiom,
% 15.02/14.77 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 15.02/14.77 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_number__of__code__numeral__def,axiom,
% 15.02/14.77 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__map__fst__snd,axiom,
% 15.02/14.77 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_plus__code__numeral__code,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_less__eq__code__numeral__code,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_subtract__code__numeral__code,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_pick__member,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_i_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_zip__eq__conv,axiom,
% 15.02/14.77 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 15.02/14.77 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 15.02/14.77 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2
% 15.02/14.77 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__size__conv__listsum,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_code__numeral__not__eq__zero,axiom,
% 15.02/14.77 ! [V_i_2] :
% 15.02/14.77 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 15.02/14.77 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select__weight__member,axiom,
% 15.02/14.77 ! [V_s_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select__weight__def,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select__def,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsum__mono,axiom,
% 15.02/14.77 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 15.02/14.77 ( ( class_Groups_Omonoid__add(T_c)
% 15.02/14.77 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 15.02/14.77 => ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__of__inverse,axiom,
% 15.02/14.77 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 15.02/14.77
% 15.02/14.77 fof(fact_of__nat__nat__of,axiom,
% 15.02/14.77 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__of__of__nat,axiom,
% 15.02/14.77 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 15.02/14.77
% 15.02/14.77 fof(fact_times__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 15.02/14.77 ! [V_l_2,V_k_2] :
% 15.02/14.77 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 15.02/14.77 <=> V_k_2 = V_l_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_code__numeral_Onat__of__inject,axiom,
% 15.02/14.77 ! [V_y_2,V_x_2] :
% 15.02/14.77 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 15.02/14.77 <=> V_x_2 = V_y_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_type__definition__code__numeral,axiom,
% 15.02/14.77 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_less__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__of,axiom,
% 15.02/14.77 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__of__number,axiom,
% 15.02/14.77 ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_int__of__def,axiom,
% 15.02/14.77 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_less__eq__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__of__code,axiom,
% 15.02/14.77 ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nat__of__aux__def,axiom,
% 15.02/14.77 ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Suc__code__numeral__def,axiom,
% 15.02/14.77 ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_minus__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_of__nat__inverse,axiom,
% 15.02/14.77 ! [V_y_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 15.02/14.77 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_plus__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_div__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_mod__code__numeral__def,axiom,
% 15.02/14.77 ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_code__numeral__decr,axiom,
% 15.02/14.77 ! [V_k] :
% 15.02/14.77 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 15.02/14.77 ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition__set,axiom,
% 15.02/14.77 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 15.02/14.77 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 15.02/14.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition__P,axiom,
% 15.02/14.77 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 15.02/14.77 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 15.02/14.77 => ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 15.02/14.77 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.77 & ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__IntI,axiom,
% 15.02/14.77 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 15.02/14.77 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_lists__Int__eq,axiom,
% 15.02/14.77 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp_ONil,axiom,
% 15.02/14.77 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp_Oequations_I1_J,axiom,
% 15.02/14.77 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_in__listsp__conv__set,axiom,
% 15.02/14.77 ! [V_xs_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp__conj__eq,axiom,
% 15.02/14.77 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
% 15.02/14.77 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 15.02/14.77 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp__inf__eq,axiom,
% 15.02/14.77 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp__infI,axiom,
% 15.02/14.77 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 15.02/14.77 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp_Oequations_I2_J,axiom,
% 15.02/14.77 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 15.02/14.77 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_append__in__listsp__conv,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 15.02/14.77 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 15.02/14.77 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp__mono,axiom,
% 15.02/14.77 ! [V_B_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_listsp__lists__eq,axiom,
% 15.02/14.77 ! [V_x_2,V_A_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 15.02/14.77 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_product_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__def,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 15.02/14.77 & ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__map2,axiom,
% 15.02/14.77 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 15.02/14.77 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__map1,axiom,
% 15.02/14.77 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 15.02/14.77 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__dropI,axiom,
% 15.02/14.77 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
% 15.02/14.77 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__appendI,axiom,
% 15.02/14.77 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
% 15.02/14.77 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
% 15.02/14.77 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__append,axiom,
% 15.02/14.77 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 15.02/14.77 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
% 15.02/14.77 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__Cons,axiom,
% 15.02/14.77 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 15.02/14.77 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__takeI,axiom,
% 15.02/14.77 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__eq,axiom,
% 15.02/14.77 ! [T_b,V_ys_2,V_xs_2] :
% 15.02/14.77 ( V_xs_2 = V_ys_2
% 15.02/14.77 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__lengthD,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__Nil,axiom,
% 15.02/14.77 ! [V_ys_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
% 15.02/14.77 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__Nil2,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
% 15.02/14.77 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_product_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__conv__all__nth,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 15.02/14.77 & ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__nthD,axiom,
% 15.02/14.77 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__nthD2,axiom,
% 15.02/14.77 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 15.02/14.77 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__update__cong,axiom,
% 15.02/14.77 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 15.02/14.77 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2__update__cong2,axiom,
% 15.02/14.77 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.77 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 15.02/14.77 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__product,axiom,
% 15.02/14.77 ! [V_ys,T_b,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_product__list__set,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublists__powset,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__sublists,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublists_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublists_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__set__sublists,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__n__lists,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_enum__the__def,axiom,
% 15.02/14.77 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__n__lists,axiom,
% 15.02/14.77 ! [V_n,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_n__lists__Nil,axiom,
% 15.02/14.77 ! [T_a,V_n] :
% 15.02/14.77 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) )
% 15.02/14.77 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_n__lists_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__n__lists,axiom,
% 15.02/14.77 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__n__lists__elem,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_list__all2I,axiom,
% 15.02/14.77 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
% 15.02/14.77 ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
% 15.02/14.77 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 15.02/14.77 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_all__nth__imp__all__set,axiom,
% 15.02/14.77 ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
% 15.02/14.77 ( ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 15.02/14.77 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 15.02/14.77 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__removeAll__inj__on,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__remdups,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__remdups__leq,axiom,
% 15.02/14.77 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__remdups__id,axiom,
% 15.02/14.77 ! [V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__removeAll,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups__id__iff__distinct,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 15.02/14.77 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__remdups,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__remdups__eq,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 15.02/14.77 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups__remdups,axiom,
% 15.02/14.77 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups__eq__nil__iff,axiom,
% 15.02/14.77 ! [V_x_2,T_b] :
% 15.02/14.77 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_removeAll_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups__eq__nil__right__iff,axiom,
% 15.02/14.77 ! [V_x_2,T_b] :
% 15.02/14.77 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 15.02/14.77 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_removeAll_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs,T_a,V_y,V_x] :
% 15.02/14.77 ( ( V_x = V_y
% 15.02/14.77 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) )
% 15.02/14.77 & ( V_x != V_y
% 15.02/14.77 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_removeAll__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups__map__remdups,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1__remdups,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_removeAll__id,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__remove1__removeAll,axiom,
% 15.02/14.77 ! [V_x,V_xs,T_a] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.77 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__remdups__card__conv,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__removeAll__inj,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 15.02/14.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.77 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__removeAll,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__remdups__concat,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sort__key__simps_I1_J,axiom,
% 15.02/14.77 ! [V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__conv__concat,axiom,
% 15.02/14.77 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat__conv__foldl,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__sort,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__sort,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__sort,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 15.02/14.77 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat__eq__Nil__conv,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] :
% 15.02/14.77 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 15.02/14.77 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_Nil__eq__concat__conv,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] :
% 15.02/14.77 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 15.02/14.77 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__concat,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__concat,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__concat,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sort__key__simps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat__append,axiom,
% 15.02/14.77 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sort__foldl__insort,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat__eq__concat__iff,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 15.02/14.77 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 15.02/14.77 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 15.02/14.77 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat__injective,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.77 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 15.02/14.77 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 15.02/14.77 => ( ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 15.02/14.77 => V_xs_2 = V_ys_2 ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_concat__map__singleton,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_n__lists_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose_Osimps_I3_J,axiom,
% 15.02/14.77 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__aux__filter__head,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__concat,axiom,
% 15.02/14.77 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__sort,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__filter,axiom,
% 15.02/14.77 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__is__subset,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__id__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.77 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sum__length__filter__compl,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__filter__le,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__filter,axiom,
% 15.02/14.77 ! [V_xs_2,V_Q_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_Pa_2)),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__remove1,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remove1__filter__not,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.77 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.77 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__insort__triv,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.77 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition__filter1,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose_Osimps_I1_J,axiom,
% 15.02/14.77 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.77 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.77 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.77 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__append,axiom,
% 15.02/14.77 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__empty__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.77 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_removeAll__filter__not__eq,axiom,
% 15.02/14.77 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_remdups__filter,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_removeAll__filter__not,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.77 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.77 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition__filter2,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__transpose,axiom,
% 15.02/14.77 ! [V_xs_2,T_b,V_i_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__map__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__filter,axiom,
% 15.02/14.77 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__filter__map,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__filter__less,axiom,
% 15.02/14.77 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_partition__filter__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__minus__filter__out,axiom,
% 15.02/14.77 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_filter__in__sublist,axiom,
% 15.02/14.77 ! [V_s_2,V_xs_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.77 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__empty,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 15.02/14.77 <=> ! [B_x] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.77 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__filter__conv__card,axiom,
% 15.02/14.77 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__aux__filter__tail,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose_Opsimps_I3_J,axiom,
% 15.02/14.77 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 15.02/14.77 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose_Opsimps_I2_J,axiom,
% 15.02/14.77 ! [V_xss_2,T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 15.02/14.77 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__shift__lemma__Suc,axiom,
% 15.02/14.77 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_select__weigth__drop__zero,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_pick__drop__zero,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose_Opsimps_I1_J,axiom,
% 15.02/14.77 ! [T_b] :
% 15.02/14.77 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 15.02/14.77 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__max__length,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__aux__max,axiom,
% 15.02/14.77 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldr_Osimps_I1_J,axiom,
% 15.02/14.77 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldr_Osimps_I2_J,axiom,
% 15.02/14.77 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldr__append,axiom,
% 15.02/14.77 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldr__conv__foldl,axiom,
% 15.02/14.77 ! [V_a_2,V_xs_2,T_b] :
% 15.02/14.77 ( class_Groups_Oab__semigroup__add(T_b)
% 15.02/14.77 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldr__map,axiom,
% 15.02/14.77 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__foldr1,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_foldl__foldr1__lemma,axiom,
% 15.02/14.77 ! [V_xs_2,V_a_2,T_b] :
% 15.02/14.77 ( class_Groups_Omonoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__transpose,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__def,axiom,
% 15.02/14.77 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sublist__shift__lemma,axiom,
% 15.02/14.77 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_atLeastLessThan__upt,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_set__upt,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__Suc,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__Suc__append,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__add__eq__append,axiom,
% 15.02/14.77 ! [V_k,V_j,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__rec,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__conv__Cons,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__conv__Nil,axiom,
% 15.02/14.77 ! [V_i,V_j] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 15.02/14.77 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__eq__Nil__conv,axiom,
% 15.02/14.77 ! [V_j_2,V_i_2] :
% 15.02/14.77 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 15.02/14.77 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__0,axiom,
% 15.02/14.77 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_take__upt,axiom,
% 15.02/14.77 ! [V_n,V_m,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
% 15.02/14.77 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__list__of__set__range,axiom,
% 15.02/14.77 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_hd__upt,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_drop__upt,axiom,
% 15.02/14.77 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_distinct__upt,axiom,
% 15.02/14.77 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_length__upt,axiom,
% 15.02/14.77 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__rec__number__of,axiom,
% 15.02/14.77 ! [V_n,V_m] :
% 15.02/14.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 15.02/14.77 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
% 15.02/14.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 15.02/14.77 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_upt__eq__Cons__conv,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 15.02/14.77 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 15.02/14.77 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 15.02/14.77 & V_i_2 = V_x_2
% 15.02/14.77 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_last__upt,axiom,
% 15.02/14.77 ! [V_j,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 15.02/14.77 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__Suc__upt,axiom,
% 15.02/14.77 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_atLeastAtMost__upt,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_atLeast__upt,axiom,
% 15.02/14.77 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__upt,axiom,
% 15.02/14.77 ! [V_j,V_k,V_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_greaterThanAtMost__upt,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_greaterThanLessThan__upt,axiom,
% 15.02/14.77 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_atMost__upto,axiom,
% 15.02/14.77 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_map__nth,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 15.02/14.77
% 15.02/14.77 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 15.02/14.77 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 15.02/14.77 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 15.02/14.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 15.02/14.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_nth__map__upt,axiom,
% 15.02/14.77 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 15.02/14.77 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_transpose__rectangle,axiom,
% 15.02/14.77 ! [V_n_2,T_b,V_xs_2] :
% 15.02/14.77 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 15.02/14.77 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.02/14.77 => ( ! [B_i] :
% 15.02/14.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.77 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 15.02/14.77 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_insort__key__remove1,axiom,
% 15.02/14.77 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_c)
% 15.02/14.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 15.02/14.77 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 15.02/14.77 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted_ONil,axiom,
% 15.02/14.77 ! [T_a] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_a)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__single,axiom,
% 15.02/14.77 ! [V_x,T_a] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_a)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__upt,axiom,
% 15.02/14.77 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__sort,axiom,
% 15.02/14.77 ! [V_xs_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__insort__insert,axiom,
% 15.02/14.77 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__drop,axiom,
% 15.02/14.77 ! [V_n,V_xs,T_a] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_a)
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__upto,axiom,
% 15.02/14.77 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__take,axiom,
% 15.02/14.77 ! [V_n,V_xs,T_a] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_a)
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__remove1,axiom,
% 15.02/14.77 ! [V_a,V_xs,T_a] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_a)
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__tl,axiom,
% 15.02/14.77 ! [V_xs,T_a] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_a)
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 15.02/14.77 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 15.02/14.77
% 15.02/14.77 fof(fact_sorted__insort,axiom,
% 15.02/14.77 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.77 ( class_Orderings_Olinorder(T_b)
% 15.02/14.77 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 15.02/14.78 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__butlast,axiom,
% 15.02/14.78 ! [V_xs,T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted_Oequations_I1_J,axiom,
% 15.02/14.78 ! [T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__many__eq,axiom,
% 15.02/14.78 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 15.02/14.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__many,axiom,
% 15.02/14.78 ! [V_zs,V_y,V_x,T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__remdups,axiom,
% 15.02/14.78 ! [V_l,T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__distinct__set__unique,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 15.02/14.78 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 15.02/14.78 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 15.02/14.78 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__sort__key,axiom,
% 15.02/14.78 ! [V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__insort__insert__key,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__map__remove1,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__insort__key,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 15.02/14.78 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__map__same,axiom,
% 15.02/14.78 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__filter,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__same,axiom,
% 15.02/14.78 ! [V_xs_2,V_g_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__Cons,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 15.02/14.78 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 & ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__append,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 15.02/14.78 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 15.02/14.78 & ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => ! [B_xa] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_filter__insort,axiom,
% 15.02/14.78 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 15.02/14.78 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted_Oequations_I2_J,axiom,
% 15.02/14.78 ! [V_a1_2,V_a2_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 15.02/14.78 <=> ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__list__of__set,axiom,
% 15.02/14.78 ! [V_A_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.78 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 15.02/14.78 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_insort__remove1,axiom,
% 15.02/14.78 ! [V_xs_2,V_a_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__nth__mono,axiom,
% 15.02/14.78 ! [V_j,V_i,V_xs,T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__equals__nth__mono,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 <=> ! [B_j] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => ! [B_i] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_map__sorted__distinct__set__unique,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_c)
% 15.02/14.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 15.02/14.78 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 15.02/14.78 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 15.02/14.78 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 15.02/14.78 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transpose__column,axiom,
% 15.02/14.78 ! [V_i_2,V_xs_2,T_b] :
% 15.02/14.78 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nth__nth__transpose__sorted,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 15.02/14.78 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 15.02/14.78 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inj__on__rev,axiom,
% 15.02/14.78 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_distinct__rev,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 15.02/14.78 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__is__Nil__conv,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.78 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Nil__is__rev__conv,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 15.02/14.78 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev_Osimps_I1_J,axiom,
% 15.02/14.78 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_singleton__rev__conv,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 15.02/14.78 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__singleton__conv,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.78 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 15.02/14.78 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__append,axiom,
% 15.02/14.78 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__concat,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__map,axiom,
% 15.02/14.78 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__filter,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_zip__rev,axiom,
% 15.02/14.78 ! [V_ys,T_b,V_xs,T_a] :
% 15.02/14.78 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
% 15.02/14.78 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_set__rev,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all2__rev,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.78 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 15.02/14.78 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all2__rev1,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 15.02/14.78 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 15.02/14.78 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__rev__ident,axiom,
% 15.02/14.78 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__swap,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.78 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 15.02/14.78 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__is__rev__conv,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,T_b] :
% 15.02/14.78 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 15.02/14.78 <=> V_xs_2 = V_ys_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_listsum__rev,axiom,
% 15.02/14.78 ! [V_xs,T_a] :
% 15.02/14.78 ( class_Groups_Ocomm__monoid__add(T_a)
% 15.02/14.78 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__rev,axiom,
% 15.02/14.78 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_foldl__foldr,axiom,
% 15.02/14.78 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_foldr__foldl,axiom,
% 15.02/14.78 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__eq__Cons__iff,axiom,
% 15.02/14.78 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 15.02/14.78 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 15.02/14.78 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev_Osimps_I2_J,axiom,
% 15.02/14.78 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_hd__rev,axiom,
% 15.02/14.78 ! [T_a,V_xs] :
% 15.02/14.78 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.78 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_last__rev,axiom,
% 15.02/14.78 ! [T_a,V_xs] :
% 15.02/14.78 ( V_xs != c_List_Olist_ONil(T_a)
% 15.02/14.78 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__transpose,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__foldl__cons,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__drop,axiom,
% 15.02/14.78 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__take,axiom,
% 15.02/14.78 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rotate__rev,axiom,
% 15.02/14.78 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__nth,axiom,
% 15.02/14.78 ! [V_xs,T_a,V_n] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.78 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__update,axiom,
% 15.02/14.78 ! [V_y,V_xs,T_a,V_k] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.78 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__rev__nth__mono,axiom,
% 15.02/14.78 ! [V_j,V_i,V_xs,T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_foldr__max__sorted,axiom,
% 15.02/14.78 ! [V_y_2,V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 15.02/14.78 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 15.02/14.78 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 15.02/14.78 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.78 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__transpose__sorted,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 15.02/14.78 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 15.02/14.78 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 15.02/14.78 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transpose__column__length,axiom,
% 15.02/14.78 ! [V_i_2,V_xs_2,T_b] :
% 15.02/14.78 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transpose__transpose,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 15.02/14.78 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 15.02/14.78 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__takeWhile,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__takeWhile__le,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__eq__all__conv,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_set__takeWhileD,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_zip__takeWhile__snd,axiom,
% 15.02/14.78 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_zip__takeWhile__fst,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__map,axiom,
% 15.02/14.78 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__tail,axiom,
% 15.02/14.78 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 15.02/14.78 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.78 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__eq__take,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_distinct__takeWhile,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.78 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_return__list__def,axiom,
% 15.02/14.78 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__append1,axiom,
% 15.02/14.78 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__nth,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 15.02/14.78 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nth__length__takeWhile,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__not__last,axiom,
% 15.02/14.78 ! [T_b,V_xs_2] :
% 15.02/14.78 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.78 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 15.02/14.78 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 15.02/14.78 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 15.02/14.78 ! [V_l] :
% 15.02/14.78 ( c_List_Onat__list(V_l)
% 15.02/14.78 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 15.02/14.78 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_embed__list__def,axiom,
% 15.02/14.78 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__neq__rev,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__neq__rev,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__dropWhile__id,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__dropWhile,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__dropWhile__le,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 15.02/14.78 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.78 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_distinct__dropWhile,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 15.02/14.78 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_hd__dropWhile,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 15.02/14.78 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__map,axiom,
% 15.02/14.78 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__append1,axiom,
% 15.02/14.78 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 15.02/14.78 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 15.02/14.78 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 15.02/14.78 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__eq__drop,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__nth,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 15.02/14.78 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_listsum__map__filter,axiom,
% 15.02/14.78 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 15.02/14.78 ( class_Groups_Omonoid__add(T_c)
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 15.02/14.78 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted__nth__monoI,axiom,
% 15.02/14.78 ! [V_xs,T_a] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_a)
% 15.02/14.78 => ( ! [B_i,B_j] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__eq__filter,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 15.02/14.78 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 15.02/14.78 ( ! [B_i] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 15.02/14.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__takeWhile__less__P__nth,axiom,
% 15.02/14.78 ! [V_xs_2,T_b,V_Pa_2,V_j_2] :
% 15.02/14.78 ( ! [B_i] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted_Osimps,axiom,
% 15.02/14.78 ! [V_a_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 15.02/14.78 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 15.02/14.78 | ? [B_xs,B_x] :
% 15.02/14.78 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 15.02/14.78 & ! [B_xa] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_List_Oinsert__def,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 15.02/14.78 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_not__in__set__insert,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_insert__remdups,axiom,
% 15.02/14.78 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_distinct__insert,axiom,
% 15.02/14.78 ! [V_x,V_xs,T_a] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 15.02/14.78 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__set__insert,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_List_Oset__insert,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_insert__Nil,axiom,
% 15.02/14.78 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_maps__def,axiom,
% 15.02/14.78 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_concat__map__maps,axiom,
% 15.02/14.78 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_maps__simps_I2_J,axiom,
% 15.02/14.78 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_maps__simps_I1_J,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_distinct__concat,axiom,
% 15.02/14.78 ! [V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 15.02/14.78 => ( ! [B_ys] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 15.02/14.78 => ( ! [B_ys] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => ! [B_zs] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => ( B_ys != B_zs
% 15.02/14.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 15.02/14.78 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measures__lesseq,axiom,
% 15.02/14.78 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_wf__measures,axiom,
% 15.02/14.78 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__measures_I1_J,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measures__def,axiom,
% 15.02/14.78 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measures__less,axiom,
% 15.02/14.78 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__measures_I2_J,axiom,
% 15.02/14.78 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 15.02/14.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 15.02/14.78 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 15.02/14.78 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_foldl__apply,axiom,
% 15.02/14.78 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
% 15.02/14.78 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_order__fun_I2_J,axiom,
% 15.02/14.78 ! [V_g_2,V_f_2,T_b,T_c] :
% 15.02/14.78 ( ( class_Orderings_Oorder(T_c)
% 15.02/14.78 & class_Enum_Oenum(T_b) )
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 15.02/14.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 15.02/14.78 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2)))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_enum__ex__prod__def,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b,T_c] :
% 15.02/14.78 ( ( class_Enum_Oenum(T_c)
% 15.02/14.78 & class_Enum_Oenum(T_b) )
% 15.02/14.78 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
% 15.02/14.78 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_enum__ex,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] :
% 15.02/14.78 ( class_Enum_Oenum(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
% 15.02/14.78 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_exists__code,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] :
% 15.02/14.78 ( class_Enum_Oenum(T_b)
% 15.02/14.78 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 15.02/14.78 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_zip__obtain__same__length,axiom,
% 15.02/14.78 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 15.02/14.78 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_pos__not__random__dseq__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dropWhile__append2,axiom,
% 15.02/14.78 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all2__all__nthI,axiom,
% 15.02/14.78 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
% 15.02/14.78 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 15.02/14.78 => ( ! [B_n] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
% 15.02/14.78 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_finite__sorted__distinct__unique,axiom,
% 15.02/14.78 ! [V_A_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.78 => ? [B_x] :
% 15.02/14.78 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 15.02/14.78 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 15.02/14.78 & ! [B_y] :
% 15.02/14.78 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 15.02/14.78 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 15.02/14.78 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 15.02/14.78 => B_y = B_x ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_takeWhile__append2,axiom,
% 15.02/14.78 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_insort__is__Cons,axiom,
% 15.02/14.78 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_c)
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 15.02/14.78 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Cons__eq__filter__iff,axiom,
% 15.02/14.78 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)
% 15.02/14.78 <=> ? [B_us,B_vs] :
% 15.02/14.78 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 15.02/14.78 & ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 15.02/14.78 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_filter__eq__Cons__iff,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
% 15.02/14.78 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 15.02/14.78 <=> ? [B_us,B_vs] :
% 15.02/14.78 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 15.02/14.78 & ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 15.02/14.78 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_order__fun_I1_J,axiom,
% 15.02/14.78 ! [V_g_2,V_f_2,T_b,T_c] :
% 15.02/14.78 ( ( class_Orderings_Oorder(T_c)
% 15.02/14.78 & class_Enum_Oenum(T_b) )
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 15.02/14.78 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_all__code,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] :
% 15.02/14.78 ( class_Enum_Oenum(T_b)
% 15.02/14.78 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 15.02/14.78 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_enum__all,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] :
% 15.02/14.78 ( class_Enum_Oenum(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
% 15.02/14.78 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_enum__all__prod__def,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b,T_c] :
% 15.02/14.78 ( ( class_Enum_Oenum(T_c)
% 15.02/14.78 & class_Enum_Oenum(T_b) )
% 15.02/14.78 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
% 15.02/14.78 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ball__nth,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sorted_OCons,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.78 ( class_Orderings_Olinorder(T_b)
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 15.02/14.78 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 15.02/14.78 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__length,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ? [B_n] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__set__conv__decomp,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__simps_I2_J,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__append,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 15.02/14.78 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__iff,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__rev,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 15.02/14.78 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__simps_I1_J,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 15.02/14.78 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__set__conv__decomp__first,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 <=> ? [B_ys] :
% 15.02/14.78 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__set__conv__decomp__last,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 <=> ? [B_ys,B_zs] :
% 15.02/14.78 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__length,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ! [B_n] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measure__function__int,axiom,
% 15.02/14.78 c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__simps_I2_J,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__append,axiom,
% 15.02/14.78 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 15.02/14.78 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measure__size,axiom,
% 15.02/14.78 ! [T_b] :
% 15.02/14.78 ( class_Nat_Osize(T_b)
% 15.02/14.78 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_is__measure_Osimps,axiom,
% 15.02/14.78 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_is__measure_Oequations,axiom,
% 15.02/14.78 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_is__measure_Ointros,axiom,
% 15.02/14.78 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__iff,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measure__fst,axiom,
% 15.02/14.78 ! [T_c,V_f_2,T_b] :
% 15.02/14.78 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 15.02/14.78 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_measure__snd,axiom,
% 15.02/14.78 ! [T_c,V_f_2,T_b] :
% 15.02/14.78 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 15.02/14.78 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__rev,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 15.02/14.78 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__simps_I1_J,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 15.02/14.78 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Ball__set__list__all,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__iff__raw,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex1__simps_I2_J,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 15.02/14.78 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transfer__morphism__int__nat,axiom,
% 15.02/14.78 c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex1__simps_I1_J,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bool_Osize_I3_J,axiom,
% 15.02/14.78 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bool_Osize_I4_J,axiom,
% 15.02/14.78 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex1__iff,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.78 & ! [B_y] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 15.02/14.78 => B_y = B_x ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 15.02/14.78 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 15.02/14.78 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.78 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) )
% 15.02/14.78 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.78 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 15.02/14.78 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 15.02/14.78 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.78 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) )
% 15.02/14.78 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 15.02/14.78 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 15.02/14.78 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 15.02/14.78 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_pos__empty__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_neg__bind__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 15.02/14.78 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_neg__map__def,axiom,
% 15.02/14.78 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_neg__single__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_pos__bind__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 15.02/14.78 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_pos__map__def,axiom,
% 15.02/14.78 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_pos__single__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__splice,axiom,
% 15.02/14.78 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_splice_Osimps_I3_J,axiom,
% 15.02/14.78 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_splice_Osimps_I1_J,axiom,
% 15.02/14.78 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 15.02/14.78
% 15.02/14.78 fof(fact_splice__Nil2,axiom,
% 15.02/14.78 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 15.02/14.78
% 15.02/14.78 fof(fact_splice_Osimps_I2_J,axiom,
% 15.02/14.78 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Opos__single__def,axiom,
% 15.02/14.78 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_acyclicP__converse,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
% 15.02/14.78 <=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_converse__meet,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_converse__join,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_converse__pred__comp,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep__noteq,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 15.02/14.78 <=> V_x_2 != V_y_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversepD,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep_Ointros,axiom,
% 15.02/14.78 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep_Oequations,axiom,
% 15.02/14.78 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep__iff,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep__conversep,axiom,
% 15.02/14.78 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep__eq,axiom,
% 15.02/14.78 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 15.02/14.78
% 15.02/14.78 fof(fact_conversep__converse__eq,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_,axiom,
% 15.02/14.78 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_tl__replicate,axiom,
% 15.02/14.78 ! [V_x,T_a,V_n] :
% 15.02/14.78 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__length__filter,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_length__replicate,axiom,
% 15.02/14.78 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ).
% 15.02/14.78
% 15.02/14.78 fof(fact_map__replicate__const,axiom,
% 15.02/14.78 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__app__Cons__same,axiom,
% 15.02/14.78 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__Suc,axiom,
% 15.02/14.78 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rev__replicate,axiom,
% 15.02/14.78 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_take__replicate,axiom,
% 15.02/14.78 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_drop__replicate,axiom,
% 15.02/14.78 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_hd__replicate,axiom,
% 15.02/14.78 ! [V_x,T_a,V_n] :
% 15.02/14.78 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_last__replicate,axiom,
% 15.02/14.78 ! [V_x,T_a,V_n] :
% 15.02/14.78 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_zip__replicate,axiom,
% 15.02/14.78 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Bex__set__replicate,axiom,
% 15.02/14.78 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 15.02/14.78 ( ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 15.02/14.78 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Ball__set__replicate,axiom,
% 15.02/14.78 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 15.02/14.78 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__eq__replicate,axiom,
% 15.02/14.78 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 15.02/14.78 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 15.02/14.78 <=> ( V_m_2 = V_n_2
% 15.02/14.78 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => V_x_2 = V_y_2 ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nth__replicate,axiom,
% 15.02/14.78 ! [V_x,T_a,V_n,V_i] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 15.02/14.78 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__add,axiom,
% 15.02/14.78 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_append__replicate__commute,axiom,
% 15.02/14.78 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_filter__replicate,axiom,
% 15.02/14.78 ! [V_n_2,T_b,V_x_2,V_Pa_2] :
% 15.02/14.78 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 15.02/14.78 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_concat__replicate__trivial,axiom,
% 15.02/14.78 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__0,axiom,
% 15.02/14.78 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_empty__replicate,axiom,
% 15.02/14.78 ! [V_x_2,V_n_2,T_b] :
% 15.02/14.78 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 15.02/14.78 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__empty,axiom,
% 15.02/14.78 ! [V_x_2,V_n_2,T_b] :
% 15.02/14.78 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 15.02/14.78 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_map__replicate,axiom,
% 15.02/14.78 ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__set__replicate,axiom,
% 15.02/14.78 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
% 15.02/14.78 <=> ( V_x_2 = V_y_2
% 15.02/14.78 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_replicate__append__same,axiom,
% 15.02/14.78 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_map__replicate__trivial,axiom,
% 15.02/14.78 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_set__replicate,axiom,
% 15.02/14.78 ! [V_x_2,T_b,V_n_2] :
% 15.02/14.78 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_set__replicate__conv__if,axiom,
% 15.02/14.78 ! [V_x_2,T_b,V_n_2] :
% 15.02/14.78 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 15.02/14.78 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_set__replicate__Suc,axiom,
% 15.02/14.78 ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_small__lazy__list_Osimps,axiom,
% 15.02/14.78 ! [V_d_2,T_b] :
% 15.02/14.78 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 15.02/14.78 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_eq__comp__r,axiom,
% 15.02/14.78 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_small__lazy__prod__def,axiom,
% 15.02/14.78 ! [V_d,T_b,T_a] :
% 15.02/14.78 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 15.02/14.78 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 15.02/14.78 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Opos__union__def,axiom,
% 15.02/14.78 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 15.02/14.78 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__01,axiom,
% 15.02/14.78 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Oinject,axiom,
% 15.02/14.78 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 15.02/14.78 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
% 15.02/14.78 <=> ( V_a_2 = V_a_H_2
% 15.02/14.78 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_pos__union__def,axiom,
% 15.02/14.78 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 15.02/14.78 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_small__lazy_H_Osimps,axiom,
% 15.02/14.78 ! [V_i,V_d] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 15.02/14.78 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 15.02/14.78 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_small__lazy_H_Opsimps,axiom,
% 15.02/14.78 ! [V_i_2,V_d_2] :
% 15.02/14.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
% 15.02/14.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 15.02/14.78 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 15.02/14.78 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_small__lazy__int__def,axiom,
% 15.02/14.78 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_small__lazy_H_Opinduct,axiom,
% 15.02/14.78 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 15.02/14.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 15.02/14.78 => ( ! [B_d,B_i] :
% 15.02/14.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
% 15.02/14.78 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_size__code,axiom,
% 15.02/14.78 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence__size__code,axiom,
% 15.02/14.78 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_seq__case,axiom,
% 15.02/14.78 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_yieldn__def,axiom,
% 15.02/14.78 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 15.02/14.78 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_refl__on__INTER,axiom,
% 15.02/14.78 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 15.02/14.78 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 15.02/14.78 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_List_Omember__def,axiom,
% 15.02/14.78 ! [V_x_2,V_xs_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_member__rec_I2_J,axiom,
% 15.02/14.78 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_member__set,axiom,
% 15.02/14.78 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_member__rec_I1_J,axiom,
% 15.02/14.78 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
% 15.02/14.78 <=> ( V_x_2 = V_y_2
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__set__member,axiom,
% 15.02/14.78 ! [V_xs_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex1__iff__raw,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.78 & ! [B_y] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 15.02/14.78 => B_y = B_x ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_setsum__UNION__zero,axiom,
% 15.02/14.78 ! [V_f_2,V_S_2,T_b,T_c] :
% 15.02/14.78 ( class_Groups_Ocomm__monoid__add(T_c)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 15.02/14.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 15.02/14.78 => ( ! [B_T1] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 15.02/14.78 => ! [B_T2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 15.02/14.78 => ( B_T1 != B_T2
% 15.02/14.78 => ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 15.02/14.78 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 15.02/14.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_THE__default__def,axiom,
% 15.02/14.78 ! [V_d_2,T_b,V_Pa_2] :
% 15.02/14.78 ( ( ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.78 & ! [B_y] :
% 15.02/14.78 ( hBOOL(hAPP(V_Pa_2,B_y))
% 15.02/14.78 => B_y = B_x ) )
% 15.02/14.78 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) )
% 15.02/14.78 & ( ~ ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(V_Pa_2,B_x))
% 15.02/14.78 & ! [B_y] :
% 15.02/14.78 ( hBOOL(hAPP(V_Pa_2,B_y))
% 15.02/14.78 => B_y = B_x ) )
% 15.02/14.78 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_SUP2__E,axiom,
% 15.02/14.78 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 15.02/14.78 => ~ ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.78 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_INF2__I,axiom,
% 15.02/14.78 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_finite__maxlen,axiom,
% 15.02/14.78 ! [V_M_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 15.02/14.78 => ? [B_n] :
% 15.02/14.78 ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 15.02/14.78 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 15.02/14.78 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__02,axiom,
% 15.02/14.78 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 15.02/14.78 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 15.02/14.78 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 15.02/14.78 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__iff__all__interval__int,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_Pa_2] :
% 15.02/14.78 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 15.02/14.78 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_Pa_2] :
% 15.02/14.78 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 15.02/14.78 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_all__interval__int__def,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_Pa_2] :
% 15.02/14.78 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 15.02/14.78 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Random_Osimps,axiom,
% 15.02/14.78 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 15.02/14.78 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) )
% 15.02/14.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 15.02/14.78 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 15.02/14.78 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Random__Sequence_Oempty__def,axiom,
% 15.02/14.78 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Random__Sequence_Osingle__def,axiom,
% 15.02/14.78 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Random__Sequence_Omap__def,axiom,
% 15.02/14.78 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_exE__realizer,axiom,
% 15.02/14.78 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 15.02/14.78 => ( ! [B_x,B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 15.02/14.78 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 15.02/14.78 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Image__Collect__split,axiom,
% 15.02/14.78 ! [V_A_2,V_Pa_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lexord__trans,axiom,
% 15.02/14.78 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
% 15.02/14.78 => ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__less__than,axiom,
% 15.02/14.78 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__lex__prod,axiom,
% 15.02/14.78 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_R1_2)
% 15.02/14.78 => ( c_Relation_Otrans(T_c,V_R2_2)
% 15.02/14.78 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transD,axiom,
% 15.02/14.78 ! [V_ca_2,V_b_2,V_a_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),V_r_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__def,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 <=> ! [B_x,B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 15.02/14.78 => ! [B_z] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__rtrancl,axiom,
% 15.02/14.78 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__finite__psubset,axiom,
% 15.02/14.78 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__Id__on,axiom,
% 15.02/14.78 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trancl__id,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__trancl,axiom,
% 15.02/14.78 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__Id,axiom,
% 15.02/14.78 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lexord__transI,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__converse,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.78 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bex__empty,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] :
% 15.02/14.78 ~ ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_listrel__trans,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_finite__Collect__bex,axiom,
% 15.02/14.78 ! [V_Q_2,T_c,V_A_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bex__UNIV,axiom,
% 15.02/14.78 ! [V_Pa_2,T_b] :
% 15.02/14.78 ( ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__Int,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => ( c_Relation_Otrans(T_b,V_s_2)
% 15.02/14.78 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_SUPR__bool__eq,axiom,
% 15.02/14.78 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__O__subset,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__reflclI,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__inv__image,axiom,
% 15.02/14.78 ! [V_f_2,T_c,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Union__eq,axiom,
% 15.02/14.78 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__iff__raw,axiom,
% 15.02/14.78 ! [V_xs_2,V_Pa_2,T_b] :
% 15.02/14.78 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 15.02/14.78 <=> ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Bex__set__list__ex,axiom,
% 15.02/14.78 ! [V_Pa_2,V_xs_2,T_b] :
% 15.02/14.78 ( ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_UN__eq,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_INT__eq,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Sup__fun__def,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,T_c,T_b] :
% 15.02/14.78 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.78 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Sup__apply,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,T_c,T_b] :
% 15.02/14.78 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.78 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Inf__fun__def,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,T_c,T_b] :
% 15.02/14.78 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.78 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Inf__apply,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,T_c,T_b] :
% 15.02/14.78 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 15.02/14.78 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_max__extp_Ointros,axiom,
% 15.02/14.78 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 15.02/14.78 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 15.02/14.78 => ? [B_xa] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 15.02/14.78 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 15.02/14.78 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transp__def,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Predicate_Otransp(T_b,V_r_2)
% 15.02/14.78 <=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_transpE,axiom,
% 15.02/14.78 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Predicate_Otransp(T_b,V_r_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equivpE,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 15.02/14.78 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 15.02/14.78 => ( c_Predicate_Osymp(T_b,V_R_2)
% 15.02/14.78 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equivpI,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Predicate_Oreflp(T_b,V_R_2)
% 15.02/14.78 => ( c_Predicate_Osymp(T_b,V_R_2)
% 15.02/14.78 => ( c_Predicate_Otransp(T_b,V_R_2)
% 15.02/14.78 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sympE,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Predicate_Osymp(T_b,V_r_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equivp__reflp__symp__transp,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 15.02/14.78 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 15.02/14.78 & c_Predicate_Osymp(T_b,V_R_2)
% 15.02/14.78 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_max__extp_Osimps,axiom,
% 15.02/14.78 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 15.02/14.78 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 15.02/14.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 15.02/14.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 15.02/14.78 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 & ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 15.02/14.78 => ? [B_xa] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 15.02/14.78 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_trans__diff__Id,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => ( c_Relation_Oantisym(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__Id__on,axiom,
% 15.02/14.78 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__empty,axiom,
% 15.02/14.78 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__converse,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.78 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__Id,axiom,
% 15.02/14.78 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__subset,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 15.02/14.78 => ( c_Relation_Oantisym(T_b,V_s_2)
% 15.02/14.78 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisymD,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Oantisym(T_b,V_r_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
% 15.02/14.78 => V_a_2 = V_b_2 ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__def,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Oantisym(T_b,V_r_2)
% 15.02/14.78 <=> ! [B_x,B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 15.02/14.78 => B_x = B_y ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_antisym__reflcl,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 15.02/14.78 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_fun__lub__def,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__trans__comp__subset,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_symD,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__def,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 <=> ! [B_x,B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__rtrancl,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__Id__on,axiom,
% 15.02/14.78 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__trancl,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__Un,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => ( c_Relation_Osym(T_b,V_s_2)
% 15.02/14.78 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__Id,axiom,
% 15.02/14.78 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__conv__converse__eq,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__converse,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 15.02/14.78 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_listrel__sym,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__Int,axiom,
% 15.02/14.78 ! [V_s_2,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => ( c_Relation_Osym(T_b,V_s_2)
% 15.02/14.78 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__Un__converse,axiom,
% 15.02/14.78 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__inv__image,axiom,
% 15.02/14.78 ! [V_f_2,T_c,V_r_2,T_b] :
% 15.02/14.78 ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_sym__Int__converse,axiom,
% 15.02/14.78 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equiv__def,axiom,
% 15.02/14.78 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 15.02/14.78 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 15.02/14.78 & c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equivI,axiom,
% 15.02/14.78 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 15.02/14.78 => ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => ( c_Relation_Otrans(T_b,V_r_2)
% 15.02/14.78 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equivE,axiom,
% 15.02/14.78 ! [V_r_2,V_A_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 15.02/14.78 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 15.02/14.78 => ( c_Relation_Osym(T_b,V_r_2)
% 15.02/14.78 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_symp__def,axiom,
% 15.02/14.78 ! [V_r_2,T_b] :
% 15.02/14.78 ( c_Predicate_Osymp(T_b,V_r_2)
% 15.02/14.78 <=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivpI,axiom,
% 15.02/14.78 ! [T_b,V_R_2] :
% 15.02/14.78 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 15.02/14.78 => ( c_Predicate_Osymp(T_b,V_R_2)
% 15.02/14.78 => ( c_Predicate_Otransp(T_b,V_R_2)
% 15.02/14.78 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivp__refl__symp__transp,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 15.02/14.78 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 15.02/14.78 & c_Predicate_Osymp(T_b,V_R_2)
% 15.02/14.78 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivp__transp,axiom,
% 15.02/14.78 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivp__symp,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivp__def,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 15.02/14.78 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 15.02/14.78 & ! [B_x,B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 15.02/14.78 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 15.02/14.78 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 15.02/14.78 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_equivp__implies__part__equivp,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 15.02/14.78 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivpE,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 15.02/14.78 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 15.02/14.78 => ( c_Predicate_Osymp(T_b,V_R_2)
% 15.02/14.78 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_part__equivp__typedef,axiom,
% 15.02/14.78 ! [V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 15.02/14.78 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__o__cancel,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inj__iff,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__id,axiom,
% 15.02/14.78 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__f__f,axiom,
% 15.02/14.78 ! [V_x_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__f__eq,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 15.02/14.78 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__f__eq,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.78 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 15.02/14.78 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__f__f,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 15.02/14.78 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__injective,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 15.02/14.78 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 15.02/14.78 => V_x_2 = V_y_2 ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__into,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_f__inv__into__f,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 15.02/14.78 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_surj__iff__all,axiom,
% 15.02/14.78 ! [V_f_2,T_b,T_c] :
% 15.02/14.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_surj__f__inv__f,axiom,
% 15.02/14.78 ! [V_y_2,V_f_2,T_b,T_c] :
% 15.02/14.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_image__surj__f__inv__f,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_b,T_c] :
% 15.02/14.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_image__inv__into__cancel,axiom,
% 15.02/14.78 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 15.02/14.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__def,axiom,
% 15.02/14.78 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__def,axiom,
% 15.02/14.78 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_o__inv__o__cancel,axiom,
% 15.02/14.78 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_surj__imp__inj__inv,axiom,
% 15.02/14.78 ! [V_f_2,T_b,T_c] :
% 15.02/14.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__image__comp,axiom,
% 15.02/14.78 ! [V_X_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_image__inv__f__f,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inj__imp__surj__inv,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__image__cancel,axiom,
% 15.02/14.78 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inj__on__inv__into,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 15.02/14.78 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__comp,axiom,
% 15.02/14.78 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 15.02/14.78 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 15.02/14.78 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_surj__iff,axiom,
% 15.02/14.78 ! [V_f_2,T_b,T_c] :
% 15.02/14.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inj__transfer,axiom,
% 15.02/14.78 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => ( ! [B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_fold__image__UN__disjoint,axiom,
% 15.02/14.78 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 15.02/14.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 15.02/14.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 15.02/14.78 => ! [B_xa] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 15.02/14.78 => ( B_x != B_xa
% 15.02/14.78 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
% 15.02/14.78 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nat__of__induct,axiom,
% 15.02/14.78 ! [V_Pa_2,V_y_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 15.02/14.78 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nat__of__cases,axiom,
% 15.02/14.78 ! [V_y_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 15.02/14.78 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_of__nat__induct,axiom,
% 15.02/14.78 ! [V_x_2,V_Pa_2] :
% 15.02/14.78 ( ! [B_y] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_of__nat__cases,axiom,
% 15.02/14.78 ! [V_x_2] :
% 15.02/14.78 ~ ! [B_y] :
% 15.02/14.78 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 15.02/14.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 15.02/14.78 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_beyond__def,axiom,
% 15.02/14.78 ! [V_l,V_k] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 15.02/14.78 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 15.02/14.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 15.02/14.78 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_beyond__zero,axiom,
% 15.02/14.78 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 15.02/14.78 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__image__Collect__eq,axiom,
% 15.02/14.78 ! [V_Pa_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_curry__def,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_curryI,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 15.02/14.78 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__id,axiom,
% 15.02/14.78 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__inv__into,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__into__inv__into__eq,axiom,
% 15.02/14.78 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 15.02/14.78 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inv__inv__eq,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__imp__bij__inv,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_o__inv__distrib,axiom,
% 15.02/14.78 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__image__INT,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__comp__iff2,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
% 15.02/14.78 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 15.02/14.78 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__trans,axiom,
% 15.02/14.78 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__comp__iff,axiom,
% 15.02/14.78 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 15.02/14.78 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 15.02/14.78 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__comp,axiom,
% 15.02/14.78 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_curryE,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 15.02/14.78 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_curryD,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 15.02/14.78 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_curry__conv,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_finite__vimage__iff,axiom,
% 15.02/14.78 ! [V_F_2,V_h_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 15.02/14.78 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__image__Compl__eq,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__def,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bijI,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 15.02/14.78 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__combine,axiom,
% 15.02/14.78 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 15.02/14.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__Disj__Un,axiom,
% 15.02/14.78 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 15.02/14.78 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 15.02/14.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 15.02/14.78 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 15.02/14.78 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__subset,axiom,
% 15.02/14.78 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 15.02/14.78 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__is__surj,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__imp__surj,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__def,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.78 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inj__on__imp__bij__betw,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.78 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__imp__inj__on,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__is__inj,axiom,
% 15.02/14.78 ! [V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__the__inv__into,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__same__card,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__empty2,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__empty1,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 15.02/14.78 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__finite,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.78 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_BIJ,axiom,
% 15.02/14.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 15.02/14.78 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 15.02/14.78 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__betw__id__iff,axiom,
% 15.02/14.78 ! [V_B_2,V_A_2,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 15.02/14.78 <=> V_A_2 = V_B_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__id,axiom,
% 15.02/14.78 ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_split__curry,axiom,
% 15.02/14.78 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_curry__split,axiom,
% 15.02/14.78 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ).
% 15.02/14.78
% 15.02/14.78 fof(fact_vimage__subset__eq,axiom,
% 15.02/14.78 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bij__vimage__eq__inv__image,axiom,
% 15.02/14.78 ! [V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 15.02/14.78 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 15.02/14.78 ! [V_M_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 15.02/14.78 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Cantor__Bernstein,axiom,
% 15.02/14.78 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 15.02/14.78 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 15.02/14.78 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_ex__bij__betw__nat__finite,axiom,
% 15.02/14.78 ! [V_M_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 15.02/14.78 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_ex__bij__betw__finite__nat,axiom,
% 15.02/14.78 ! [V_M_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 15.02/14.78 => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_refl__on__UNION,axiom,
% 15.02/14.78 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 15.02/14.78 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 15.02/14.78 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bex__reg__eqv,axiom,
% 15.02/14.78 ! [V_Pa_2,V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 15.02/14.78 => ( ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_in__respects,axiom,
% 15.02/14.78 ! [V_R_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Respects__def,axiom,
% 15.02/14.78 ! [V_x_2,V_R_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_bex__reg__right,axiom,
% 15.02/14.78 ! [V_Pa_2,V_Q_2,V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(V_Q_2,B_x))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 15.02/14.78 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 15.02/14.78 => ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_babs__reg__eqv,axiom,
% 15.02/14.78 ! [V_Pa_2,T_c,V_R_2,T_b] :
% 15.02/14.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 15.02/14.78 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_Babs__def,axiom,
% 15.02/14.78 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 15.02/14.78 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_wf__weak__decr__stable,axiom,
% 15.02/14.78 ! [V_r_2,V_f_2,T_b] :
% 15.02/14.78 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 15.02/14.78 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 15.02/14.78 => ? [B_i] :
% 15.02/14.78 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_INT__anti__mono,axiom,
% 15.02/14.78 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_INT__greatest,axiom,
% 15.02/14.78 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 15.02/14.78 ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_rtrancl__induct2,axiom,
% 15.02/14.78 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
% 15.02/14.78 => ( ! [B_a,B_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 15.02/14.78 => ! [B_aa,B_ba] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_converse__rtranclE2,axiom,
% 15.02/14.78 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 15.02/14.78 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
% 15.02/14.78 => ~ ! [B_a,B_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
% 15.02/14.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_converse__rtrancl__induct2,axiom,
% 15.02/14.78 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
% 15.02/14.78 => ( ! [B_a,B_b,B_aa,B_ba] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
% 15.02/14.78 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_congruent2I_H,axiom,
% 15.02/14.78 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 15.02/14.78 ( ! [B_y1,B_z1] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
% 15.02/14.78 => ! [B_y2,B_z2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
% 15.02/14.78 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 15.02/14.78 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_congruentI,axiom,
% 15.02/14.78 ! [T_c,V_f_2,V_r_2,T_b] :
% 15.02/14.78 ( ! [B_y,B_z] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 15.02/14.78 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 15.02/14.78 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__03,axiom,
% 15.02/14.78 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_all__interval__nat__def,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_Pa_2] :
% 15.02/14.78 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
% 15.02/14.78 <=> ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
% 15.02/14.78 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__04,axiom,
% 15.02/14.78 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__all__iff__all__interval__nat,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_Pa_2] :
% 15.02/14.78 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 15.02/14.78 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 15.02/14.78 ! [V_j_2,V_i_2,V_Pa_2] :
% 15.02/14.78 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 15.02/14.78 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__05,axiom,
% 15.02/14.78 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_folding__image_Ocong,axiom,
% 15.02/14.78 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 15.02/14.78 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 15.02/14.78 => ( ! [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 15.02/14.78 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 15.02/14.78 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__06,axiom,
% 15.02/14.78 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact__07,axiom,
% 15.02/14.78 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_New__DSequence_Opos__map__def,axiom,
% 15.02/14.78 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_power__dvd__imp__le,axiom,
% 15.02/14.78 ! [V_n,V_m,V_i] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_Oorder__refl,axiom,
% 15.02/14.78 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__0__right,axiom,
% 15.02/14.78 ! [V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__1__left,axiom,
% 15.02/14.78 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult__cancel,axiom,
% 15.02/14.78 ! [V_n,V_m,V_k] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nat__mult__dvd__cancel1,axiom,
% 15.02/14.78 ! [V_n_2,V_m_2,V_k_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_setprod__dvd__setprod__subset,axiom,
% 15.02/14.78 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 15.02/14.78 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 15.02/14.78 & class_Rings_Odvd(T_c) )
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inf__period_I4_J,axiom,
% 15.02/14.78 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 15.02/14.78 ( ( class_Rings_Ocomm__ring(T_b)
% 15.02/14.78 & class_Rings_Odvd(T_b) )
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 15.02/14.78 => ! [B_x,B_k] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_inf__period_I3_J,axiom,
% 15.02/14.78 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 15.02/14.78 ( ( class_Rings_Ocomm__ring(T_b)
% 15.02/14.78 & class_Rings_Odvd(T_b) )
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 15.02/14.78 => ! [B_x,B_k] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__div__div__eq__mult,axiom,
% 15.02/14.78 ! [V_d_2,V_b_2,V_ca_2,V_a_2,T_b] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_b)
% 15.02/14.78 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 15.02/14.78 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))
% 15.02/14.78 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_ca_2)
% 15.02/14.78 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__div__eq__mult,axiom,
% 15.02/14.78 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_b)
% 15.02/14.78 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 15.02/14.78 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_ca_2
% 15.02/14.78 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_unity__coeff__ex,axiom,
% 15.02/14.78 ! [V_l_2,V_Pa_2,T_b] :
% 15.02/14.78 ( ( class_Rings_Odvd(T_b)
% 15.02/14.78 & class_Rings_Osemiring__0(T_b) )
% 15.02/14.78 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 15.02/14.78 <=> ? [B_x] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))
% 15.02/14.78 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult__div__cancel,axiom,
% 15.02/14.78 ! [V_b,V_a,T_a] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_div__mult__swap,axiom,
% 15.02/14.78 ! [V_a,V_b,V_c,T_a] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 15.02/14.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__div__mult__self,axiom,
% 15.02/14.78 ! [V_b,V_a,T_a] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__div__mult,axiom,
% 15.02/14.78 ! [V_c,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_div__mult__div__if__dvd,axiom,
% 15.02/14.78 ! [V_w,V_z,V_x,V_y,T_a] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 15.02/14.78 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult__cancel__left,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 15.02/14.78 ( class_Rings_Oidom(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 15.02/14.78 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult__cancel__right,axiom,
% 15.02/14.78 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 15.02/14.78 ( class_Rings_Oidom(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
% 15.02/14.78 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__triv__left,axiom,
% 15.02/14.78 ! [V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__triv__right,axiom,
% 15.02/14.78 ! [V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult2,axiom,
% 15.02/14.78 ! [V_c,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult,axiom,
% 15.02/14.78 ! [V_b,V_c,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_mult__dvd__mono,axiom,
% 15.02/14.78 ! [V_d,V_c,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvdI,axiom,
% 15.02/14.78 ! [V_k,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Odvd(T_a)
% 15.02/14.78 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult__left,axiom,
% 15.02/14.78 ! [V_c,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__mult__right,axiom,
% 15.02/14.78 ! [V_c,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 15.02/14.78 ! [V_n_2,V_m_2,V_k_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 15.02/14.78 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__setprod,axiom,
% 15.02/14.78 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_c)
% 15.02/14.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 15.02/14.78 ! [V_ca_2,V_b_2,V_a_2] :
% 15.02/14.78 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 15.02/14.78 <=> ( V_a_2 = V_b_2
% 15.02/14.78 & V_b_2 = V_ca_2 ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 15.02/14.78 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2] :
% 15.02/14.78 ( V_a_2 = V_b_2
% 15.02/14.78 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2] :
% 15.02/14.78 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 15.02/14.78 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2] :
% 15.02/14.78 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 15.02/14.78 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 15.02/14.78 ! [V_a_2,V_b_2] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 15.02/14.78 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 15.02/14.78 ! [V_k_2,V_l_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 15.02/14.78 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 15.02/14.78 ! [V_a_2,V_b_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 15.02/14.78 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 15.02/14.78 ! [V_k_2,V_l_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 15.02/14.78 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 15.02/14.78 ! [V_l_2,V_k_2] :
% 15.02/14.78 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 15.02/14.78 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2] :
% 15.02/14.78 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 15.02/14.78 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 15.02/14.78 ! [V_l_2,V_k_2] :
% 15.02/14.78 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 15.02/14.78 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2] :
% 15.02/14.78 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 15.02/14.78 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__diff__nat,axiom,
% 15.02/14.78 ! [V_n,V_m,V_k] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__diff,axiom,
% 15.02/14.78 ! [V_z,V_y,V_x,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__ring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__minus__iff,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,T_b] :
% 15.02/14.78 ( class_Rings_Ocomm__ring__1(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_minus__dvd__iff,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2,T_b] :
% 15.02/14.78 ( class_Rings_Ocomm__ring__1(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__neg__div,axiom,
% 15.02/14.78 ! [V_x,V_y,T_a] :
% 15.02/14.78 ( class_Divides_Oring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.02/14.78 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__div__neg,axiom,
% 15.02/14.78 ! [V_x,V_y,T_a] :
% 15.02/14.78 ( class_Divides_Oring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 15.02/14.78 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__eq__mod__eq__0,axiom,
% 15.02/14.78 ! [V_b_2,V_a_2,T_b] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 15.02/14.78 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__imp__mod__0,axiom,
% 15.02/14.78 ! [V_b,V_a,T_a] :
% 15.02/14.78 ( class_Divides_Osemiring__div(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 15.02/14.78 ! [V_d_2,V_ca_2,V_b_2,V_a_2] :
% 15.02/14.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2)))
% 15.02/14.78 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 15.02/14.78 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2))
% 15.02/14.78 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 15.02/14.78 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ca_2)) )
% 15.02/14.78 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 15.02/14.78 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_d_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__abs__iff,axiom,
% 15.02/14.78 ! [V_k_2,V_m_2,T_b] :
% 15.02/14.78 ( class_Rings_Olinordered__idom(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_abs__dvd__iff,axiom,
% 15.02/14.78 ! [V_k_2,V_m_2,T_b] :
% 15.02/14.78 ( class_Rings_Olinordered__idom(T_b)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 15.02/14.78 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__if__abs__eq,axiom,
% 15.02/14.78 ! [V_k,V_l,T_a] :
% 15.02/14.78 ( class_Rings_Olinordered__idom(T_a)
% 15.02/14.78 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__trans,axiom,
% 15.02/14.78 ! [V_c,V_b,V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd__refl,axiom,
% 15.02/14.78 ! [V_a,T_a] :
% 15.02/14.78 ( class_Rings_Ocomm__semiring__1(T_a)
% 15.02/14.78 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_Oless__asym,axiom,
% 15.02/14.78 ! [V_y,V_x] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.02/14.78 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 15.02/14.78
% 15.02/14.78 fof(fact_dvd_Oless__trans,axiom,
% 15.02/14.78 ! [V_z,V_y,V_x] :
% 15.02/14.78 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 15.02/14.78 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 15.02/14.78 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 15.02/14.78 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 15.02/14.78
% 15.02/14.78 %----Arity declarations (222)
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 15.02/14.78 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Obounded__lattice(T_1)
% 15.02/14.78 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 15.02/14.78 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Obounded__lattice(T_1)
% 15.02/14.78 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Obounded__lattice(T_1)
% 15.02/14.78 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Olattice(T_1)
% 15.02/14.78 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Olattice(T_1)
% 15.02/14.78 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Odistrib__lattice(T_1)
% 15.02/14.78 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Oboolean__algebra(T_1)
% 15.02/14.78 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Orderings_Opreorder,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Orderings_Opreorder(T_1)
% 15.02/14.78 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Finite__Set_Ofinite(T_2)
% 15.02/14.78 & class_Finite__Set_Ofinite(T_1) )
% 15.02/14.78 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Lattices_Olattice,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Lattices_Olattice(T_1)
% 15.02/14.78 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Orderings_Oorder,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Orderings_Oorder(T_1)
% 15.02/14.78 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Orderings_Otop,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Orderings_Otop(T_1)
% 15.02/14.78 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Orderings_Oord,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Orderings_Oord(T_1)
% 15.02/14.78 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Orderings_Obot,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Orderings_Obot(T_1)
% 15.02/14.78 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Groups_Ouminus,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Groups_Ouminus(T_1)
% 15.02/14.78 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Groups_Ominus,axiom,
% 15.02/14.78 ! [T_2,T_1] :
% 15.02/14.78 ( class_Groups_Ominus(T_1)
% 15.02/14.78 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_fun__Enum_Oenum,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Enum_Oenum(T_2)
% 15.02/14.78 & class_Enum_Oenum(T_1) )
% 15.02/14.78 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_Com_Ocom) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 15.02/14.78 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 15.02/14.78 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 15.02/14.78 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 15.02/14.78 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 15.02/14.78 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 15.02/14.78 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 15.02/14.78 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 15.02/14.78 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 15.02/14.78 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 15.02/14.78 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 15.02/14.78 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 15.02/14.78 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 15.02/14.78 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 15.02/14.78 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 15.02/14.78 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 15.02/14.78 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 15.02/14.78 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 15.02/14.78 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 15.02/14.78 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 15.02/14.78 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 15.02/14.78 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 15.02/14.78 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 15.02/14.78 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 15.02/14.78 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 15.02/14.78 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 15.02/14.78 class_Orderings_Opreorder(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 15.02/14.78 class_Orderings_Olinorder(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 15.02/14.78 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 15.02/14.78 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 15.02/14.78 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 15.02/14.78 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 15.02/14.78 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 15.02/14.78 class_Lattices_Olattice(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 15.02/14.78 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 15.02/14.78 class_Divides_Oring__div(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 15.02/14.78 class_Rings_Omult__zero(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 15.02/14.78 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 15.02/14.78 class_Orderings_Oorder(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 15.02/14.78 class_Int_Oring__char__0(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 15.02/14.78 class_Int_Onumber__ring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 15.02/14.78 class_Rings_Osemiring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 15.02/14.78 class_Orderings_Oord(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 15.02/14.78 class_Groups_Ouminus(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 15.02/14.78 class_Groups_Osgn__if(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 15.02/14.78 class_Groups_Oabs__if(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 15.02/14.78 class_Rings_Oring__1(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 15.02/14.78 class_Groups_Ominus(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Power_Opower,axiom,
% 15.02/14.78 class_Power_Opower(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 15.02/14.78 class_Groups_Ozero(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oring,axiom,
% 15.02/14.78 class_Rings_Oring(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 15.02/14.78 class_Rings_Oidom(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Int_Onumber,axiom,
% 15.02/14.78 class_Int_Onumber(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Groups_Oone,axiom,
% 15.02/14.78 class_Groups_Oone(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 15.02/14.78 class_Rings_Odvd(tc_Int_Oint) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 15.02/14.78 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 15.02/14.78 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 15.02/14.78 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 15.02/14.78 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 15.02/14.78 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 15.02/14.78 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 15.02/14.78 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 15.02/14.78 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 15.02/14.78 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 15.02/14.78 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 15.02/14.78 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 15.02/14.78 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 15.02/14.78 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 15.02/14.78 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 15.02/14.78 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 15.02/14.78 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 15.02/14.78 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 15.02/14.78 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 15.02/14.78 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 15.02/14.78 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 15.02/14.78 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 15.02/14.78 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 15.02/14.78 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 15.02/14.78 class_Lattices_Olattice(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 15.02/14.78 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 15.02/14.78 class_Orderings_Oorder(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 15.02/14.78 class_Rings_Osemiring(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 15.02/14.78 class_Orderings_Oord(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 15.02/14.78 class_Orderings_Obot(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 15.02/14.78 class_Groups_Ominus(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Power_Opower,axiom,
% 15.02/14.78 class_Power_Opower(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 15.02/14.78 class_Groups_Ozero(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 15.02/14.78 class_Int_Onumber(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 15.02/14.78 class_Groups_Oone(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 15.02/14.78 class_Rings_Odvd(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_Nat_Onat) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 15.02/14.78 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 15.02/14.78 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 15.02/14.78 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 15.02/14.78 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 15.02/14.78 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 15.02/14.78 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 15.02/14.78 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 15.02/14.78 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 15.02/14.78 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 15.02/14.78 class_Lattices_Olattice(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 15.02/14.78 class_Orderings_Oorder(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 15.02/14.78 class_Orderings_Otop(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 15.02/14.78 class_Orderings_Oord(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 15.02/14.78 class_Orderings_Obot(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 15.02/14.78 class_Groups_Ouminus(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 15.02/14.78 class_Groups_Ominus(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 15.02/14.78 class_Enum_Oenum(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_HOL_Obool) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_Com_Ostate) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 15.02/14.78 ! [T_1] :
% 15.02/14.78 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 15.02/14.78 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_List__Olist__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Finite__Set_Ofinite(T_2)
% 15.02/14.78 & class_Finite__Set_Ofinite(T_1) )
% 15.02/14.78 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_sum__Enum_Oenum,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Enum_Oenum(T_2)
% 15.02/14.78 & class_Enum_Oenum(T_1) )
% 15.02/14.78 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_sum__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 15.02/14.78 ! [T_1] :
% 15.02/14.78 ( class_Finite__Set_Ofinite(T_1)
% 15.02/14.78 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 15.02/14.78 ! [T_1] :
% 15.02/14.78 ( class_Enum_Oenum(T_1)
% 15.02/14.78 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 15.02/14.78 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 15.02/14.78 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Finite__Set_Ofinite(T_2)
% 15.02/14.78 & class_Finite__Set_Ofinite(T_1) )
% 15.02/14.78 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_prod__Enum_Oenum,axiom,
% 15.02/14.78 ! [T_1,T_2] :
% 15.02/14.78 ( ( class_Enum_Oenum(T_2)
% 15.02/14.78 & class_Enum_Oenum(T_1) )
% 15.02/14.78 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_prod__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 15.02/14.78 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 15.02/14.78 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 15.02/14.78 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 15.02/14.78 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 15.02/14.78 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 15.02/14.78 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 15.02/14.78 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 15.02/14.78 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 15.02/14.78 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 15.02/14.78 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 15.02/14.78 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 15.02/14.78 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 15.02/14.78 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 15.02/14.78 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 15.02/14.78 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 15.02/14.78 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 15.02/14.78 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 15.02/14.78 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 15.02/14.78 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 15.02/14.78 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 15.02/14.78 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 15.02/14.78 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 15.02/14.78 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 15.02/14.78 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 15.02/14.78 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 15.02/14.78 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 15.02/14.78 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 15.02/14.78 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 15.02/14.78 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 15.02/14.78 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 15.02/14.78 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 15.02/14.78 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 15.02/14.78 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 15.02/14.78 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 15.02/14.78 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 15.02/14.78
% 15.02/14.78 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 15.02/14.78 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 15.02/14.78
% 15.02/14.78 %----Helper facts (20)
% 15.02/14.78 fof(help_c__COMBI__1,axiom,
% 15.02/14.78 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__COMBK__1,axiom,
% 15.02/14.78 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__COMBB__1,axiom,
% 15.02/14.78 ! [V_R_2,V_Q_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__COMBC__1,axiom,
% 15.02/14.78 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__COMBS__1,axiom,
% 15.02/14.78 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fequal__1,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 15.02/14.78 | V_x_2 = V_y_2 ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fequal__2,axiom,
% 15.02/14.78 ! [V_y_2,V_x_2] :
% 15.02/14.78 ( V_x_2 != V_y_2
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fFalse__1,axiom,
% 15.02/14.78 ~ hBOOL(c_fFalse) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fTrue__1,axiom,
% 15.02/14.78 hBOOL(c_fTrue) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fNot__1,axiom,
% 15.02/14.78 ! [V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 15.02/14.78 | ~ hBOOL(V_Pa_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fNot__2,axiom,
% 15.02/14.78 ! [V_Pa_2] :
% 15.02/14.78 ( ~ ~ hBOOL(V_Pa_2)
% 15.02/14.78 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fconj__1,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(V_Pa_2)
% 15.02/14.78 | ~ hBOOL(V_Q_2)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fconj__2,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
% 15.02/14.78 | hBOOL(V_Pa_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fconj__3,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
% 15.02/14.78 | hBOOL(V_Q_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fdisj__1,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(V_Pa_2)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fdisj__2,axiom,
% 15.02/14.78 ! [V_Pa_2,V_Q_2] :
% 15.02/14.78 ( ~ hBOOL(V_Q_2)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fdisj__3,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2))
% 15.02/14.78 | hBOOL(V_Pa_2)
% 15.02/14.78 | hBOOL(V_Q_2) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fimplies__1,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( hBOOL(V_Pa_2)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fimplies__2,axiom,
% 15.02/14.78 ! [V_Pa_2,V_Q_2] :
% 15.02/14.78 ( ~ hBOOL(V_Q_2)
% 15.02/14.78 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ).
% 15.02/14.78
% 15.02/14.78 fof(help_c__fimplies__3,axiom,
% 15.02/14.78 ! [V_Q_2,V_Pa_2] :
% 15.02/14.78 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2))
% 15.02/14.78 | ~ hBOOL(V_Pa_2)
% 15.02/14.78 | hBOOL(V_Q_2) ) ).
% 15.02/14.78
% 15.02/14.78 %----Conjectures (1)
% 15.02/14.78 fof(conj_0,conjecture,
% 15.02/14.78 ( ? [B_Z,B_x1] : v_P(B_Z,B_x1)
% 15.02/14.78 => ? [B_P_H,B_Q_H] : c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ) ).
% 15.02/14.78
% 15.02/14.78 %------------------------------------------------------------------------------
% 15.02/14.78 %-------------------------------------------
% 15.02/14.78 % Proof found
% 15.02/14.78 % SZS status Theorem for theBenchmark
% 15.02/14.78 % SZS output start Proof
% 15.02/14.79 %ClaNum:10486(EqnAxiom:3121)
% 15.02/14.79 %VarNum:71283(SingletonVarNum:20610)
% 15.02/14.79 %MaxLitNum:8
% 15.02/14.79 %MaxfuncDepth:13
% 15.02/14.79 %SharedTerms:1016
% 15.02/14.79 %goalClause: 3333 4757
% 15.02/14.79 %singleGoalClaCount:2
% 15.02/14.79 [3125]P1(a915)
% 15.02/14.79 [3126]P1(a919)
% 15.02/14.79 [3127]P106(a187)
% 15.02/14.79 [3128]P107(a915)
% 15.02/14.79 [3129]P107(a919)
% 15.02/14.79 [3130]P107(a1)
% 15.02/14.79 [3131]P107(a99)
% 15.02/14.79 [3132]P108(a915)
% 15.02/14.79 [3133]P108(a919)
% 15.02/14.79 [3134]P108(a1)
% 15.02/14.79 [3135]P108(a99)
% 15.02/14.79 [3136]P109(a919)
% 15.02/14.79 [3137]P109(a1)
% 15.02/14.79 [3138]P109(a99)
% 15.02/14.79 [3139]P110(a915)
% 15.02/14.79 [3140]P110(a919)
% 15.02/14.79 [3141]P110(a1)
% 15.02/14.79 [3142]P110(a99)
% 15.02/14.79 [3143]P2(a915)
% 15.02/14.79 [3144]P2(a919)
% 15.02/14.79 [3145]P2(a1)
% 15.02/14.79 [3146]P3(a915)
% 15.02/14.79 [3147]P101(a915)
% 15.02/14.79 [3148]P101(a919)
% 15.02/14.79 [3149]P101(a1)
% 15.02/14.79 [3150]P4(a915)
% 15.02/14.79 [3151]P4(a919)
% 15.02/14.79 [3152]P4(a1)
% 15.02/14.79 [3153]P4(a99)
% 15.02/14.79 [3154]P5(a915)
% 15.02/14.79 [3155]P5(a922)
% 15.02/14.79 [3156]P80(a1)
% 15.02/14.79 [3157]P69(a1)
% 15.02/14.79 [3158]P111(a1)
% 15.02/14.79 [3159]P70(a919)
% 15.02/14.79 [3160]P70(a1)
% 15.02/14.79 [3161]P70(a99)
% 15.02/14.79 [3162]P102(a915)
% 15.02/14.79 [3163]P102(a919)
% 15.02/14.79 [3164]P102(a1)
% 15.02/14.79 [3165]P99(a915)
% 15.02/14.79 [3166]P99(a919)
% 15.02/14.79 [3167]P99(a1)
% 15.02/14.79 [3168]P72(a919)
% 15.02/14.79 [3169]P72(a1)
% 15.02/14.79 [3170]P72(a99)
% 15.02/14.79 [3171]P84(a919)
% 15.02/14.79 [3172]P84(a1)
% 15.02/14.79 [3173]P84(a99)
% 15.02/14.79 [3174]P73(a919)
% 15.02/14.79 [3175]P73(a1)
% 15.02/14.79 [3176]P73(a99)
% 15.02/14.79 [3177]P74(a919)
% 15.02/14.79 [3178]P74(a1)
% 15.02/14.79 [3179]P74(a99)
% 15.02/14.79 [3180]P71(a919)
% 15.02/14.79 [3181]P71(a1)
% 15.02/14.79 [3182]P71(a99)
% 15.02/14.79 [3183]P85(a919)
% 15.02/14.79 [3184]P85(a1)
% 15.02/14.79 [3185]P85(a99)
% 15.02/14.79 [3186]P86(a919)
% 15.02/14.79 [3187]P86(a1)
% 15.02/14.79 [3188]P86(a99)
% 15.02/14.79 [3189]P76(a1)
% 15.02/14.79 [3190]P112(a1)
% 15.02/14.79 [3191]P113(a919)
% 15.02/14.79 [3192]P113(a1)
% 15.02/14.79 [3193]P113(a99)
% 15.02/14.79 [3194]P120(a1)
% 15.02/14.79 [3195]P140(a919)
% 15.02/14.79 [3196]P140(a1)
% 15.02/14.79 [3197]P141(a919)
% 15.02/14.79 [3198]P141(a1)
% 15.02/14.79 [3199]P141(a99)
% 15.02/14.79 [3200]P114(a919)
% 15.02/14.79 [3201]P114(a1)
% 15.02/14.79 [3202]P114(a99)
% 15.02/14.79 [3203]P77(a919)
% 15.02/14.79 [3204]P77(a1)
% 15.02/14.79 [3205]P77(a99)
% 15.02/14.79 [3206]P81(a919)
% 15.02/14.79 [3207]P81(a1)
% 15.02/14.79 [3208]P81(a99)
% 15.02/14.79 [3209]P82(a919)
% 15.02/14.79 [3210]P82(a1)
% 15.02/14.79 [3211]P82(a99)
% 15.02/14.79 [3212]P127(a919)
% 15.02/14.79 [3213]P127(a1)
% 15.02/14.79 [3214]P127(a99)
% 15.02/14.79 [3215]P6(a915)
% 15.02/14.79 [3216]P130(a1)
% 15.02/14.79 [3217]P88(a919)
% 15.02/14.79 [3218]P88(a1)
% 15.02/14.79 [3219]P88(a99)
% 15.02/14.79 [3220]P83(a919)
% 15.02/14.79 [3221]P83(a1)
% 15.02/14.79 [3222]P83(a99)
% 15.02/14.79 [3223]P78(a1)
% 15.02/14.79 [3224]P133(a919)
% 15.02/14.79 [3225]P133(a1)
% 15.02/14.79 [3226]P133(a99)
% 15.02/14.79 [3227]P142(a1)
% 15.02/14.79 [3228]P134(a919)
% 15.02/14.79 [3229]P134(a1)
% 15.02/14.79 [3230]P134(a99)
% 15.02/14.79 [3231]P145(a919)
% 15.02/14.79 [3232]P145(a1)
% 15.02/14.79 [3233]P145(a99)
% 15.02/14.79 [3234]P89(a919)
% 15.02/14.79 [3235]P89(a1)
% 15.02/14.79 [3236]P89(a99)
% 15.02/14.79 [3237]P128(a1)
% 15.02/14.79 [3238]P129(a1)
% 15.02/14.79 [3239]P136(a919)
% 15.02/14.79 [3240]P136(a1)
% 15.02/14.79 [3241]P136(a99)
% 15.02/14.79 [3242]P138(a919)
% 15.02/14.79 [3243]P138(a1)
% 15.02/14.79 [3244]P138(a99)
% 15.02/14.79 [3245]P137(a919)
% 15.02/14.79 [3246]P137(a1)
% 15.02/14.79 [3247]P137(a99)
% 15.02/14.79 [3248]P121(a919)
% 15.02/14.79 [3249]P121(a1)
% 15.02/14.79 [3250]P121(a99)
% 15.02/14.79 [3251]P135(a919)
% 15.02/14.79 [3252]P135(a1)
% 15.02/14.79 [3253]P135(a99)
% 15.02/14.79 [3254]P131(a919)
% 15.02/14.79 [3255]P131(a1)
% 15.02/14.79 [3256]P131(a99)
% 15.02/14.79 [3257]P132(a1)
% 15.02/14.79 [3258]P143(a1)
% 15.02/14.79 [3259]P93(a1)
% 15.02/14.79 [3260]P94(a1)
% 15.02/14.79 [3261]P95(a919)
% 15.02/14.79 [3262]P95(a1)
% 15.02/14.79 [3263]P95(a99)
% 15.02/14.79 [3264]P103(a919)
% 15.02/14.79 [3265]P103(a1)
% 15.02/14.79 [3266]P103(a99)
% 15.02/14.79 [3267]P146(a919)
% 15.02/14.79 [3268]P146(a1)
% 15.02/14.79 [3269]P146(a99)
% 15.02/14.79 [3270]P87(a1)
% 15.02/14.79 [3271]P139(a1)
% 15.02/14.79 [3272]P62(a919)
% 15.02/14.79 [3273]P62(a1)
% 15.02/14.79 [3274]P62(a99)
% 15.02/14.79 [3275]P63(a1)
% 15.02/14.79 [3276]P96(a915)
% 15.02/14.79 [3277]P90(a915)
% 15.02/14.79 [3278]P90(a1)
% 15.02/14.79 [3279]P122(a1)
% 15.02/14.79 [3280]P115(a1)
% 15.02/14.79 [3281]P144(a1)
% 15.02/14.79 [3282]P75(a1)
% 15.02/14.79 [3283]P116(a919)
% 15.02/14.79 [3284]P116(a1)
% 15.02/14.79 [3285]P116(a99)
% 15.02/14.79 [3286]P147(a919)
% 15.02/14.79 [3287]P147(a1)
% 15.02/14.79 [3288]P147(a99)
% 15.02/14.79 [3289]P91(a1)
% 15.02/14.79 [3290]P117(a915)
% 15.02/14.79 [3291]P100(a915)
% 15.02/14.79 [3292]P79(a919)
% 15.02/14.79 [3293]P79(a1)
% 15.02/14.79 [3294]P79(a99)
% 15.02/14.79 [3295]P118(a919)
% 15.02/14.79 [3296]P92(a919)
% 15.02/14.79 [3297]P92(a1)
% 15.02/14.79 [3298]P92(a99)
% 15.02/14.79 [3299]P64(a915)
% 15.02/14.79 [3300]P64(a922)
% 15.02/14.79 [3301]P105(a915)
% 15.02/14.79 [3302]P105(a919)
% 15.02/14.79 [3303]P105(a916)
% 15.02/14.79 [3304]P105(a99)
% 15.02/14.79 [3305]P105(a922)
% 15.02/14.79 [3306]P105(a917)
% 15.02/14.79 [3307]P105(a322)
% 15.02/14.79 [3308]P104(a1)
% 15.02/14.79 [3309]P104(a922)
% 15.02/14.79 [3310]P123(a919)
% 15.02/14.79 [3311]P123(a1)
% 15.02/14.79 [3312]P123(a99)
% 15.02/14.79 [3313]P119(a1)
% 15.02/14.79 [3314]P98(a915)
% 15.02/14.79 [3330]P39(a919,a239)
% 15.02/14.79 [3331]P39(a919,a316)
% 15.02/14.79 [3332]P40(a919,a239)
% 15.02/14.79 [3333]P150(a323,a856)
% 15.02/14.79 [4674]~E(a97,a82)
% 15.02/14.79 [4675]~P106(a238)
% 15.02/14.79 [3122]E(f2(a1),a82)
% 15.02/14.79 [3123]E(f3(a99),a4)
% 15.02/14.79 [3124]E(f100(a99),a5)
% 15.02/14.79 [3315]E(f101(a919),f188(a919))
% 15.02/14.79 [3316]E(f189(a919),f2(a919))
% 15.02/14.79 [3317]E(f28(a25),f2(a919))
% 15.02/14.79 [3318]E(f110(a919),f233(a919))
% 15.02/14.79 [3319]E(f102(a1),f31(a1))
% 15.02/14.79 [3320]E(f83(a238),f2(a919))
% 15.02/14.79 [3321]E(f83(a187),f2(a919))
% 15.02/14.79 [3322]P7(f77(a1))
% 15.02/14.79 [3323]P7(f2(a1))
% 15.02/14.79 [3380]P39(f926(a919,a919),a32)
% 15.02/14.79 [3725]E(f318(a919,a919,a239,a239),a32)
% 15.02/14.79 [4676]~E(f77(a1),f2(a1))
% 15.02/14.79 [3324]E(f6(f2(a99)),f2(a919))
% 15.02/14.79 [3325]E(f111(f2(a919)),f2(a919))
% 15.02/14.79 [3335]E(f857(f78(a1),a82),a82)
% 15.02/14.79 [3338]E(f857(a112,f2(a919)),f77(a919))
% 15.02/14.79 [3339]E(f857(a104,f77(a1)),f77(a919))
% 15.02/14.79 [3340]E(f857(a5,f77(a919)),f77(a99))
% 15.02/14.79 [3342]E(f857(a5,f2(a919)),f2(a99))
% 15.02/14.79 [3344]E(f857(f103(a1),a82),f2(a1))
% 15.02/14.79 [3345]E(f857(f103(a99),a82),f2(a99))
% 15.02/14.79 [3346]E(f857(a104,f2(a1)),f2(a919))
% 15.02/14.79 [3347]E(f857(f190(a915),a238),f2(a919))
% 15.02/14.79 [3348]E(f857(f190(a915),a187),f2(a919))
% 15.02/14.79 [3349]E(f857(f190(a916),a25),f2(a919))
% 15.02/14.79 [3350]E(f857(f103(a919),a82),f2(a919))
% 15.02/14.79 [3356]E(f857(f78(a1),f77(a1)),a97)
% 15.02/14.79 [3364]E(f857(f190(a99),f2(a99)),f2(a919))
% 15.02/14.79 [3365]E(f857(f100(a1),f77(a919)),f77(a1))
% 15.02/14.79 [3366]E(f857(f100(a1),f2(a919)),f2(a1))
% 15.02/14.79 [3367]E(f857(f78(a1),f2(a1)),f2(a1))
% 15.02/14.79 [3377]E(f857(a104,f77(a1)),f857(a112,f2(a919)))
% 15.02/14.79 [3378]E(f317(f926(a919,a919),a32),a33)
% 15.02/14.79 [3379]E(f319(f926(a919,a919),a32),a68)
% 15.02/14.79 [3406]E(f857(f281(a919),f2(a919)),f189(f927(a919,a915)))
% 15.02/14.79 [3407]E(f857(f282(a919),f2(a919)),f241(f927(a919,a915)))
% 15.02/14.79 [3415]P42(f189(f927(a1,a915)))
% 15.02/14.79 [3449]E(f857(f857(f3(a99),f2(a99)),f77(a99)),f2(a99))
% 15.02/14.79 [3524]P106(f857(f857(f235(a1),a97),f2(a1)))
% 15.02/14.79 [3548]P106(f857(f857(f234(a1),f2(a1)),f77(a1)))
% 15.02/14.79 [3550]P106(f857(f857(f235(a1),f2(a1)),f77(a1)))
% 15.02/14.79 [3756]E(f857(f857(f288(a919,a919,a919),a316),f306(a919,a316)),a239)
% 15.02/14.79 [3795]P43(a1,a919,a104,f857(f234(a1),f2(a1)))
% 15.02/14.79 [3799]E(f857(f857(f38(a919,f927(a919,a915)),f241(f927(a919,a915))),f303(a919)),f189(f927(a919,a915)))
% 15.02/14.79 [3800]E(f857(f857(f39(a919,f927(a919,a915)),f241(f927(a919,a915))),f281(a919)),f241(f927(a919,a915)))
% 15.02/14.79 [3801]E(f857(f857(f39(a919,f927(a919,a915)),f241(f927(a919,a915))),f300(a919)),f241(f927(a919,a915)))
% 15.02/14.79 [3802]E(f857(f857(f39(a919,f927(a919,a915)),f241(f927(a919,a915))),f282(a919)),f241(f927(a919,a915)))
% 15.02/14.79 [3818]P26(a919,a1,f100(a1),f241(f927(a919,a915)))
% 15.02/14.79 [3832]P43(a919,a1,f100(a1),f857(f18(a915,a919),a187))
% 15.02/14.79 [3969]E(f857(f72(a919,a99,a1,a5),a104),f103(a99))
% 15.02/14.79 [4192]P58(a99,a919,a22,a5,f241(f927(a919,a915)))
% 15.02/14.79 [4198]P58(a1,f927(f926(a919,a919),a915),a106,a88,a98)
% 15.02/14.79 [4452]E(f257(a1,a1,a1,a1,f31(a1),f78(a1)),a50)
% 15.02/14.79 [4691]~E(f857(f103(a1),a97),f857(f103(a1),a82))
% 15.02/14.79 [4692]~P106(f857(a194,f77(a1)))
% 15.02/14.79 [4693]~P106(f857(a194,f2(a1)))
% 15.02/14.79 [4730]~P106(f857(f857(f235(a1),a82),f2(a1)))
% 15.02/14.79 [3398]E(f857(f857(f3(a1),a97),a97),a82)
% 15.02/14.79 [3413]E(f857(f100(a1),f857(a112,f2(a919))),f77(a1))
% 15.02/14.79 [3478]E(f857(f34(a922),f241(f927(a922,a915))),f77(a919))
% 15.02/14.79 [3498]P106(f857(a194,f857(f103(a1),a97)))
% 15.02/14.79 [3500]P106(f857(f857(f234(a1),a97),a82))
% 15.02/14.79 [3502]P106(f857(f857(f235(a1),a97),a82))
% 15.02/14.79 [3559]E(f857(f857(f308(a919),f2(a919)),f189(f927(a919,a915))),f857(f300(a919),f2(a919)))
% 15.02/14.79 [3614]P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),a82)))
% 15.02/14.79 [3626]E(f857(f309(a919,a919,a112),f241(f927(a919,a915))),f857(f303(a919),f2(a919)))
% 15.02/14.79 [3663]P9(f926(a919,a919),f241(f927(f926(a919,a919),a915)),a108)
% 15.02/14.79 [3976]E(f857(f72(a919,a1,a99,f100(a1)),a22),a24)
% 15.02/14.79 [4037]P39(a919,f857(f261(f926(a919,a919)),f857(f256(a919,a919,a915),f235(a919))))
% 15.02/14.79 [4721]~P106(f857(a194,f857(f103(a1),a82)))
% 15.02/14.79 [4722]~P106(f857(f857(f234(a1),a82),a97))
% 15.02/14.79 [4723]~P106(f857(f857(f235(a1),a82),a82))
% 15.02/14.79 [4724]~P106(f857(f857(f235(a1),a82),a97))
% 15.02/14.79 [4725]~P106(f857(f857(f235(a1),a97),a97))
% 15.02/14.79 [4736]~P106(f857(f60(a919),f241(f927(a919,a915))))
% 15.02/14.79 [4737]~P106(f857(f60(a1),f241(f927(a1,a915))))
% 15.02/14.79 [4619]E(f857(f256(a1,a1,a915),f857(f857(f10(f927(a1,a915),f927(a1,a915),a1),f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f235(a1),f2(a1))))),f857(f857(f9(a1,a1,f927(a1,a915)),f857(f857(f10(f927(a1,f927(a1,a915)),f927(a1,f927(a1,a915)),a1),f9(a1,a1,a915)),f857(f857(f10(f927(a1,a1),f927(a1,f927(a1,a915)),a1),f857(f10(a1,f927(a1,a915),a1),a324)),a218))),f77(a1)))),a214)
% 15.02/14.79 [3700]E(f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97),f857(f78(a1),a97))
% 15.02/14.79 [3738]E(f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97),f857(f857(f3(a1),a82),a97))
% 15.02/14.79 [3902]E(f857(f857(f59(f926(a919,a919)),f241(f927(f926(a919,a919),a915))),a108),a98)
% 15.02/14.79 [3931]E(f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f77(a1))
% 15.02/14.79 [3932]E(f857(f103(a99),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f77(a99))
% 15.02/14.79 [3933]E(f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f77(a919))
% 15.02/14.79 [3937]E(f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(a112,f2(a919)))
% 15.02/14.79 [4320]E(f857(f857(f110(f927(f926(f926(a919,a919),f926(a919,a919)),a915)),a32),f306(f926(a919,a919),f189(f927(f926(f926(a919,a919),f926(a919,a919)),a915)))),a70)
% 15.02/14.79 [4386]E(f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),f77(a919)),f2(a919))),f189(f927(f926(a919,a919),a915))))),f77(a1))
% 15.02/14.79 [4387]E(f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),f2(a919)),f2(a919))),f189(f927(f926(a919,a919),a915))))),f2(a1))
% 15.02/14.79 [4400]E(f857(f261(f926(a919,a919)),f857(f256(a919,a919,a915),f857(f857(f10(a919,f927(a919,a915),a919),f857(f9(a919,a919,a915),a324)),a112))),a316)
% 15.02/14.79 [4372]E(f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),f857(a112,f857(a112,f2(a919))))
% 15.02/14.79 [4375]E(f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),f857(f857(f79(a919),f77(a919)),f77(a919)))
% 15.02/14.79 [4376]E(f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),f857(f34(a915),f241(f927(a915,a915))))
% 15.02/14.79 [4439]P7(f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))
% 15.02/14.79 [4508]P28(f927(f926(a919,a919),a915),f857(f857(f251(f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915),f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915)),a33),a69))
% 15.02/14.79 [4509]P28(f927(f926(a919,a919),a915),f857(f857(f251(f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915),f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915)),a68),a71))
% 15.02/14.79 [4550]E(f857(f857(f110(f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915)),f319(f926(a919,a919),a70)),f857(f857(f308(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),f189(f927(f926(a919,a919),a915))),f189(f927(f926(a919,a919),a915)))),f189(f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915)))),a71)
% 15.02/14.79 [4551]E(f857(f857(f110(f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915)),f317(f926(a919,a919),a70)),f857(f857(f308(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),f189(f927(f926(a919,a919),a915))),f189(f927(f926(a919,a919),a915)))),f189(f927(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a915)))),a69)
% 15.02/14.79 [4441]E(f857(a104,f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(a112,f857(a112,f2(a919))))
% 15.02/14.79 [4486]E(f857(f100(a1),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))
% 15.02/14.79 [4520]P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [4521]E(f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97)),f857(a112,f857(a112,f857(a112,f2(a919)))))
% 15.02/14.79 [4565]P7(f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97)))
% 15.02/14.79 [4591]E(f857(f100(a1),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97)))
% 15.02/14.79 [4604]P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))))
% 15.02/14.79 [3334]P8(x33341,a324)
% 15.02/14.79 [3726]P26(a919,a919,a112,x37261)
% 15.02/14.79 [3326]P105(f918(x33261))
% 15.02/14.79 [3327]P105(f923(x33271))
% 15.02/14.79 [3328]P105(f920(x33281))
% 15.02/14.79 [3329]P105(f921(x33291))
% 15.02/14.79 [3351]P39(a1,f105(x33511))
% 15.02/14.79 [3352]P39(a1,f107(x33521))
% 15.02/14.79 [3402]P39(f927(x34021,a915),f313(x34021))
% 15.02/14.79 [3403]P40(f927(x34031,a915),f313(x34031))
% 15.02/14.79 [3427]E(f242(x34271,x34271,a324),a324)
% 15.02/14.79 [3442]E(f44(a1,x34421,x34421),f2(a1))
% 15.02/14.79 [3495]P15(x34951,f927(x34951,a915),f308(x34951))
% 15.02/14.79 [4678]~E(f857(a112,x46781),x46781)
% 15.02/14.79 [4688]~E(f857(a112,x46881),f2(a919))
% 15.02/14.79 [3336]E(f857(f190(a919),x33361),x33361)
% 15.02/14.79 [3337]E(f857(f103(a1),x33371),x33371)
% 15.02/14.79 [3353]E(f857(a88,f327(x33531)),x33531)
% 15.02/14.79 [3354]E(f857(a5,f579(x33541)),x33541)
% 15.02/14.79 [3355]E(f240(x33551,f2(a99)),f2(a99))
% 15.02/14.79 [3368]E(f114(x33681,f113(x33681)),f113(x33681))
% 15.02/14.79 [3369]E(f152(x33691,f113(x33691)),f113(x33691))
% 15.02/14.79 [3374]E(f857(f167(x33741),f113(x33741)),f113(x33741))
% 15.02/14.79 [3375]E(f857(f171(x33751),f113(x33751)),f113(x33751))
% 15.02/14.79 [3376]E(f857(f168(x33761),f113(x33761)),f113(x33761))
% 15.02/14.79 [3381]E(f857(f103(a1),x33811),f857(f102(a1),x33811))
% 15.02/14.79 [3382]E(f857(a88,f857(a106,x33821)),x33821)
% 15.02/14.79 [3384]E(f857(a5,f857(a22,x33841)),x33841)
% 15.02/14.79 [3385]E(f857(a22,f857(a5,x33851)),x33851)
% 15.02/14.79 [3387]P7(f857(f100(a1),x33871))
% 15.02/14.79 [3396]E(f857(f190(f920(x33961)),f113(x33961)),f2(a919))
% 15.02/14.79 [3397]E(f857(f190(f921(x33971)),f119(x33971)),f2(a919))
% 15.02/14.79 [3418]E(f857(f857(f3(a919),x34181),f2(a919)),x34181)
% 15.02/14.79 [3419]E(f857(f857(f80(a919),x34191),f77(a919)),x34191)
% 15.02/14.79 [3420]E(f857(f857(f80(a1),x34201),f77(a1)),x34201)
% 15.02/14.79 [3421]E(f857(f857(f79(a919),x34211),f2(a919)),x34211)
% 15.02/14.79 [3422]E(f857(f857(f79(a1),x34221),f2(a1)),x34221)
% 15.02/14.79 [3423]E(f857(f857(f233(a919),x34231),f2(a919)),x34231)
% 15.02/14.79 [3424]E(f857(f857(f80(a919),x34241),f2(a919)),f2(a919))
% 15.02/14.79 [3425]E(f857(f857(f188(a919),x34251),f2(a919)),f2(a919))
% 15.02/14.79 [3426]E(f857(f857(f35(a1),x34261),f2(a1)),f2(a1))
% 15.02/14.79 [3433]E(f857(f172(x34331),f113(x34331)),f189(f927(x34331,a915)))
% 15.02/14.79 [3437]P106(f857(f137(x34371),f113(x34371)))
% 15.02/14.79 [3443]E(f857(f154(x34431,x34431),f7(x34431)),f31(f920(x34431)))
% 15.02/14.79 [3444]E(f857(f154(x34441,x34441),f31(x34441)),f31(f920(x34441)))
% 15.02/14.79 [3445]E(f44(a1,x34451,f2(a1)),x34451)
% 15.02/14.79 [3446]E(f857(f234(a919),f857(a112,x34461)),f857(f235(a919),x34461))
% 15.02/14.79 [3447]E(f857(f281(a919),f857(a112,x34471)),f857(f300(a919),x34471))
% 15.02/14.79 [3448]E(f857(f282(a919),f857(a112,x34481)),f857(f303(a919),x34481))
% 15.02/14.79 [3450]E(f44(a1,f2(a1),x34501),f2(a1))
% 15.02/14.79 [3463]E(f857(f857(f79(a919),x34631),f77(a919)),f857(a112,x34631))
% 15.02/14.79 [3472]E(f857(f301(a919,x34721),f2(a919)),f189(f927(a919,a915)))
% 15.02/14.79 [3484]E(f302(a919,f2(a919),x34841),f857(f300(a919),x34841))
% 15.02/14.79 [3527]E(f857(f857(f3(a919),f857(a112,x35271)),f77(a919)),x35271)
% 15.02/14.79 [3539]E(f46(f2(a1),x35391),f857(f857(f251(a1,a1),f2(a1)),f2(a1)))
% 15.02/14.79 [3589]P106(f857(f857(f235(a919),x35891),f857(a112,x35891)))
% 15.02/14.79 [3601]P106(f857(f857(f235(a919),f2(a919)),f857(a112,x36011)))
% 15.02/14.79 [3831]E(f91(x38311,x38311,f241(f927(x38311,a915)),f31(x38311)),f31(x38311))
% 15.02/14.79 [3889]E(f857(f857(f3(a99),f857(a5,f857(a112,f857(a22,x38891)))),f77(a99)),x38891)
% 15.02/14.79 [3960]P106(f857(f857(f234(a1),f857(f78(a1),f857(f100(a1),x39601))),f2(a1)))
% 15.02/14.79 [4107]P106(f857(f857(f235(a1),f857(f78(a1),f857(f100(a1),f857(a112,x41071)))),f2(a1)))
% 15.02/14.79 [4698]~E(f241(f927(x46981,a915)),f189(f927(x46981,a915)))
% 15.02/14.79 [4733]~P106(f857(f857(f235(a919),x47331),f2(a919)))
% 15.02/14.79 [4746]~P106(f857(f857(f235(a1),f857(f100(a1),x47461)),f2(a1)))
% 15.02/14.79 [3386]E(f120(x33861,f119(f921(x33861))),f119(x33861))
% 15.02/14.79 [3401]E(f179(x34011,f113(f920(x34011))),f113(f920(x34011)))
% 15.02/14.79 [3404]E(f857(f857(f80(a1),a82),x34041),a82)
% 15.02/14.79 [3405]E(f857(f857(f79(a1),a82),x34051),x34051)
% 15.02/14.79 [3408]E(f857(a104,f857(f100(a1),x34081)),x34081)
% 15.02/14.79 [3409]E(f857(f857(f3(a1),x34091),a82),x34091)
% 15.02/14.79 [3410]E(f857(f857(f79(a1),x34101),a82),x34101)
% 15.02/14.79 [3412]E(f857(f857(f3(a919),x34121),x34121),f2(a919))
% 15.02/14.79 [3416]E(f857(f34(a919),f857(f281(a919),x34161)),x34161)
% 15.02/14.79 [3417]E(f857(f78(a1),f857(f78(a1),x34171)),x34171)
% 15.02/14.79 [3428]E(f857(f857(f80(a919),f77(a919)),x34281),x34281)
% 15.02/14.79 [3429]E(f857(f857(f80(a1),f77(a1)),x34291),x34291)
% 15.02/14.79 [3430]E(f857(f857(f79(a919),f2(a919)),x34301),x34301)
% 15.02/14.79 [3431]E(f857(f857(f79(a1),f2(a1)),x34311),x34311)
% 15.02/14.79 [3432]E(f857(f857(f233(a919),f2(a919)),x34321),x34321)
% 15.02/14.79 [3438]E(f857(f857(f3(a919),f2(a919)),x34381),f2(a919))
% 15.02/14.79 [3439]E(f857(f857(f80(a919),f2(a919)),x34391),f2(a919))
% 15.02/14.79 [3440]E(f857(f857(f188(a919),f2(a919)),x34401),f2(a919))
% 15.02/14.79 [3441]E(f857(f857(f35(a1),f2(a1)),x34411),f2(a1))
% 15.02/14.79 [3451]E(f128(x34511,f857(f78(a1),x34511)),f132(a1,x34511))
% 15.02/14.79 [3456]E(f857(f301(a919,f2(a919)),x34561),f857(f281(a919),x34561))
% 15.02/14.79 [3457]E(f857(f857(f80(a1),a97),x34571),f857(f78(a1),x34571))
% 15.02/14.79 [3465]E(f857(a104,f857(f103(a1),x34651)),f857(f103(a919),x34651))
% 15.02/14.79 [3466]E(f857(a22,f857(f103(a99),x34661)),f857(f103(a919),x34661))
% 15.02/14.79 [3467]E(f857(f34(a919),f857(f300(a919),x34671)),f857(a112,x34671))
% 15.02/14.79 [3476]E(f857(f857(f79(a919),f77(a919)),x34761),f857(a112,x34761))
% 15.02/14.79 [3480]E(f857(f75(a1),f857(f100(a1),x34801)),f857(f100(a1),x34801))
% 15.02/14.79 [3481]E(f857(f102(a1),f857(f100(a1),x34811)),f857(f100(a1),x34811))
% 15.02/14.79 [3485]E(f857(f34(x34851),f189(f927(x34851,a915))),f2(a919))
% 15.02/14.79 [3487]E(f857(f857(f35(a919),x34871),f857(a112,f2(a919))),x34871)
% 15.02/14.79 [3496]E(f44(a919,x34961,f857(a112,f2(a919))),f2(a919))
% 15.02/14.79 [3497]E(f44(a1,x34971,f857(f103(a1),a97)),f2(a1))
% 15.02/14.79 [3511]E(f857(f857(f35(a1),x35111),f857(f103(a1),a97)),f857(f78(a1),x35111))
% 15.02/14.79 [3515]E(f139(a919,f857(f301(a919,x35151),f2(a919))),f113(a919))
% 15.02/14.79 [3516]E(f857(f857(f79(a1),x35161),f77(a1)),f857(f857(f3(a1),x35161),a97))
% 15.02/14.79 [3517]E(f857(f857(f3(a1),x35171),f77(a1)),f857(f857(f79(a1),x35171),a97))
% 15.02/14.79 [3521]P106(f857(f857(f234(a919),x35211),x35211))
% 15.02/14.79 [3522]P106(f857(f857(f234(a1),x35221),x35221))
% 15.02/14.79 [3523]P106(f857(f857(f286(a919),x35231),x35231))
% 15.02/14.79 [3528]E(f857(f78(a1),f857(f103(a1),x35281)),f857(f103(a1),f857(f78(a1),x35281)))
% 15.02/14.79 [3529]P106(f857(f60(a919),f857(f281(a919),x35291)))
% 15.02/14.79 [3530]P106(f857(f60(a919),f857(f300(a919),x35301)))
% 15.02/14.79 [3537]E(f161(x35371,f241(f927(x35371,a915))),f241(f927(f920(x35371),a915)))
% 15.02/14.79 [3542]P106(f857(f857(f234(a919),f2(a919)),x35421))
% 15.02/14.79 [3552]E(f857(f857(f79(a919),f111(x35521)),f857(a112,f2(a919))),f111(f857(a112,x35521)))
% 15.02/14.79 [3553]E(f857(f261(x35531),f857(f18(a915,x35531),a238)),f189(f927(x35531,a915)))
% 15.02/14.79 [3554]E(f857(f261(x35541),f857(f18(a915,x35541),a187)),f241(f927(x35541,a915)))
% 15.02/14.79 [3558]E(f857(f857(f308(a919),x35581),f857(f281(a919),x35581)),f857(f281(a919),f857(a112,x35581)))
% 15.02/14.79 [3570]E(f857(f857(f79(a1),f77(a1)),f857(f100(a1),x35701)),f857(f100(a1),f857(a112,x35701)))
% 15.02/14.79 [3572]E(f857(f857(f151(f920(x35721)),f113(x35721)),f113(f920(x35721))),f53(x35721,f113(x35721)))
% 15.02/14.79 [3592]E(f189(f927(f926(x35921,x35921),a915)),f262(x35921,f189(f927(x35921,a915))))
% 15.02/14.79 [3593]E(f857(f307(x35931),f241(f927(x35931,a915))),f241(f927(f927(x35931,a915),a915)))
% 15.02/14.79 [3594]E(f857(f78(f927(x35941,a915)),f189(f927(x35941,a915))),f241(f927(x35941,a915)))
% 15.02/14.79 [3595]E(f857(f78(f927(x35951,a915)),f241(f927(x35951,a915))),f189(f927(x35951,a915)))
% 15.02/14.79 [3597]P106(f857(f60(x35971),f189(f927(x35971,a915))))
% 15.02/14.79 [3599]E(f857(f301(a919,x35991),f857(a112,x35991)),f857(f857(f308(a919),x35991),f189(f927(a919,a915))))
% 15.02/14.79 [3600]E(f84(f926(a919,a919),f47(x36001,f2(a919))),f857(f857(f251(a919,a919),f2(a919)),x36001))
% 15.02/14.79 [3613]E(f857(f857(f308(a919),f857(a112,x36131)),f857(f300(a919),x36131)),f857(f300(a919),f857(a112,x36131)))
% 15.02/14.79 [3617]P39(x36171,f189(f927(f926(x36171,x36171),a915)))
% 15.02/14.79 [3618]P41(x36181,f189(f927(f926(x36181,x36181),a915)))
% 15.02/14.79 [3621]P106(f857(f857(f234(a1),f2(a1)),f857(f100(a1),x36211)))
% 15.02/14.79 [3628]E(f857(f857(f79(a919),f857(f190(a919),x36281)),f857(a112,f2(a919))),f857(f190(a919),f857(a112,x36281)))
% 15.02/14.79 [3733]P42(f857(f309(a919,a1,f100(a1)),x37331))
% 15.02/14.79 [3771]P54(x37711,f189(f927(x37711,a915)),f189(f927(f926(x37711,x37711),a915)))
% 15.02/14.79 [3791]E(f857(f857(f251(a1,a1),f857(f103(a1),a97)),f857(f857(f3(a1),x37911),f77(a1))),f49(f857(f103(a1),a97),x37911))
% 15.02/14.79 [3844]P61(x38441,f857(f18(f927(x38441,a915),x38441),f857(f18(a915,x38441),a238)))
% 15.02/14.79 [3856]E(f289(a919,f286(a919),x38561,x38561),f857(f857(f308(a919),x38561),f189(f927(a919,a915))))
% 15.02/14.79 [4049]P106(f857(f857(f328(f927(f926(a919,a919),a915)),f327(x40491)),a98))
% 15.02/14.79 [4075]P106(f857(f857(f328(f927(f926(a919,a919),a915)),f857(a106,x40751)),a98))
% 15.02/14.79 [4207]P26(x42071,f927(x42071,a915),f857(f857(f9(x42071,f927(x42071,a915),f927(x42071,a915)),f308(x42071)),f189(f927(x42071,a915))),f241(f927(x42071,a915)))
% 15.02/14.79 [4695]~E(f857(f857(f79(a1),x46951),x46951),a97)
% 15.02/14.79 [4720]~E(f857(a5,f857(a112,f857(a22,x47201))),f2(a99))
% 15.02/14.79 [4726]~P106(f857(a194,f857(f100(a1),x47261)))
% 15.02/14.79 [4729]~P106(f857(f857(f235(a919),x47291),x47291))
% 15.02/14.79 [4739]~P106(f857(f857(f234(a919),f857(a112,x47391)),x47391))
% 15.02/14.79 [3544]E(f857(a104,f857(f78(a1),f857(f100(a1),x35441))),f2(a919))
% 15.02/14.79 [3547]E(f857(f857(f79(a1),f857(f78(a1),x35471)),x35471),f2(a1))
% 15.02/14.79 [3551]E(f857(f34(a1),f857(f301(a1,f2(a1)),x35511)),f857(a104,x35511))
% 15.02/14.79 [3563]E(f857(f857(f243(a919),f857(a112,f2(a919))),x35631),f857(a112,f2(a919)))
% 15.02/14.79 [3660]E(f857(f280(x36601),f189(f927(f926(x36601,x36601),a915))),f189(f927(x36601,a915)))
% 15.02/14.79 [3668]E(f36(f927(x36681,a915),f189(f927(f927(x36681,a915),a915))),f189(f927(x36681,a915)))
% 15.02/14.79 [3669]E(f36(f927(x36691,a915),f241(f927(f927(x36691,a915),a915))),f241(f927(x36691,a915)))
% 15.02/14.79 [3670]E(f37(f927(x36701,a915),f189(f927(f927(x36701,a915),a915))),f241(f927(x36701,a915)))
% 15.02/14.79 [3671]E(f37(f927(x36711,a915),f241(f927(f927(x36711,a915),a915))),f189(f927(x36711,a915)))
% 15.02/14.79 [3675]P106(f857(f857(f286(a919),f857(a112,f2(a919))),x36751))
% 15.02/14.79 [3716]E(f857(f857(f308(f920(x37161)),f113(x37161)),f189(f927(f920(x37161),a915))),f161(x37161,f189(f927(x37161,a915))))
% 15.02/14.79 [3717]E(f857(f857(f308(f920(x37171)),f113(x37171)),f189(f927(f920(x37171),a915))),f162(x37171,f113(f927(x37171,a915))))
% 15.02/14.79 [3755]E(f857(f857(f79(a919),f6(x37551)),f857(a112,f2(a919))),f6(f857(a5,f857(a112,f857(a22,x37551)))))
% 15.02/14.79 [3782]E(f857(f34(a1),f857(f309(a919,a1,f100(a1)),x37821)),f857(f34(a919),x37821))
% 15.02/14.79 [3783]P106(f857(f857(f234(a919),x37831),f857(f857(f80(a919),x37831),x37831)))
% 15.02/14.79 [3822]E(f857(f309(a1,a919,a104),f302(a1,f2(a1),f857(f100(a1),x38221))),f857(f300(a919),x38221))
% 15.02/14.79 [3839]E(f857(f857(f35(a919),f857(a112,f2(a919))),f857(f103(a919),x38391)),f857(a104,f857(f857(f35(a1),f77(a1)),f857(f103(a1),x38391))))
% 15.02/14.79 [3841]E(f857(f172(a919),f139(a919,f857(f301(a919,f2(a919)),f857(a112,x38411)))),f857(f300(a919),x38411))
% 15.02/14.79 [3842]E(f857(f857(f79(a919),f857(f190(a99),x38421)),f857(a112,f2(a919))),f857(f190(a99),f857(a5,f857(a112,f857(a22,x38421)))))
% 15.02/14.79 [3862]P41(x38621,f306(x38621,f189(f927(f926(x38621,x38621),a915))))
% 15.02/14.79 [3863]P53(x38631,f306(x38631,f189(f927(f926(x38631,x38631),a915))))
% 15.02/14.79 [3864]E(f857(f309(a1,a919,a104),f857(f309(a919,a1,f100(a1)),x38641)),x38641)
% 15.02/14.79 [3895]E(f857(f857(f308(a919),f2(a919)),f857(f309(a919,a919,a112),f857(f281(a919),x38951))),f857(f281(a919),f857(a112,x38951)))
% 15.02/14.79 [3901]P56(x39011,x39011,f306(x39011,f189(f927(f926(x39011,x39011),a915))))
% 15.02/14.79 [3907]P106(f857(a194,f857(f78(a1),f857(f100(a1),f857(a112,x39071)))))
% 15.02/14.79 [3917]E(f857(f857(f3(f927(a919,a915)),f857(f282(a919),x39171)),f857(f857(f308(a919),x39171),f189(f927(a919,a915)))),f857(f282(a919),f857(a112,x39171)))
% 15.02/14.79 [3934]E(f857(f857(f79(a1),f857(f857(f3(a1),a82),x39341)),f857(f857(f3(a1),a82),x39341)),f857(f857(f3(a1),a82),f857(f857(f79(a1),x39341),x39341)))
% 15.02/14.79 [3949]E(f857(f857(f308(f927(x39491,a915)),f189(f927(x39491,a915))),f189(f927(f927(x39491,a915),a915))),f857(f307(x39491),f189(f927(x39491,a915))))
% 15.02/14.79 [3977]E(f857(f857(f3(f927(a919,a915)),f857(f303(a919),x39771)),f857(f857(f308(a919),f857(a112,x39771)),f189(f927(a919,a915)))),f857(f303(a919),f857(a112,x39771)))
% 15.02/14.79 [4087]E(f857(f103(a919),f857(f857(f79(a1),x40871),x40871)),f857(f857(f85(a919,a919),f857(f103(a919),x40871)),f857(f857(f20(a919,a919,a919),f79(a919)),f7(a919))))
% 15.02/14.79 [4461]P15(x44611,f927(x44611,a915),f857(f857(f10(f927(x44611,a915),f927(f927(x44611,a915),f927(x44611,a915)),x44611),f857(f9(f927(x44611,a915),f927(x44611,a915),f927(x44611,a915)),f3(f927(x44611,a915)))),f857(f857(f9(x44611,f927(x44611,a915),f927(x44611,a915)),f308(x44611)),f189(f927(x44611,a915)))))
% 15.02/14.79 [4549]E(f857(f261(f926(a1,a1)),f857(f256(a1,a1,a915),f857(f857(f10(f927(a1,a915),f927(a1,a915),a1),f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),x45491)))),f235(a1)))),f107(x45491))
% 15.02/14.79 [4582]E(f857(f261(f926(a1,a1)),f857(f256(a1,a1,a915),f857(f857(f20(a1,f927(a1,a915),f927(a1,a915)),f857(f857(f10(f927(a915,a915),f927(f927(a1,a915),f927(a1,a915)),a1),f10(a915,a915,a1)),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),x45821)))),f235(a1)))),f105(x45821))
% 15.02/14.79 [4635]E(f857(f261(f926(f927(x46351,a915),f927(x46351,a915))),f857(f256(f927(x46351,a915),f927(x46351,a915),a915),f857(f857(f9(f927(x46351,a915),f927(f927(x46351,a915),a915),f927(f927(x46351,a915),a915)),f857(f857(f10(f927(f927(x46351,a915),f927(a915,a915)),f927(f927(f927(x46351,a915),a915),f927(f927(x46351,a915),a915)),f927(x46351,a915)),f20(f927(x46351,a915),a915,a915)),f857(f857(f10(f927(f927(x46351,a915),a915),f927(f927(x46351,a915),f927(a915,a915)),f927(x46351,a915)),f857(f10(a915,f927(a915,a915),f927(x46351,a915)),a325)),f235(f927(x46351,a915))))),f60(x46351)))),f313(x46351))
% 15.02/14.79 [4743]~P106(f857(f60(f920(x47431)),f241(f927(f920(x47431),a915))))
% 15.02/14.79 [4755]~P106(f857(f857(f234(a1),f2(a1)),f857(f78(a1),f857(f100(a1),f857(a112,x47551)))))
% 15.02/14.79 [3695]E(f857(f857(f3(a1),f857(f857(f79(a1),x36951),a97)),a97),x36951)
% 15.02/14.79 [3709]E(f857(f172(a919),f139(a919,f857(f301(a919,f2(a919)),x37091))),f857(f281(a919),x37091))
% 15.02/14.79 [3956]E(f857(f857(f79(a1),f857(f857(f79(a1),f77(a1)),x39561)),x39561),f857(f857(f3(a1),f857(f857(f79(a1),x39561),x39561)),a97))
% 15.02/14.79 [4004]E(f857(f285(x40041,x40041),f306(x40041,f189(f927(f926(x40041,x40041),a915)))),f306(x40041,f189(f927(f926(x40041,x40041),a915))))
% 15.02/14.79 [4052]P106(f857(f857(f234(a919),x40521),f857(f857(f80(a919),x40521),f857(f857(f80(a919),x40521),x40521))))
% 15.02/14.79 [4324]P106(f857(f60(a919),f857(f261(a919),f857(f857(f9(a919,a919,a915),f234(a919)),x43241))))
% 15.02/14.79 [4325]P106(f857(f60(a919),f857(f261(a919),f857(f857(f9(a919,a919,a915),f235(a919)),x43251))))
% 15.02/14.79 [4598]E(f857(f261(f926(x45981,x45981)),f857(f857(f10(f927(x45981,a915),a915,f926(x45981,x45981)),f86(x45981)),f857(f857(f9(f926(x45981,x45981),f927(x45981,f926(x45981,x45981)),f927(x45981,a915)),f857(f857(f10(f927(f926(x45981,x45981),a915),f927(f927(x45981,f926(x45981,x45981)),f927(x45981,a915)),f926(x45981,x45981)),f10(f926(x45981,x45981),a915,x45981)),a324)),f857(f857(f20(x45981,x45981,f926(x45981,x45981)),f251(x45981,x45981)),f7(x45981))))),f306(x45981,f189(f927(f926(x45981,x45981),a915))))
% 15.02/14.79 [4745]~E(f857(f857(f3(a1),f857(f857(f79(a1),x47451),x47451)),a97),a82)
% 15.02/14.79 [4747]~E(f857(f857(f79(a1),f857(f857(f79(a1),f77(a1)),x47471)),x47471),f2(a1))
% 15.02/14.79 [4098]E(f857(f857(f79(a1),f857(f857(f3(a1),a97),x40981)),f857(f857(f3(a1),a97),x40981)),f857(f857(f3(a1),a97),f857(f857(f3(a1),f857(f857(f79(a1),x40981),x40981)),a97)))
% 15.02/14.79 [4215]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),a97),x42151)),f857(f857(f3(a1),a97),x42151))),a97),f857(f857(f3(a1),a97),f857(f857(f79(a1),x42151),x42151)))
% 15.02/14.79 [4247]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f79(a1),x42471),a97)),f857(f857(f79(a1),x42471),a97))),a97),f857(f857(f79(a1),f857(f857(f79(a1),x42471),x42471)),a97))
% 15.02/14.79 [4285]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),a97),x42851)),f857(f857(f3(a1),a97),x42851))),a97),f857(f857(f3(a1),a82),f857(f857(f3(a1),f857(f857(f79(a1),x42851),x42851)),a97)))
% 15.02/14.79 [4382]E(f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x43821),f2(a919))),f189(f927(f926(a919,a919),a915))))),f857(f100(a1),x43821))
% 15.02/14.79 [4392]E(f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),f331(x43921)),f405(x43921))),f189(f927(f926(a919,a919),a915))))),x43921)
% 15.02/14.79 [4425]E(f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x44251)),f857(f309(a919,a1,f100(a1)),f857(f261(a919),f857(f857(f10(a1,a915,a919),x44251),f100(a1)))))
% 15.02/14.79 [4469]P42(f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x44691)))
% 15.02/14.79 [4489]P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x44891),f189(f927(f926(a919,a919),a915)))),a71))
% 15.02/14.79 [4494]E(f857(f309(a1,a919,a104),f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),f857(f857(f10(a919,a915,a1),x44941),a104)))),f857(f261(a919),x44941))
% 15.02/14.79 [4650]E(f311(a919,f857(f857(f39(f926(a919,a919),f927(a919,a915)),f857(a106,x46501)),f857(f256(a919,a919,f927(a919,a915)),f857(f857(f9(a919,f927(a919,a915),f927(a919,f927(a919,a915))),f857(f857(f10(f927(a919,f927(f927(a919,a915),f927(a919,a915))),f927(f927(a919,a915),f927(a919,f927(a919,a915))),a919),f9(a919,f927(a919,a915),f927(a919,a915))),f857(f857(f10(f927(a919,a919),f927(a919,f927(f927(a919,a915),f927(a919,a915))),a919),f857(f10(a919,f927(f927(a919,a915),f927(a919,a915)),a919),f308(a919))),f3(a919)))),f189(f927(a919,a915)))))),f857(a104,x46501))
% 15.02/14.79 [4143]E(f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),x41431),x41431)),a97)),a97),f857(f857(f79(a1),x41431),x41431))
% 15.02/14.79 [4193]E(f857(f857(f3(a1),f857(f857(f3(a1),f857(f857(f79(a1),x41931),x41931)),a97)),a97),f857(f857(f79(a1),f857(f857(f3(a1),x41931),a97)),f857(f857(f3(a1),x41931),a97)))
% 15.02/14.79 [4398]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f79(a1),f857(f78(a1),x43981)),a97)),f857(f857(f79(a1),f857(f78(a1),x43981)),a97))),a97),f857(f78(a1),f857(f857(f3(a1),f857(f857(f79(a1),x43981),x43981)),a97)))
% 15.02/14.79 [4442]E(f857(f857(f79(a919),x44421),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(a112,f857(a112,x44421)))
% 15.02/14.79 [4443]E(f857(f857(f80(a919),x44431),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f79(a919),x44431),x44431))
% 15.02/14.79 [4444]E(f857(f857(f35(a919),f857(f857(f79(a919),x44441),x44441)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x44441)
% 15.02/14.79 [4523]E(f44(a919,f857(a112,f857(a112,x45231)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f44(a919,x45231,f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [4665]E(f857(a88,f857(f857(f39(f926(a919,a919),f927(f926(a919,a919),a915)),f857(a106,x46651)),f857(f256(a919,a919,f927(f926(a919,a919),a915)),f857(f857(f10(f927(a919,f927(f926(a919,a919),a915)),f927(a919,f927(f926(a919,a919),a915)),a919),f857(f10(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915),a919),f284(f926(a919,a919),f926(a919,a919),a108))),f857(f857(f9(a919,f927(f926(a919,a919),a915),f927(a919,f927(f926(a919,a919),a915))),f857(f857(f10(f927(a919,f927(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f927(f927(f926(a919,a919),a915),f927(a919,f927(f926(a919,a919),a915))),a919),f9(a919,f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f10(f927(a919,f926(a919,a919)),f927(a919,f927(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),a919),f857(f10(f926(a919,a919),f927(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),a919),f308(f926(a919,a919)))),f857(f9(a919,a919,f926(a919,a919)),f251(a919,a919))))),f189(f927(f926(a919,a919),a915))))))),f857(f78(a1),x46651))
% 15.02/14.79 [4518]E(f857(f857(f79(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x45181),f857(a112,f857(a112,x45181)))
% 15.02/14.79 [4519]E(f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x45191),f857(f857(f79(a919),x45191),x45191))
% 15.02/14.79 [4555]E(f857(f857(f35(a919),f857(a112,f857(a112,x45551))),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(a112,f857(f857(f35(a919),x45551),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.79 [4605]E(f857(f857(f79(a919),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),x46051),f857(a112,f857(a112,f857(a112,x46051))))
% 15.02/14.79 [4672]E(f857(f256(a1,a1,f926(a1,a1)),f857(f857(f20(a1,f927(a1,f926(a1,a1)),f927(a1,f926(a1,a1))),f857(f857(f10(f927(a1,f927(f926(a1,a1),f926(a1,a1))),f927(f927(a1,f926(a1,a1)),f927(a1,f926(a1,a1))),a1),f20(a1,f926(a1,a1),f926(a1,a1))),f857(f857(f10(f927(a1,f926(a1,a1)),f927(a1,f927(f926(a1,a1),f926(a1,a1))),a1),f857(f20(a1,f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),f857(f857(f10(a915,f927(f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),a1),f96(f926(a1,a1))),f857(f857(f10(a1,a915,a1),f857(f234(a1),f2(a1))),f857(f857(f9(a1,a1,a1),f3(a1)),x46721))))),f857(f857(f9(a1,f927(a1,a1),f927(a1,f926(a1,a1))),f857(f857(f10(f927(a1,f926(a1,a1)),f927(f927(a1,a1),f927(a1,f926(a1,a1))),a1),f10(a1,f926(a1,a1),a1)),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f857(f857(f9(a1,a1,a1),f857(f857(f10(a1,f927(a1,a1),a1),f79(a1)),f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f77(a1))))),f857(f857(f9(a1,a1,a1),f3(a1)),x46721))))),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))),f42(x46721))
% 15.02/14.79 [3371]P105(f925(x33711,x33712))
% 15.02/14.79 [3372]P105(f926(x33721,x33722))
% 15.02/14.79 [3373]P105(f924(x33731,x33732))
% 15.02/14.79 [3390]P14(a1,f178(x33901,x33902))
% 15.02/14.79 [3391]P39(x33911,f153(x33911,x33912))
% 15.02/14.79 [3392]P40(x33921,f262(x33921,x33922))
% 15.02/14.79 [3393]P40(x33931,f306(x33931,x33932))
% 15.02/14.79 [3394]P41(x33941,f262(x33941,x33942))
% 15.02/14.79 [3395]P53(x33951,f262(x33951,x33952))
% 15.02/14.79 [3458]P33(x34581,x34582,f113(x34581))
% 15.02/14.79 [3491]P54(x34911,x34912,f262(x34911,x34912))
% 15.02/14.79 [3492]P56(x34921,x34921,f262(x34921,x34922))
% 15.02/14.79 [3758]P26(x37581,x37581,f7(x37581),x37582)
% 15.02/14.79 [3759]P26(x37591,x37591,f31(x37591),x37592)
% 15.02/14.79 [3767]P34(x37671,x37672,f113(x37671),f113(x37671))
% 15.02/14.79 [3776]P26(f920(x37761),f920(x37761),f168(x37761),x37762)
% 15.02/14.79 [4183]P27(x41831,x41831,f31(x41831),x41832,x41832)
% 15.02/14.79 [4681]~E(f30(x46811,x46812),a25)
% 15.02/14.79 [4682]~E(f29(x46821,x46822),a25)
% 15.02/14.79 [4707]~P35(x47071,x47072,f113(x47071))
% 15.02/14.79 [4708]~P37(x47081,x47082,f113(x47081))
% 15.02/14.79 [3357]E(f857(f7(x33571),x33572),x33572)
% 15.02/14.79 [3358]E(f857(f261(x33581),x33582),x33582)
% 15.02/14.79 [3360]E(f857(f31(x33601),x33602),x33602)
% 15.02/14.79 [3370]E(f857(f192(x33701),x33702),f115(x33701))
% 15.02/14.79 [3388]E(f84(x33881,f857(a324,x33882)),x33882)
% 15.02/14.79 [3389]E(f89(x33891,f857(a324,x33892)),x33892)
% 15.02/14.79 [3411]E(f857(f125(x34111,x34112),f119(x34111)),f2(a919))
% 15.02/14.79 [3414]E(f857(f136(x34141,x34142),f113(x34141)),f113(x34141))
% 15.02/14.79 [3434]E(f306(x34341,f306(x34341,x34342)),f306(x34341,x34342))
% 15.02/14.79 [3435]E(f152(x34351,f152(x34351,x34352)),f152(x34351,x34352))
% 15.02/14.79 [3453]E(f857(f857(f134(x34531),x34532),f113(x34531)),x34532)
% 15.02/14.79 [3459]E(f173(x34591,x34592,f113(x34591)),x34592)
% 15.02/14.79 [3460]E(f173(x34601,f113(x34601),x34602),x34602)
% 15.02/14.79 [3461]E(f116(x34611,f119(x34611),x34612),x34612)
% 15.02/14.79 [3462]E(f169(x34621,f2(a919),x34622),f113(x34621))
% 15.02/14.79 [3468]E(f857(f857(f175(x34681),x34682),f113(x34681)),f113(x34681))
% 15.02/14.79 [3469]E(f857(f857(f138(x34691),x34692),f113(x34691)),f113(x34691))
% 15.02/14.79 [3471]E(f155(x34711,x34712,f113(x34711)),f2(a919))
% 15.02/14.79 [3473]E(f170(x34731,x34732,f113(x34731)),f113(x34731))
% 15.02/14.79 [3474]E(f177(x34741,x34742,f113(x34741)),f113(x34741))
% 15.02/14.79 [3475]E(f176(x34751,f113(x34751),x34752),f113(x34751))
% 15.02/14.79 [3479]E(f857(f172(x34791),f152(x34791,x34792)),f857(f172(x34791),x34792))
% 15.02/14.79 [3482]E(f857(f283(x34821,x34821),f262(x34821,x34822)),x34822)
% 15.02/14.79 [3483]E(f857(f263(x34831,x34831),f262(x34831,x34832)),x34832)
% 15.02/14.79 [3490]E(f857(f285(x34901,x34901),f262(x34901,x34902)),f262(x34901,x34902))
% 15.02/14.79 [3503]E(f306(f920(x35031),f157(x35031,x35032)),f158(x35031,f306(x35031,x35032)))
% 15.02/14.79 [3505]P106(f857(f137(a1),f178(x35051,x35052)))
% 15.02/14.79 [3513]E(f857(f283(x35131,x35131),f306(x35131,x35132)),f241(f927(x35131,a915)))
% 15.02/14.79 [3514]E(f857(f263(x35141,x35141),f306(x35141,x35142)),f241(f927(x35141,a915)))
% 15.02/14.79 [3518]P106(f857(f137(x35181),f152(x35181,x35182)))
% 15.02/14.79 [3520]P106(f857(f160(x35201,x35202),f113(x35201)))
% 15.02/14.79 [3526]E(f857(f172(a1),f178(x35261,x35262)),f302(a1,x35261,x35262))
% 15.02/14.79 [3540]P57(x35401,f189(f927(x35401,a915)),x35402)
% 15.02/14.79 [3545]E(f857(f255(a1,a1),f45(x35451,x35452)),f44(a1,x35451,x35452))
% 15.02/14.79 [3546]E(f857(f301(a919,x35461),f857(a112,x35462)),f302(a919,x35461,x35462))
% 15.02/14.79 [3562]E(f857(f857(f151(x35621),x35622),f113(x35621)),f140(x35621,x35622,f113(x35621)))
% 15.02/14.79 [3574]E(f302(a919,f857(a112,x35741),x35742),f304(a919,x35741,x35742))
% 15.02/14.79 [3577]P54(x35771,f241(f927(x35771,a915)),f306(x35771,x35772))
% 15.02/14.79 [3640]E(f857(f857(f3(a919),x36401),f857(a112,x36402)),f857(f34(a919),f305(a919,x36402,x36401)))
% 15.02/14.79 [3696]E(f166(x36961,x36962,f113(x36961)),f857(f857(f251(f920(x36961),f920(x36961)),f113(x36961)),f113(x36961)))
% 15.02/14.79 [3714]E(f857(f256(x37141,x37142,f926(x37141,x37142)),f251(x37141,x37142)),f31(f926(x37141,x37142)))
% 15.02/14.79 [3718]P106(f857(f857(f328(f920(x37181)),f113(x37181)),f161(x37181,x37182)))
% 15.02/14.79 [3719]E(f857(f190(f920(x37191)),f114(x37191,x37192)),f857(f857(f3(a919),f857(f190(f920(x37191)),x37192)),f77(a919)))
% 15.02/14.79 [3727]P106(f857(f60(a919),f302(a919,x37271,x37272)))
% 15.02/14.79 [3728]P106(f857(f60(a919),f305(a919,x37281,x37282)))
% 15.02/14.79 [3729]P106(f857(f60(a919),f304(a919,x37291,x37292)))
% 15.02/14.79 [3730]P106(f857(f60(a1),f302(a1,x37301,x37302)))
% 15.02/14.79 [3731]P106(f857(f60(a1),f305(a1,x37311,x37312)))
% 15.02/14.79 [3732]P106(f857(f60(a1),f304(a1,x37321,x37322)))
% 15.02/14.79 [3838]E(f857(f309(a919,a919,a112),f302(a919,x38381,x38382)),f302(a919,f857(a112,x38381),f857(a112,x38382)))
% 15.02/14.79 [3858]E(f857(f857(f288(x38581,x38581,x38581),f306(x38581,x38582)),f306(x38581,x38582)),f306(x38581,x38582))
% 15.02/14.79 [3893]E(f857(f857(f251(a99,a99),f857(f857(f35(a99),x38931),x38932)),f44(a99,x38931,x38932)),f23(x38931,x38932))
% 15.02/14.79 [3894]E(f857(f857(f251(a1,a1),f857(f857(f35(a1),x38941),x38942)),f44(a1,x38941,x38942)),f45(x38941,x38942))
% 15.02/14.79 [3921]E(f857(f857(f251(a919,a919),f857(f857(f35(a919),x39211),x39212)),f44(a919,x39211,x39212)),f84(f926(a919,a919),f47(x39211,x39212)))
% 15.02/14.79 [3973]P106(f857(f857(f235(a919),f857(f857(f3(a919),x39731),x39732)),f857(a112,x39731)))
% 15.02/14.79 [4023]P40(x40231,f857(f857(f288(x40231,x40231,x40231),x40232),f306(x40231,x40232)))
% 15.02/14.79 [4074]E(f857(f857(f79(a1),f857(f857(f80(a1),x40741),f857(f857(f35(a1),x40742),x40741))),f44(a1,x40742,x40741)),x40742)
% 15.02/14.79 [4078]E(f857(f857(f39(a919,f927(f926(f920(x40781),f920(x40781)),a915)),f241(f927(a919,a915))),f143(x40781,x40782)),f145(x40781,x40782))
% 15.02/14.79 [4301]P106(f857(f857(f328(f926(f920(x43011),f920(x43011))),f857(f857(f251(f920(x43011),f920(x43011)),f113(x43011)),f113(x43011))),f158(x43011,x43012)))
% 15.02/14.79 [4410]E(f252(x44101,x44101,x44101,a324,f252(x44101,x44101,x44101,x44102,a324)),x44102)
% 15.02/14.79 [4454]E(f257(x44541,x44541,x44542,x44542,f7(x44541),f7(x44542)),f31(f926(x44541,x44542)))
% 15.02/14.79 [4456]E(f257(x44561,x44561,x44562,x44562,f31(x44561),f31(x44562)),f31(f926(x44561,x44562)))
% 15.02/14.79 [3452]E(f857(f168(x34521),f857(f168(x34521),x34522)),x34522)
% 15.02/14.79 [3454]E(f857(f857(f138(x34541),f2(a919)),x34542),x34542)
% 15.02/14.79 [3470]E(f857(f857(f175(x34701),f2(a919)),x34702),f113(x34701))
% 15.02/14.79 [3477]E(f857(f857(f134(x34771),f113(x34771)),x34772),x34772)
% 15.02/14.79 [3486]E(f36(f927(x34861,a915),f857(f307(x34861),x34862)),x34862)
% 15.02/14.79 [3488]E(f857(f172(x34881),f857(f167(x34881),x34882)),f857(f172(x34881),x34882))
% 15.02/14.79 [3489]E(f857(f172(x34891),f857(f168(x34891),x34892)),f857(f172(x34891),x34892))
% 15.02/14.79 [3494]E(f857(f857(f3(a99),x34941),x34942),f857(f857(a4,x34941),x34942))
% 15.02/14.79 [3507]E(f857(f857(f80(a919),x35071),x35072),f857(f857(f80(a919),x35072),x35071))
% 15.02/14.79 [3508]E(f857(f857(f80(a1),x35081),x35082),f857(f857(f80(a1),x35082),x35081))
% 15.02/14.79 [3509]E(f857(f857(f79(a919),x35091),x35092),f857(f857(f79(a919),x35092),x35091))
% 15.02/14.79 [3510]E(f857(f857(f79(a1),x35101),x35102),f857(f857(f79(a1),x35102),x35101))
% 15.02/14.79 [3532]E(f857(f857(f183(x35321,x35321),f2(a919)),x35322),f31(x35321))
% 15.02/14.79 [3533]E(f857(f190(f920(x35331)),f857(f167(x35331),x35332)),f857(f190(f920(x35331)),x35332))
% 15.02/14.79 [3534]E(f857(f190(f920(x35341)),f857(f168(x35341),x35342)),f857(f190(f920(x35341)),x35342))
% 15.02/14.79 [3535]E(f176(x35351,x35352,f189(f927(a919,a915))),f113(x35351))
% 15.02/14.79 [3536]E(f857(f857(f154(x35361,x35361),f7(x35361)),x35362),x35362)
% 15.02/14.79 [3538]E(f857(f250(a1,a1),f45(x35381,x35382)),f857(f857(f35(a1),x35381),x35382))
% 15.02/14.79 [3555]E(f857(f190(f920(x35551)),f152(x35551,x35552)),f857(f34(x35551),f857(f172(x35551),x35552)))
% 15.02/14.79 [3556]E(f28(f29(x35561,x35562)),f857(f857(f79(a919),f28(x35562)),f857(a112,f2(a919))))
% 15.02/14.79 [3557]E(f857(f280(x35571),f857(f285(x35571,x35571),x35572)),f857(f280(x35571),x35572))
% 15.02/14.79 [3561]P106(f857(f60(x35611),f857(f172(x35611),x35612)))
% 15.02/14.79 [3569]E(f857(f857(f79(a1),x35691),f857(f78(a1),x35692)),f857(f857(f3(a1),x35691),x35692))
% 15.02/14.79 [3576]P25(x35761,x35762,f189(f927(f918(x35761),a915)))
% 15.02/14.79 [3578]E(f857(f310(x35781,x35781,f7(x35781)),x35782),x35782)
% 15.02/14.79 [3579]E(f857(f310(x35791,x35791,f31(x35791)),x35792),x35792)
% 15.02/14.79 [3580]E(f857(f309(x35801,x35801,f7(x35801)),x35802),x35802)
% 15.02/14.79 [3581]E(f857(f309(x35811,x35811,f31(x35811)),x35812),x35812)
% 15.02/14.79 [3582]P106(f857(f241(f927(x35821,a915)),x35822))
% 15.02/14.79 [3584]E(f857(f34(a919),f857(f301(a919,x35841),x35842)),f857(f857(f3(a919),x35842),x35841))
% 15.02/14.79 [3585]E(f857(f301(a919,f857(a112,x35851)),x35852),f305(a919,x35851,x35852))
% 15.02/14.79 [3598]E(f857(f857(f308(x35981),x35982),f189(f927(x35981,a915))),f857(f261(x35981),f857(a324,x35982)))
% 15.02/14.79 [3603]E(f306(x36031,f857(f285(x36031,x36031),x36032)),f857(f285(x36031,x36031),f306(x36031,x36032)))
% 15.02/14.79 [3608]E(f857(f857(f79(a919),f857(a112,x36081)),x36082),f857(f857(f79(a919),x36081),f857(a112,x36082)))
% 15.02/14.79 [3609]E(f857(f857(f3(a919),f857(a112,x36091)),f857(a112,x36092)),f857(f857(f3(a919),x36091),x36092))
% 15.02/14.79 [3615]E(f54(x36151,f2(a919),x36152),f857(f857(f151(f920(x36151)),f113(x36151)),f113(f920(x36151))))
% 15.02/14.79 [3616]E(f857(f34(a919),f304(a919,x36161,x36162)),f857(f857(f3(a919),x36162),x36161))
% 15.02/14.79 [3625]P39(x36251,f857(f857(f287(a919,x36251),a239),x36252))
% 15.02/14.79 [3627]P14(a919,f139(a919,f857(f301(a919,x36271),x36272)))
% 15.02/14.79 [3629]P106(f857(f60(a919),f857(f301(a919,x36291),x36292)))
% 15.02/14.79 [3630]P106(f857(f60(a1),f857(f301(a1,x36301),x36302)))
% 15.02/14.79 [3633]E(f857(f285(f920(x36331),f920(x36331)),f157(x36331,x36332)),f157(x36331,f857(f285(x36331,x36331),x36332)))
% 15.02/14.79 [3634]E(f857(f190(a916),f29(x36341,x36342)),f857(f857(f79(a919),f857(f190(a916),x36342)),f857(a112,f2(a919))))
% 15.02/14.79 [3636]E(f857(f301(a1,x36361),f857(f857(f79(a1),x36362),f77(a1))),f302(a1,x36361,x36362))
% 15.02/14.79 [3639]E(f857(f857(f35(a1),f857(f78(a1),x36391)),f857(f78(a1),x36392)),f857(f857(f35(a1),x36391),x36392))
% 15.02/14.79 [3647]E(f857(f857(f183(f926(x36471,x36471),a915),f77(a919)),x36472),x36472)
% 15.02/14.79 [3649]E(f857(f857(f110(f927(x36491,a915)),x36492),f189(f927(x36491,a915))),x36492)
% 15.02/14.79 [3650]E(f857(f857(f3(f927(x36501,a915)),x36502),f189(f927(x36501,a915))),x36502)
% 15.02/14.79 [3651]E(f857(f857(f101(f927(x36511,a915)),x36512),f241(f927(x36511,a915))),x36512)
% 15.02/14.79 [3652]E(f857(f250(a919,a919),f84(f926(a919,a919),f47(x36521,x36522))),f857(f857(f35(a919),x36521),x36522))
% 15.02/14.79 [3659]E(f302(a1,f857(f857(f79(a1),x36591),f77(a1)),x36592),f304(a1,x36591,x36592))
% 15.02/14.79 [3664]E(f857(f255(a919,a919),f84(f926(a919,a919),f47(x36641,x36642))),f44(a919,x36641,x36642))
% 15.02/14.79 [3674]P106(f857(f857(f328(x36741),x36742),f241(f927(x36741,a915))))
% 15.02/14.79 [3679]E(f857(f857(f3(a919),f857(a112,x36791)),x36792),f857(f34(a919),f302(a919,x36792,x36791)))
% 15.02/14.79 [3705]E(f857(f857(f110(f927(x37051,a915)),x37052),f241(f927(x37051,a915))),f241(f927(x37051,a915)))
% 15.02/14.79 [3706]E(f857(f857(f3(f927(x37061,a915)),x37062),f241(f927(x37061,a915))),f189(f927(x37061,a915)))
% 15.02/14.79 [3707]E(f857(f857(f101(f927(x37071,a915)),x37072),f189(f927(x37071,a915))),f189(f927(x37071,a915)))
% 15.02/14.79 [3722]E(f44(a1,f857(f100(a1),x37221),f857(f100(a1),x37222)),f857(f100(a1),f44(a919,x37221,x37222)))
% 15.02/14.79 [3723]E(f44(a1,f857(f78(a1),x37231),f857(f78(a1),x37232)),f857(f78(a1),f44(a1,x37231,x37232)))
% 15.02/14.79 [3734]E(f857(f190(f920(x37341)),f857(f171(x37341),x37342)),f857(f857(f3(a919),f857(f190(f920(x37341)),x37342)),f77(a919)))
% 15.02/14.79 [3760]E(f857(f857(f35(a1),f44(a1,x37601,x37602)),x37602),f2(a1))
% 15.02/14.79 [3769]E(f857(a5,f44(a919,f857(a22,x37691),f857(a22,x37692))),f44(a99,x37691,x37692))
% 15.02/14.79 [3804]E(f857(a5,f857(f857(f3(a919),f857(a22,x38041)),f857(a22,x38042))),f857(f857(f3(a99),x38041),x38042))
% 15.02/14.79 [3805]E(f857(a5,f857(f857(f80(a919),f857(a22,x38051)),f857(a22,x38052))),f857(f857(f80(a99),x38051),x38052))
% 15.02/14.79 [3806]E(f857(a5,f857(f857(f79(a919),f857(a22,x38061)),f857(a22,x38062))),f857(f857(f79(a99),x38061),x38062))
% 15.02/14.79 [3807]E(f857(a5,f857(f857(f35(a919),f857(a22,x38071)),f857(a22,x38072))),f857(f857(f35(a99),x38071),x38072))
% 15.02/14.79 [3816]E(f857(f309(a919,a919,a112),f857(f301(a919,x38161),x38162)),f857(f301(a919,f857(a112,x38161)),f857(a112,x38162)))
% 15.02/14.79 [3843]P106(f857(f47(x38431,x38432),f84(f926(a919,a919),f47(x38431,x38432))))
% 15.02/14.79 [3867]E(f857(f857(f79(a919),f857(f857(f79(a919),f28(x38671)),f28(x38672))),f857(a112,f2(a919))),f28(f30(x38671,x38672)))
% 15.02/14.79 [3868]E(f44(a919,f857(a112,f44(a919,x38681,x38682)),x38682),f44(a919,f857(a112,x38681),x38682))
% 15.02/14.79 [3880]E(f857(f857(f39(f927(x38801,a915),f927(x38801,a915)),x38802),f7(f927(x38801,a915))),f36(f927(x38801,a915),x38802))
% 15.02/14.79 [3881]E(f857(f857(f38(f927(x38811,a915),f927(x38811,a915)),x38812),f7(f927(x38811,a915))),f37(f927(x38811,a915),x38812))
% 15.02/14.79 [3882]E(f857(f309(f920(x38821),f927(x38821,a915),f172(x38821)),f857(f172(f920(x38821)),f53(x38821,x38822))),f857(f307(x38821),f857(f172(x38821),x38822)))
% 15.02/14.79 [3886]P106(f857(f857(f328(f927(x38861,a915)),x38862),f857(f307(x38861),x38862)))
% 15.02/14.79 [3892]E(f44(a1,f857(f78(a1),f44(a1,x38921,x38922)),x38922),f44(a1,f857(f78(a1),x38921),x38922))
% 15.02/14.79 [3903]P106(f857(f857(f234(f927(x39031,a915)),x39032),f241(f927(x39031,a915))))
% 15.02/14.79 [3905]E(f857(f857(f288(x39051,x39051,x39051),f306(x39051,x39052)),f306(x39051,f306(x39051,x39052))),f306(x39051,x39052))
% 15.02/14.79 [3906]E(f857(f857(f110(f927(x39061,a915)),f857(f263(x39061,x39061),x39062)),f857(f283(x39061,x39061),x39062)),f857(f280(x39061),x39062))
% 15.02/14.79 [3927]E(f312(x39271,x39272,f241(f927(x39271,a915)),f241(f927(x39272,a915))),f241(f927(f925(x39271,x39272),a915)))
% 15.02/14.79 [3978]P106(f857(f857(f234(a919),f44(a919,x39781,x39782)),x39781))
% 15.02/14.79 [4002]P106(f857(f857(f234(a1),f857(f78(a1),f857(f100(a1),x40021))),f857(f100(a1),x40022)))
% 15.02/14.79 [4028]P106(f857(f857(f328(f927(x40281,a915)),f189(f927(x40281,a915))),f857(f307(x40281),x40282)))
% 15.02/14.79 [4033]E(f306(x40331,f857(f857(f288(x40331,x40331,x40331),x40332),f306(x40331,x40332))),f306(x40331,x40332))
% 15.02/14.79 [4036]E(f857(f857(f288(x40361,x40361,x40361),f306(x40361,x40362)),x40362),f857(f857(f288(x40361,x40361,x40361),x40362),f306(x40361,x40362)))
% 15.02/14.79 [4038]E(f857(a104,f857(f857(f79(a1),f857(f857(f3(a1),x40381),x40382)),f77(a1))),f857(f34(a1),f302(a1,x40382,x40381)))
% 15.02/14.79 [4053]E(f857(f283(x40531,x40531),f857(f857(f288(x40531,x40531,x40531),x40532),f306(x40531,x40532))),f857(f283(x40531,x40531),x40532))
% 15.02/14.79 [4054]E(f857(f263(x40541,x40541),f857(f857(f288(x40541,x40541,x40541),x40542),f306(x40541,x40542))),f857(f263(x40541,x40541),x40542))
% 15.02/14.79 [4070]E(f857(f857(f79(a919),f857(f857(f79(a919),f857(f190(a916),x40701)),f857(f190(a916),x40702))),f857(a112,f2(a919))),f857(f190(a916),f30(x40701,x40702)))
% 15.02/14.79 [4073]E(f857(f142(f920(x40731),f920(x40731),f134(x40731),f113(x40731)),f169(f920(x40731),x40732,f113(x40731))),f113(x40731))
% 15.02/14.79 [4082]P26(a919,a919,f857(f857(f9(a919,a919,a919),f79(a919)),x40821),x40822)
% 15.02/14.79 [4084]P14(a919,f857(f168(a919),f857(f857(f154(f920(x40841),a919),f190(f920(x40841))),f179(x40841,x40842))))
% 15.02/14.79 [4115]P53(x41151,f857(f857(f110(f927(f926(x41151,x41151),a915)),x41152),f857(f285(x41151,x41151),x41152)))
% 15.02/14.79 [4116]P53(x41161,f857(f857(f101(f927(f926(x41161,x41161),a915)),x41162),f857(f285(x41161,x41161),x41162)))
% 15.02/14.79 [4127]P106(f857(f857(f235(a1),f857(f78(a1),f857(f100(a1),f857(a112,x41271)))),f857(f100(a1),x41272)))
% 15.02/14.79 [4172]E(f857(f142(f920(x41721),x41721,f857(f9(x41721,f920(x41721),f920(x41721)),f151(x41721)),f113(x41721)),x41722),f857(f168(x41721),x41722))
% 15.02/14.79 [4222]P106(f857(f857(f234(f927(f926(f920(x42221),f920(x42221)),a915)),f158(x42221,x42222)),f306(f920(x42221),f157(x42221,x42222))))
% 15.02/14.79 [4251]P106(f857(f47(x42511,x42512),f857(f857(f251(a919,a919),f857(f857(f35(a919),x42511),x42512)),f44(a919,x42511,x42512))))
% 15.02/14.79 [4263]P106(f857(f857(f234(f927(f926(f920(x42631),f920(x42631)),a915)),f157(x42631,f306(x42631,x42632))),f306(f920(x42631),f157(x42631,x42632))))
% 15.02/14.79 [4479]E(f857(f857(f258(f926(a99,a99),a99,f926(a99,a99),f926(x44791,f926(a99,a99))),f266(f857(f165(a99),f857(f857(f154(f926(a99,x44791),a99),f250(a99,x44791)),x44792)))),f857(f857(f10(x44791,f927(f926(a99,a99),f926(x44791,f926(a99,a99))),a99),f251(x44791,f926(a99,a99))),f267(x44791,x44792))),f265(x44791,x44792))
% 15.02/14.79 [4557]E(f224(a919,f926(x45571,f921(x45571)),f2(a919),f857(f256(x45571,f921(x45571),a919),f857(f18(f927(f921(x45571),a919),x45571),f857(f857(f9(f921(x45571),a919,a919),f857(f857(f10(a919,f927(a919,a919),f921(x45571)),f79(a919)),f190(f921(x45571)))),f77(a919)))),f857(f135(x45571),x45572)),f857(f190(f921(x45571)),x45572))
% 15.02/14.79 [4664]E(f857(f256(f927(f926(x46641,x46641),a915),f927(f926(x46641,x46641),a915),f927(f927(x46642,x46641),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f857(f857(f9(f927(f926(x46641,x46641),a915),f927(f927(f926(x46641,x46641),a915),f927(f927(x46642,x46641),f927(f926(x46642,x46642),a915))),f927(f927(f926(x46641,x46641),a915),f927(f927(x46642,x46641),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915))))),f857(f857(f10(f927(f927(f927(x46642,x46641),f927(f926(x46642,x46642),a915)),f927(f927(x46642,x46641),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f927(f927(f927(f926(x46641,x46641),a915),f927(f927(x46642,x46641),f927(f926(x46642,x46642),a915))),f927(f927(f926(x46641,x46641),a915),f927(f927(x46642,x46641),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915))))),f927(f926(x46641,x46641),a915)),f10(f927(f927(x46642,x46641),f927(f926(x46642,x46642),a915)),f927(f927(x46642,x46641),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915))),f927(f926(x46641,x46641),a915))),f857(f857(f10(f927(f927(x46642,x46641),f927(f927(f926(x46642,x46642),a915),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f927(f927(f927(x46642,x46641),f927(f926(x46642,x46642),a915)),f927(f927(x46642,x46641),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f927(f926(x46641,x46641),a915)),f20(f927(x46642,x46641),f927(f926(x46642,x46642),a915),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f857(f857(f10(f927(f927(x46642,x46641),f927(f926(x46642,x46642),a915)),f927(f927(x46642,x46641),f927(f927(f926(x46642,x46642),a915),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f927(f926(x46641,x46641),a915)),f857(f10(f927(f926(x46642,x46642),a915),f927(f927(f926(x46642,x46642),a915),f926(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915))),f927(x46642,x46641)),f251(f927(f926(x46642,x46642),a915),f927(f926(x46642,x46642),a915)))),f287(x46641,x46642))))),f287(x46641,x46642))),f73(x46641,x46642))
% 15.02/14.79 [4727]~E(f857(f307(x47271),x47272),f189(f927(f927(x47271,a915),a915)))
% 15.02/14.79 [4738]~P106(f857(f857(f172(x47381),f113(x47381)),x47382))
% 15.02/14.79 [4742]~P106(f857(f857(f328(x47421),x47422),f189(f927(x47421,a915))))
% 15.02/14.79 [4750]~P106(f857(f857(f235(f927(x47501,a915)),x47502),f189(f927(x47501,a915))))
% 15.02/14.79 [3587]E(f857(f857(f3(a919),x35871),f857(f857(f79(a919),x35871),x35872)),f2(a919))
% 15.02/14.79 [3590]E(f857(f857(f110(f927(x35901,a915)),x35902),x35902),x35902)
% 15.02/14.79 [3591]E(f857(f857(f101(f927(x35911,a915)),x35912),x35912),x35912)
% 15.02/14.79 [3619]E(f857(f857(f3(f927(x36191,a915)),x36192),x36192),f189(f927(x36191,a915)))
% 15.02/14.79 [3622]E(f857(f143(x36221,x36222),f2(a919)),f189(f927(f926(f920(x36221),f920(x36221)),a915)))
% 15.02/14.79 [3623]E(f857(f857(f79(a919),x36231),f857(a112,x36232)),f857(a112,f857(f857(f79(a919),x36231),x36232)))
% 15.02/14.79 [3635]E(f195(f857(f100(a1),x36351),f857(f100(a1),x36352)),f857(f100(a1),f857(f857(f3(a919),x36351),x36352)))
% 15.02/14.79 [3638]E(f857(f857(f35(a1),f857(f78(a1),x36381)),x36382),f857(f857(f35(a1),x36381),f857(f78(a1),x36382)))
% 15.02/14.79 [3642]E(f857(f34(a1),f857(f301(a1,x36421),x36422)),f857(a104,f857(f857(f3(a1),x36422),x36421)))
% 15.02/14.79 [3645]E(f857(f857(f79(a919),f857(a112,x36451)),x36452),f857(a112,f857(f857(f79(a919),x36451),x36452)))
% 15.02/14.79 [3648]E(f857(f78(f927(x36481,a915)),f857(f78(f927(x36481,a915)),x36482)),x36482)
% 15.02/14.79 [3661]E(f179(x36611,f857(f857(f151(f920(x36611)),f113(x36611)),x36612)),f179(x36611,x36612))
% 15.02/14.79 [3665]E(f857(f857(f79(a919),x36651),f857(f857(f80(a919),x36651),x36652)),f857(f857(f80(a919),x36651),f857(a112,x36652)))
% 15.02/14.79 [3672]E(f857(f857(a4,f857(a5,x36721)),f857(a5,x36722)),f857(a5,f857(f857(f3(a919),x36721),x36722)))
% 15.02/14.79 [3687]E(f857(f857(f80(a1),f857(f78(a1),x36871)),x36872),f857(f78(a1),f857(f857(f80(a1),x36871),x36872)))
% 15.02/14.79 [3689]E(f857(f857(f243(a1),f857(f100(a1),x36891)),x36892),f857(f100(a1),f857(f857(f243(a919),x36891),x36892)))
% 15.02/14.79 [3690]E(f857(f857(f80(a99),f857(a5,x36901)),f857(a5,x36902)),f857(a5,f857(f857(f80(a919),x36901),x36902)))
% 15.02/14.79 [3691]E(f857(f857(f79(a99),f857(a5,x36911)),f857(a5,x36912)),f857(a5,f857(f857(f79(a919),x36911),x36912)))
% 15.02/14.79 [3692]E(f857(f857(f188(a919),f857(a112,x36921)),f857(a112,x36922)),f857(a112,f857(f857(f188(a919),x36921),x36922)))
% 15.02/14.79 [3693]E(f857(f857(f233(a919),f857(a112,x36931)),f857(a112,x36932)),f857(a112,f857(f857(f233(a919),x36931),x36932)))
% 15.02/14.79 [3698]E(f857(f172(a919),f139(a919,f857(f301(a919,x36981),x36982))),f857(f301(a919,x36981),x36982))
% 15.02/14.79 [3699]E(f311(x36991,f857(f857(f308(x36991),x36992),f189(f927(x36991,a915)))),x36992)
% 15.02/14.79 [3703]E(f857(f283(x37031,x37032),f189(f927(f926(x37031,x37032),a915))),f189(f927(x37032,a915)))
% 15.02/14.79 [3704]E(f857(f263(x37041,x37042),f189(f927(f926(x37041,x37042),a915))),f189(f927(x37041,a915)))
% 15.02/14.79 [3708]E(f857(a104,f857(f857(f3(a1),x37081),x37082)),f857(f34(a1),f304(a1,x37082,x37081)))
% 15.02/14.79 [3713]E(f857(f857(f79(a919),x37131),f857(f857(f80(a919),x37132),x37131)),f857(f857(f80(a919),f857(a112,x37132)),x37131))
% 15.02/14.79 [3715]E(f857(f857(f59(x37151),f189(f927(x37151,a915))),x37152),f189(f927(f927(x37151,a915),a915)))
% 15.02/14.79 [3724]E(f857(f190(f920(a919)),f139(a919,f857(f301(a919,x37241),x37242))),f857(f857(f3(a919),x37242),x37241))
% 15.02/14.79 [3739]E(f857(f857(f110(f927(x37391,a915)),f189(f927(x37391,a915))),x37392),x37392)
% 15.02/14.79 [3740]E(f857(f857(f101(f927(x37401,a915)),f241(f927(x37401,a915))),x37402),x37402)
% 15.02/14.79 [3743]E(f857(f857(f79(a1),f857(f78(a1),x37431)),f857(f78(a1),x37432)),f857(f78(a1),f857(f857(f79(a1),x37431),x37432)))
% 15.02/14.79 [3745]E(f857(f857(f80(a1),f857(f103(a1),x37451)),f857(f103(a1),x37452)),f857(f103(a1),f857(f857(f80(a1),x37451),x37452)))
% 15.02/14.79 [3747]E(f857(f857(f80(a1),f857(f100(a1),x37471)),f857(f100(a1),x37472)),f857(f100(a1),f857(f857(f80(a919),x37471),x37472)))
% 15.02/14.79 [3748]E(f857(f857(f79(a1),f857(f103(a1),x37481)),f857(f103(a1),x37482)),f857(f103(a1),f857(f857(f79(a1),x37481),x37482)))
% 15.02/14.79 [3750]E(f857(f857(f79(a1),f857(f100(a1),x37501)),f857(f100(a1),x37502)),f857(f100(a1),f857(f857(f79(a919),x37501),x37502)))
% 15.02/14.79 [3751]E(f857(f857(f35(a1),f857(f100(a1),x37511)),f857(f100(a1),x37512)),f857(f100(a1),f857(f857(f35(a919),x37511),x37512)))
% 15.02/14.79 [3770]E(f857(f857(f8(x37701,a919),f857(f18(a919,x37701),f77(a919))),x37702),f857(f34(x37701),x37702))
% 15.02/14.79 [3777]E(f857(f78(a1),f44(a1,f857(f78(a1),x37771),x37772)),f44(a1,x37771,f857(f78(a1),x37772)))
% 15.02/14.79 [3779]E(f857(f172(a1),f178(x37791,f857(f857(f3(a1),x37792),f77(a1)))),f857(f301(a1,x37791),x37792))
% 15.02/14.79 [3784]P106(f857(f857(f234(a919),x37841),f857(f857(f79(a919),x37842),x37841)))
% 15.02/14.79 [3785]P106(f857(f857(f234(a919),x37851),f857(f857(f79(a919),x37851),x37852)))
% 15.02/14.79 [3787]E(f857(f857(f110(f927(x37871,a915)),f241(f927(x37871,a915))),x37872),f241(f927(x37871,a915)))
% 15.02/14.79 [3788]E(f857(f857(f3(f927(x37881,a915)),f189(f927(x37881,a915))),x37882),f189(f927(x37881,a915)))
% 15.02/14.79 [3789]E(f857(f857(f101(f927(x37891,a915)),f189(f927(x37891,a915))),x37892),f189(f927(x37891,a915)))
% 15.02/14.79 [3796]E(f857(f857(f251(a1,a1),x37961),f857(f78(a1),x37962)),f857(a50,f857(f857(f251(a1,a1),x37961),x37962)))
% 15.02/14.79 [3797]E(f857(f301(a1,f857(f857(f79(a1),x37971),f77(a1))),x37972),f305(a1,x37971,x37972))
% 15.02/14.79 [3808]E(f857(f857(f80(a919),x38081),f857(f857(f35(a919),x38082),x38081)),f857(f857(f3(a919),x38082),f44(a919,x38082,x38081)))
% 15.02/14.79 [3809]E(f857(f857(f80(a1),x38091),f857(f857(f35(a1),x38092),x38091)),f857(f857(f3(a1),x38092),f44(a1,x38092,x38091)))
% 15.02/14.79 [3813]E(f857(f172(a1),f178(f857(f857(f79(a1),x38131),f77(a1)),x38132)),f304(a1,x38131,x38132))
% 15.02/14.79 [3817]P106(f857(f857(f234(f927(x38171,a915)),x38172),x38172))
% 15.02/14.79 [3820]E(f857(f857(f110(f927(x38201,a915)),x38202),f857(f78(f927(x38201,a915)),x38202)),f241(f927(x38201,a915)))
% 15.02/14.79 [3821]E(f857(f857(f101(f927(x38211,a915)),x38212),f857(f78(f927(x38211,a915)),x38212)),f189(f927(x38211,a915)))
% 15.02/14.79 [3829]E(f857(f857(f3(a919),f857(f857(f3(a919),x38291),f77(a919))),x38292),f857(f857(f3(a919),x38291),f857(a112,x38292)))
% 15.02/14.79 [3835]E(f857(f857(f3(f927(x38351,a915)),f241(f927(x38351,a915))),x38352),f857(f78(f927(x38351,a915)),x38352))
% 15.02/14.79 [3836]E(f857(f857(f3(a1),f857(f103(a1),x38361)),f857(f103(a1),x38362)),f857(f103(a1),f857(f857(f79(a1),x38361),f857(f78(a1),x38362))))
% 15.02/14.79 [3849]E(f857(f172(a919),f139(a919,f857(f301(a919,x38491),f857(a112,x38492)))),f302(a919,x38491,x38492))
% 15.02/14.79 [3865]E(f857(f190(f920(f920(x38651))),f53(x38651,x38652)),f857(f857(f243(a919),f857(a112,f857(a112,f2(a919)))),f857(f190(f920(x38651)),x38652)))
% 15.02/14.79 [3884]E(f857(f857(f183(f926(x38841,x38841),a915),f2(a919)),x38842),f306(x38841,f189(f927(f926(x38841,x38841),a915))))
% 15.02/14.79 [3888]P106(f857(f137(a919),f139(a919,f857(f301(a919,x38881),x38882))))
% 15.02/14.79 [3904]E(f857(f309(a1,a919,a104),f302(a1,f857(f100(a1),x39041),f857(f100(a1),x39042))),f302(a919,x39041,x39042))
% 15.02/14.79 [3913]E(f185(a919,f2(a919),f7(a919),f857(f857(f3(a919),x39131),x39132)),f857(f857(f3(a919),x39131),f857(a112,x39132)))
% 15.02/14.79 [3914]E(f857(a104,f857(f857(f3(a1),x39141),f857(f857(f79(a1),x39142),f77(a1)))),f857(f34(a1),f305(a1,x39142,x39141)))
% 15.02/14.79 [3950]E(f857(f857(f154(a919,a919),a112),f139(a919,f857(f301(a919,x39501),x39502))),f139(a919,f857(f301(a919,f857(a112,x39501)),f857(a112,x39502))))
% 15.02/14.79 [3958]E(f857(f172(a1),f178(f857(f857(f79(a1),x39581),f77(a1)),f857(f857(f3(a1),x39582),f77(a1)))),f305(a1,x39581,x39582))
% 15.02/14.79 [3970]P106(f857(f857(f234(f927(x39701,a915)),f189(f927(x39701,a915))),x39702))
% 15.02/14.79 [3974]E(f84(x39741,f857(f857(f9(x39741,x39741,a915),a324),x39742)),x39742)
% 15.02/14.79 [3975]E(f89(x39751,f857(f857(f9(x39751,x39751,a915),a324),x39752)),x39752)
% 15.02/14.79 [3979]E(f857(f172(a919),f139(a919,f857(f301(a919,f857(a112,x39791)),f857(a112,x39792)))),f304(a919,x39791,x39792))
% 15.02/14.79 [4005]E(f857(f857(f253(x40051,x40052),f241(f927(x40051,a915))),f857(f18(f927(x40052,a915),x40051),f241(f927(x40052,a915)))),f241(f927(f926(x40051,x40052),a915)))
% 15.02/14.79 [4040]E(f857(f261(x40401),f857(f857(f10(a915,a915,x40401),a321),x40402)),f857(f78(f927(x40401,a915)),f857(f261(x40401),x40402)))
% 15.02/14.79 [4043]E(f857(f261(x40431),f857(f857(f9(x40431,x40431,a915),a324),x40432)),f857(f857(f308(x40431),x40432),f189(f927(x40431,a915))))
% 15.02/14.79 [4050]E(f857(f857(f79(a1),f857(f857(f3(a1),x40501),x40502)),f857(f857(f3(a1),x40501),x40502)),f857(f857(f3(a1),f857(f857(f79(a1),x40501),x40501)),f857(f857(f79(a1),x40502),x40502)))
% 15.02/14.79 [4051]E(f857(f857(f79(a1),f857(f857(f79(a1),x40511),x40511)),f857(f857(f79(a1),x40512),x40512)),f857(f857(f79(a1),f857(f857(f79(a1),x40511),x40512)),f857(f857(f79(a1),x40511),x40512)))
% 15.02/14.79 [4067]P106(f857(f857(f234(a919),f857(f34(x40671),f857(f172(x40671),x40672))),f857(f190(f920(x40671)),x40672)))
% 15.02/14.79 [4068]P106(f857(f857(f234(a919),f857(f190(f920(x40681)),f152(x40681,x40682))),f857(f190(f920(x40681)),x40682)))
% 15.02/14.79 [4079]E(f857(f261(x40791),f857(f857(f9(x40791,f927(x40791,a915),a915),f328(x40791)),x40792)),x40792)
% 15.02/14.79 [4093]E(f857(f857(f175(x40931),f857(f857(f3(a919),f857(f190(f920(x40931)),x40932)),f77(a919))),x40932),f114(x40931,x40932))
% 15.02/14.79 [4114]E(f185(a919,f2(a919),f857(f857(f10(a919,a919,a919),a112),f857(f188(a919),x41141)),x41142),f857(f857(f188(a919),f857(a112,x41141)),x41142))
% 15.02/14.79 [4119]E(f36(f927(x41191,a915),f857(f309(f927(f926(x41191,x41191),a915),f927(x41191,a915),f280(x41191)),x41192)),f857(f280(x41191),f36(f927(f926(x41191,x41191),a915),x41192)))
% 15.02/14.79 [4120]E(f185(a919,f857(a112,x41201),f857(f857(f10(a919,a919,a919),a112),f857(f233(a919),x41201)),x41202),f857(f857(f233(a919),f857(a112,x41201)),x41202))
% 15.02/14.79 [4122]E(f857(f857(f251(a1,a1),f857(f857(f35(a1),f857(f75(a1),x41221)),f857(f75(a1),x41222))),f44(a1,f857(f75(a1),x41221),f857(f75(a1),x41222))),f52(x41221,x41222))
% 15.02/14.79 [4145]P106(f857(f857(f234(f927(f927(x41451,a915),a915)),x41452),f857(f307(x41451),f36(f927(x41451,a915),x41452))))
% 15.02/14.79 [4177]E(f857(f857(f39(x41771,f927(x41771,a915)),x41772),f857(f857(f9(x41771,f927(x41771,a915),f927(x41771,a915)),f308(x41771)),f189(f927(x41771,a915)))),x41772)
% 15.02/14.79 [4178]E(f857(f857(f288(x41781,x41781,x41781),f857(f285(x41781,x41781),x41782)),f306(x41781,f857(f285(x41781,x41781),x41782))),f857(f285(x41781,x41781),f857(f857(f288(x41781,x41781,x41781),x41782),f306(x41781,x41782))))
% 15.02/14.79 [4243]E(f857(f172(x42431),f857(f142(f920(x42431),f920(x42431),f134(x42431),f113(x42431)),x42432)),f857(f857(f39(f920(x42431),f927(x42431,a915)),f857(f172(f920(x42431)),x42432)),f172(x42431)))
% 15.02/14.79 [4274]E(f857(f857(f110(f927(f926(x42741,x42741),a915)),f306(x42741,f189(f927(f926(x42741,x42741),a915)))),f857(f857(f288(x42741,x42741,x42741),f306(x42741,x42742)),x42742)),f306(x42741,x42742))
% 15.02/14.79 [4310]E(f857(f857(f181(x43101,x43101),x43102),x43102),f857(f857(f154(x43101,f926(x43101,x43101)),f857(f857(f20(x43101,x43101,f926(x43101,x43101)),f251(x43101,x43101)),f7(x43101))),x43102))
% 15.02/14.79 [4421]E(f857(f142(a919,f920(x44211),f857(f9(f920(x44211),a919,a919),f857(f857(f10(a919,f927(a919,a919),f920(x44211)),f233(a919)),f190(f920(x44211)))),f2(a919)),f857(f168(f920(x44211)),x44212)),f857(f190(f920(f920(x44211))),f179(x44211,x44212)))
% 15.02/14.79 [4493]E(f857(f857(f287(f926(a919,f920(x44931)),f920(x44931)),f318(a919,f920(x44931),a239,f145(x44931,x44932))),f857(f857(f20(f920(x44931),f920(x44931),f926(a919,f920(x44931))),f857(f857(f10(a919,f927(f920(x44931),f926(a919,f920(x44931))),f920(x44931)),f251(a919,f920(x44931))),f190(f920(x44931)))),f7(f920(x44931)))),f146(x44931,x44932))
% 15.02/14.79 [4621]E(f857(f261(x46211),f857(f857(f10(f927(f927(x46211,a915),a915),a915,x46211),f86(f927(x46211,a915))),f857(f857(f10(f927(f927(x46211,a915),a915),f927(f927(x46211,a915),a915),x46211),f857(f20(f927(x46211,a915),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x46211,a915)),a325),f857(f857(f9(f927(x46211,a915),f927(f927(x46211,a915),a915),a915),f328(f927(x46211,a915))),x46212)))),f328(x46211)))),f36(f927(x46211,a915),x46212))
% 15.02/14.79 [4622]E(f857(f261(x46221),f857(f857(f10(f927(f927(x46221,a915),a915),a915,x46221),f87(f927(x46221,a915))),f857(f857(f10(f927(f927(x46221,a915),a915),f927(f927(x46221,a915),a915),x46221),f857(f20(f927(x46221,a915),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x46221,a915)),a329),f857(f857(f9(f927(x46221,a915),f927(f927(x46221,a915),a915),a915),f328(f927(x46221,a915))),x46222)))),f328(x46221)))),f37(f927(x46221,a915),x46222))
% 15.02/14.79 [4751]~P106(f857(f857(f235(a1),f857(f100(a1),x47511)),f857(f78(a1),f857(f100(a1),x47512))))
% 15.02/14.79 [4757]~P25(a914,a928,f857(f857(f308(f918(a914)),f857(f857(f857(f90(a914),x47571),a929),x47572)),f189(f927(f918(a914),a915))))
% 15.02/14.79 [3711]E(f857(f857(f3(a919),f857(f857(f79(a919),x37111),x37112)),x37112),x37111)
% 15.02/14.79 [3712]E(f857(f857(f3(a919),f857(f857(f79(a919),x37121),x37122)),x37121),x37122)
% 15.02/14.79 [3778]E(f857(f857(f79(a919),f857(f857(f3(a919),x37781),x37782)),x37782),f857(f857(f233(a919),x37781),x37782))
% 15.02/14.79 [3891]E(f857(f857(f80(a919),f857(f857(f35(a919),x38911),x38912)),x38912),f857(f857(f3(a919),x38911),f44(a919,x38911,x38912)))
% 15.02/14.79 [3918]E(f857(f172(a919),f139(a919,f857(f301(a919,f857(a112,x39181)),x39182))),f305(a919,x39181,x39182))
% 15.02/14.79 [3926]E(f857(f100(a1),f217(f857(a104,f857(f75(a1),x39261)),f857(a104,f857(f75(a1),x39262)))),f857(f857(a218,x39261),x39262))
% 15.02/14.79 [3928]E(f857(f857(f110(f927(x39281,a915)),f857(f78(f927(x39281,a915)),x39282)),x39282),f241(f927(x39281,a915)))
% 15.02/14.79 [3929]E(f857(f857(f101(f927(x39291,a915)),f857(f78(f927(x39291,a915)),x39292)),x39292),f189(f927(x39291,a915)))
% 15.02/14.79 [3946]P106(f857(f857(f234(a919),f857(f857(f3(a919),x39461),x39462)),x39461))
% 15.02/14.79 [3947]P106(f857(f857(f234(a919),f857(f857(f35(a919),x39471),x39472)),x39471))
% 15.02/14.79 [3971]P106(f857(f857(f235(a919),x39711),f857(a112,f857(f857(f79(a919),x39712),x39711))))
% 15.02/14.79 [3972]P106(f857(f857(f235(a919),x39721),f857(a112,f857(f857(f79(a919),x39721),x39722))))
% 15.02/14.79 [3989]E(f857(f857(f80(a919),f857(a104,f857(f75(a1),x39891))),f857(a104,f857(f75(a1),x39892))),f857(a104,f857(f75(a1),f857(f857(f80(a1),x39891),x39892))))
% 15.02/14.79 [4001]P106(f857(f857(f234(a1),f2(a1)),f857(f857(f243(a1),f857(f75(a1),x40011)),x40012)))
% 15.02/14.79 [4072]E(f857(f284(f920(x40721),f920(x40721),f158(x40721,x40722)),f857(f857(f308(f920(x40721)),f113(x40721)),f189(f927(f920(x40721),a915)))),f857(f857(f308(f920(x40721)),f113(x40721)),f189(f927(f920(x40721),a915))))
% 15.02/14.79 [4091]E(f857(f857(f110(f927(f926(x40911,x40911),a915)),f306(x40911,x40912)),f306(x40911,f189(f927(f926(x40911,x40911),a915)))),f306(x40911,x40912))
% 15.02/14.79 [4104]E(f857(f857(f35(a1),f857(f103(a1),f857(f857(f79(a1),x41041),x41041))),f857(f103(a1),f857(f857(f79(a1),x41042),x41042))),f857(f857(f35(a1),f857(f103(a1),x41041)),f857(f103(a1),x41042)))
% 15.02/14.79 [4167]E(f857(f857(f243(a1),x41671),f857(f103(a919),f857(f857(f79(a1),x41672),x41672))),f857(f857(f85(a1,a1),f857(f857(f243(a1),x41671),f857(f103(a919),x41672))),f857(f857(f20(a1,a1,a1),f80(a1)),f7(a1))))
% 15.02/14.79 [4173]E(f857(f261(f927(x41731,a915)),f857(f857(f9(f927(x41731,a915),f927(x41731,a915),a915),f234(f927(x41731,a915))),x41732)),f857(f307(x41731),x41732))
% 15.02/14.79 [4189]E(f857(f857(f154(a1,a919),a104),f857(f857(f134(a1),f857(f857(f154(a919,a1),f100(a1)),x41891)),f857(f857(f154(a919,a1),f100(a1)),x41892))),f857(f857(f134(a919),x41891),x41892))
% 15.02/14.79 [4221]E(f857(f309(a1,a1,f857(f857(f9(a1,a1,a1),f79(a1)),x42211)),f857(f301(a1,f2(a1)),f857(f857(f3(a1),x42212),x42211))),f857(f301(a1,x42211),x42212))
% 15.02/14.79 [4223]P55(x42231,f857(f857(f3(f927(f926(x42231,x42231),a915)),x42232),f306(x42231,f189(f927(f926(x42231,x42231),a915)))))
% 15.02/14.79 [4241]E(f857(f190(f920(x42411)),f857(f142(f920(x42411),f920(x42411),f134(x42411),f113(x42411)),x42412)),f857(f165(a919),f857(f857(f154(f920(x42411),a919),f190(f920(x42411))),x42412)))
% 15.02/14.79 [4245]P54(x42451,f241(f927(x42451,a915)),f857(f857(f110(f927(f926(x42451,x42451),a915)),x42452),f306(x42451,f189(f927(f926(x42451,x42451),a915)))))
% 15.02/14.79 [4290]E(f185(a919,f2(a919),f857(f857(f10(a919,a919,a919),a112),f857(f857(f9(a919,a919,a919),f188(a919)),x42901)),x42902),f857(f857(f188(a919),x42902),f857(a112,x42901)))
% 15.02/14.79 [4293]E(f185(a919,f857(a112,x42931),f857(f857(f10(a919,a919,a919),a112),f857(f857(f9(a919,a919,a919),f233(a919)),x42931)),x42932),f857(f857(f233(a919),x42932),f857(a112,x42931)))
% 15.02/14.79 [4296]E(f857(f309(x42961,f920(x42961),f857(f857(f9(x42961,f920(x42961),f920(x42961)),f151(x42961)),f113(x42961))),x42962),f174(x42961,x42962,f857(f857(f308(f920(x42961)),f113(x42961)),f189(f927(f920(x42961),a915)))))
% 15.02/14.79 [4298]E(f857(f857(f110(f927(f926(x42981,x42981),a915)),f857(f857(f288(x42981,x42981,x42981),x42982),f306(x42981,x42982))),f306(x42981,f189(f927(f926(x42981,x42981),a915)))),f306(x42981,x42982))
% 15.02/14.79 [4305]P106(f857(f857(f234(f927(f926(x43051,x43051),a915)),f262(x43051,x43052)),f857(f857(f253(x43051,x43051),x43052),f857(f18(f927(x43051,a915),x43051),x43052))))
% 15.02/14.79 [4308]E(f857(f309(a1,a919,a104),f857(f857(f110(f927(a1,a915)),f857(f309(a919,a1,f100(a1)),x43081)),f857(f309(a919,a1,f100(a1)),x43082))),f857(f857(f110(f927(a919,a915)),x43081),x43082))
% 15.02/14.79 [4309]E(f857(f309(a1,a919,a104),f857(f857(f101(f927(a1,a915)),f857(f309(a919,a1,f100(a1)),x43091)),f857(f309(a919,a1,f100(a1)),x43092))),f857(f857(f101(f927(a919,a915)),x43091),x43092))
% 15.02/14.79 [4312]E(f857(f261(x43121),f857(f857(f10(a915,a915,x43121),a321),f857(f857(f9(x43121,f927(x43121,a915),a915),f328(x43121)),x43122))),f857(f78(f927(x43121,a915)),x43122))
% 15.02/14.79 [4339]E(f857(f142(f920(x43391),f920(x43391),f134(x43391),f113(x43391)),f857(f857(f154(f920(x43391),f920(x43391)),f168(x43391)),f857(f168(f920(x43391)),x43392))),f857(f168(x43391),f857(f142(f920(x43391),f920(x43391),f134(x43391),f113(x43391)),x43392)))
% 15.02/14.79 [4365]E(f857(f857(f39(a919,f927(f926(x43651,x43651),a915)),f241(f927(a919,a915))),f857(f857(f9(a919,f927(f926(x43651,x43651),a915),f927(f926(x43651,x43651),a915)),f183(f926(x43651,x43651),a915)),x43652)),f306(x43651,x43652))
% 15.02/14.79 [4383]E(f84(x43831,f857(f857(f10(f927(x43831,a915),a915,x43831),f857(a324,x43832)),f857(f857(f9(x43831,f927(x43831,a915),f927(x43831,a915)),f308(x43831)),f189(f927(x43831,a915))))),f311(x43831,x43832))
% 15.02/14.79 [4391]E(f857(f190(f920(x43911)),f152(x43911,f857(f142(f920(x43911),f920(x43911),f134(x43911),f113(x43911)),x43912))),f857(f34(x43911),f857(f857(f39(f920(x43911),f927(x43911,a915)),f857(f172(f920(x43911)),x43912)),f172(x43911))))
% 15.02/14.79 [4405]E(f857(f857(f110(f927(f926(x44051,x44051),a915)),x44052),f857(f857(f288(x44051,x44051,x44051),f857(f857(f288(x44051,x44051,x44051),x44052),f306(x44051,x44052))),x44052)),f857(f857(f288(x44051,x44051,x44051),x44052),f306(x44051,x44052)))
% 15.02/14.79 [4429]P106(f857(f857(f234(f927(f926(x44291,x44291),a915)),f857(f857(f288(x44291,x44291,x44291),x44292),f306(x44291,x44292))),f857(f857(f253(x44291,x44291),f857(f280(x44291),x44292)),f857(f18(f927(x44291,a915),x44291),f857(f280(x44291),x44292)))))
% 15.02/14.79 [4470]E(f857(f261(f920(x44701)),f857(f857(f9(f920(x44701),f927(x44701,a915),a915),f857(f857(f10(f927(x44701,a915),f927(f927(x44701,a915),a915),f920(x44701)),f234(f927(x44701,a915))),f172(x44701))),x44702)),f161(x44701,x44702))
% 15.02/14.79 [4481]E(f857(f156(f920(x44811),x44811,f113(x44811),f857(f857(f10(f920(x44811),f927(f920(x44811),f920(x44811)),x44811),f857(f9(f920(x44811),f920(x44811),f920(x44811)),f134(x44811))),f857(f857(f9(x44811,f920(x44811),f920(x44811)),f151(x44811)),f113(x44811)))),x44812),f857(f167(x44811),x44812))
% 15.02/14.79 [4522]P26(f927(x45221,x45222),f927(f926(x45221,x45222),a915),f857(f857(f10(f927(f926(x45221,x45222),a915),f927(f926(x45221,x45222),a915),f927(x45221,x45222)),f261(f926(x45221,x45222))),f857(f857(f10(f927(x45221,f927(x45222,a915)),f927(f926(x45221,x45222),a915),f927(x45221,x45222)),f256(x45221,x45222,a915)),f857(f10(x45222,f927(x45222,a915),x45221),f857(f9(x45222,x45222,a915),a324)))),f241(f927(f927(x45221,x45222),a915)))
% 15.02/14.79 [4527]E(f44(a1,f857(f103(a1),f857(f857(f79(a1),x45271),x45271)),f857(f103(a1),f857(f857(f79(a1),x45272),x45272))),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f44(a1,f857(f103(a1),x45271),f857(f103(a1),x45272))))
% 15.02/14.79 [4571]E(f857(f857(f39(x45711,f927(f926(x45711,x45711),a915)),x45712),f857(f857(f9(x45711,f927(f926(x45711,x45711),a915),f927(f926(x45711,x45711),a915)),f857(f857(f10(f926(x45711,x45711),f927(f927(f926(x45711,x45711),a915),f927(f926(x45711,x45711),a915)),x45711),f308(f926(x45711,x45711))),f857(f857(f20(x45711,x45711,f926(x45711,x45711)),f251(x45711,x45711)),f7(x45711)))),f189(f927(f926(x45711,x45711),a915)))),f262(x45711,x45712))
% 15.02/14.79 [4579]E(f203(x45791,f857(f857(f251(a1,a1),f857(f78(a1),f857(f857(f72(f926(a1,a1),a1,x45791,f250(a1,a1)),f213(x45791)),x45792))),f857(f857(f72(f926(a1,a1),a1,x45791,f255(a1,a1)),f213(x45791)),x45792))),f228(x45791,x45792))
% 15.02/14.79 [4660]E(f857(f261(f927(x46601,a915)),f857(f857(f10(f927(f927(x46601,a915),a915),a915,f927(x46601,a915)),f86(f927(x46601,a915))),f857(f857(f9(f927(x46601,a915),f927(f927(x46601,a915),a915),f927(f927(x46601,a915),a915)),f857(f857(f10(f927(f927(x46601,a915),f927(a915,a915)),f927(f927(f927(x46601,a915),a915),f927(f927(x46601,a915),a915)),f927(x46601,a915)),f20(f927(x46601,a915),a915,a915)),f857(f857(f10(f927(f927(x46601,a915),a915),f927(f927(x46601,a915),f927(a915,a915)),f927(x46601,a915)),f857(f10(a915,f927(a915,a915),f927(x46601,a915)),a325)),f857(f857(f9(f927(x46601,a915),f927(f927(x46601,a915),f927(x46601,a915)),f927(f927(x46601,a915),a915)),f857(f857(f10(f927(f927(x46601,a915),a915),f927(f927(f927(x46601,a915),f927(x46601,a915)),f927(f927(x46601,a915),a915)),f927(x46601,a915)),f10(f927(x46601,a915),a915,f927(x46601,a915))),a324)),f78(f927(x46601,a915)))))),f857(f857(f10(f927(f927(x46601,a915),a915),a915,f927(x46601,a915)),f857(f328(f927(x46601,a915)),x46602)),f307(x46601))))),f857(f307(x46601),f857(f78(f927(x46601,a915)),x46602)))
% 15.02/14.79 [4749]~E(f857(f857(f79(a1),x47491),x47491),f857(f857(f3(a1),f857(f857(f79(a1),x47492),x47492)),a97))
% 15.02/14.79 [4753]~P106(f857(f857(f235(a919),f857(f857(f79(a919),x47531),x47532)),x47532))
% 15.02/14.79 [4754]~P106(f857(f857(f235(a919),f857(f857(f79(a919),x47541),x47542)),x47541))
% 15.02/14.79 [4006]E(f857(f857(f3(a919),x40061),f857(f857(f80(a919),f857(f857(f35(a919),x40061),x40062)),x40062)),f44(a919,x40061,x40062))
% 15.02/14.79 [4007]E(f857(f857(f3(a1),x40071),f857(f857(f80(a1),f857(f857(f35(a1),x40071),x40072)),x40072)),f44(a1,x40071,x40072))
% 15.02/14.79 [4041]E(f857(f857(f154(a919,x40411),f857(f164(x40411),x40412)),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(x40411)),x40412)))),x40412)
% 15.02/14.79 [4100]E(f857(f284(x41001,x41001,f306(x41001,f189(f927(f926(x41001,x41001),a915)))),x41002),x41002)
% 15.02/14.79 [4226]E(f306(x42261,f857(f857(f110(f927(f926(x42261,x42261),a915)),x42262),f306(x42261,f189(f927(f926(x42261,x42261),a915))))),f306(x42261,x42262))
% 15.02/14.79 [4227]E(f306(x42271,f857(f857(f3(f927(f926(x42271,x42271),a915)),x42272),f306(x42271,f189(f927(f926(x42271,x42271),a915))))),f306(x42271,x42272))
% 15.02/14.79 [4277]E(f857(f857(f3(a1),f857(f857(f3(a1),f857(f857(f79(a1),x42771),x42771)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),x42772),x42772)),a97)),f857(f857(f79(a1),f857(f857(f3(a1),x42771),x42772)),f857(f857(f3(a1),x42771),x42772)))
% 15.02/14.79 [4317]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f79(a1),x43171),x43172)),f857(f857(f79(a1),x43171),x43172))),a97),f857(f857(f79(a1),f857(f857(f79(a1),x43171),x43171)),f857(f857(f3(a1),f857(f857(f79(a1),x43172),x43172)),a97)))
% 15.02/14.79 [4342]E(f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),x43421),x43421)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),x43422),x43422)),a97)),f857(f857(f79(a1),f857(f857(f79(a1),x43421),f857(f857(f3(a1),x43422),a97))),f857(f857(f79(a1),x43421),f857(f857(f3(a1),x43422),a97))))
% 15.02/14.79 [4353]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),x43531),x43532)),f857(f857(f3(a1),x43531),x43532))),a97),f857(f857(f3(a1),f857(f857(f3(a1),f857(f857(f79(a1),x43531),x43531)),a97)),f857(f857(f79(a1),x43532),x43532)))
% 15.02/14.79 [4354]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f79(a1),x43541),x43542)),f857(f857(f79(a1),x43541),x43542))),a97),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),x43541),x43541)),a97)),f857(f857(f79(a1),x43542),x43542)))
% 15.02/14.79 [4402]E(f857(f100(a1),f857(f857(f35(a919),f857(f857(f80(a919),f857(a104,f857(f75(a1),x44021))),f857(a104,f857(f75(a1),x44022)))),f217(f857(a104,f857(f75(a1),x44021)),f857(a104,f857(f75(a1),x44022))))),f219(x44021,x44022))
% 15.02/14.79 [4447]E(f857(f857(f258(f926(a99,a99),a99,f926(a99,a99),f926(x44471,f926(a99,a99))),f266(f857(a5,f857(f190(f920(x44471)),x44472)))),f857(f857(f10(x44471,f927(f926(a99,a99),f926(x44471,f926(a99,a99))),a99),f251(x44471,f926(a99,a99))),f857(f857(f10(a919,x44471,a99),f857(f164(x44471),x44472)),a22))),f274(x44471,x44472))
% 15.02/14.79 [4528]E(f857(f142(a919,f920(x45281),f857(f9(f920(x45281),a919,a919),f857(f857(f10(a919,f927(a919,a919),f920(x45281)),f233(a919)),f190(f920(x45281)))),f2(a919)),f857(f168(f920(x45281)),f179(x45281,x45282))),f857(f190(f920(f920(x45281))),f857(f136(f920(x45281),f857(f857(f10(a915,a915,f920(x45281)),a321),f857(f857(f9(f920(x45281),f920(x45281),a915),a324),f113(x45281)))),x45282)))
% 15.02/14.79 [4534]E(f857(f857(f39(a919,f927(x45341,a915)),f241(f927(a919,a915))),f857(f857(f9(a919,f927(a919,f927(x45341,a915)),f927(x45341,a915)),f857(f857(f10(f927(a919,a915),f927(f927(a919,f927(x45341,a915)),f927(x45341,a915)),a919),f39(a919,f927(x45341,a915))),f301(a919,f2(a919)))),x45342)),f857(f857(f39(a919,f927(x45341,a915)),f241(f927(a919,a915))),x45342))
% 15.02/14.79 [4556]P106(f857(f60(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),x45561)),f857(f857(f9(a919,a919,a915),f235(a919)),x45562)))))
% 15.02/14.79 [4669]E(f857(f261(f926(f920(x46691),f920(x46691))),f857(f256(f920(x46691),f920(x46691),a915),f857(f857(f20(f920(x46691),f927(f920(x46691),a915),f927(f920(x46691),a915)),f857(f857(f10(f927(f920(x46691),f927(a915,a915)),f927(f927(f920(x46691),a915),f927(f920(x46691),a915)),f920(x46691)),f20(f920(x46691),a915,a915)),f857(f857(f10(f927(f920(x46691),a915),f927(f920(x46691),f927(a915,a915)),f920(x46691)),f857(f10(a915,f927(a915,a915),f920(x46691)),a326)),f857(f857(f9(f920(x46691),f927(f920(x46691),a919),f927(f920(x46691),a915)),f857(f857(f10(f927(a919,a915),f927(f927(f920(x46691),a919),f927(f920(x46691),a915)),f920(x46691)),f10(a919,a915,f920(x46691))),f857(f857(f10(a919,f927(a919,a915),f920(x46691)),f235(a919)),f190(f920(x46691))))),f190(f920(x46691)))))),f857(f857(f20(f920(x46691),f927(f920(x46691),a915),f927(f920(x46691),a915)),f857(f857(f10(f927(f920(x46691),f927(a915,a915)),f927(f927(f920(x46691),a915),f927(f920(x46691),a915)),f920(x46691)),f20(f920(x46691),a915,a915)),f857(f857(f10(f927(f920(x46691),a915),f927(f920(x46691),f927(a915,a915)),f920(x46691)),f857(f10(a915,f927(a915,a915),f920(x46691)),a325)),f857(f857(f9(f920(x46691),f927(f920(x46691),a919),f927(f920(x46691),a915)),f857(f857(f10(f927(a919,a915),f927(f927(f920(x46691),a919),f927(f920(x46691),a915)),f920(x46691)),f10(a919,a915,f920(x46691))),f857(f857(f10(a919,f927(a919,a915),f920(x46691)),a324),f190(f920(x46691))))),f190(f920(x46691)))))),f857(f857(f9(f920(x46691),f927(f926(f920(x46691),f920(x46691)),a915),f927(f920(x46691),a915)),f857(f857(f10(f927(f920(x46691),f927(f927(f926(f920(x46691),f920(x46691)),a915),a915)),f927(f927(f926(f920(x46691),f920(x46691)),a915),f927(f920(x46691),a915)),f920(x46691)),f9(f920(x46691),f927(f926(f920(x46691),f920(x46691)),a915),a915)),f857(f857(f10(f927(f920(x46691),f926(f920(x46691),f920(x46691))),f927(f920(x46691),f927(f927(f926(f920(x46691),f920(x46691)),a915),a915)),f920(x46691)),f857(f10(f926(f920(x46691),f920(x46691)),f927(f927(f926(f920(x46691),f920(x46691)),a915),a915),f920(x46691)),f328(f926(f920(x46691),f920(x46691))))),f251(f920(x46691),f920(x46691))))),f145(x46691,x46692)))))),f146(x46691,x46692))
% 15.02/14.79 [4345]E(f857(f857(f79(a1),f857(f857(f79(a1),f857(f857(f80(a1),x43451),x43452)),f857(f857(f80(a1),x43451),x43452))),x43452),f857(f857(f80(a1),f857(f857(f3(a1),f857(f857(f79(a1),x43451),x43451)),a97)),x43452))
% 15.02/14.79 [4446]E(f857(a104,f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x44461),x44462)),f189(f927(f926(a919,a919),a915)))))),f857(f857(f3(a919),x44461),x44462))
% 15.02/14.79 [4450]E(f857(f857(f288(x44501,x44501,x44501),f857(f857(f110(f927(f926(x44501,x44501),a915)),x44502),f306(x44501,f189(f927(f926(x44501,x44501),a915))))),f306(x44501,f857(f857(f110(f927(f926(x44501,x44501),a915)),x44502),f306(x44501,f189(f927(f926(x44501,x44501),a915)))))),f306(x44501,x44502))
% 15.02/14.79 [4487]E(f267(x44871,f857(f136(f926(a99,x44871),f857(f256(a99,x44871,a915),f857(f857(f10(a915,f927(x44871,a915),a99),f18(a915,x44871)),f857(f235(a99),f2(a99))))),x44872)),f267(x44871,x44872))
% 15.02/14.79 [4488]E(f265(x44881,f857(f136(f926(a99,x44881),f857(f256(a99,x44881,a915),f857(f857(f10(a915,f927(x44881,a915),a99),f18(a915,x44881)),f857(f235(a99),f2(a99))))),x44882)),f265(x44881,x44882))
% 15.02/14.79 [4490]E(f857(f78(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x44901),x44902)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x44902),x44901)),f189(f927(f926(a919,a919),a915))))))
% 15.02/14.79 [4547]E(f857(f857(f287(f920(a919),x45471),f145(a919,a239)),f857(f857(f9(x45471,f920(f927(x45471,a919)),f920(a919)),f857(f857(f10(f927(f927(x45471,a919),a919),f927(f920(f927(x45471,a919)),f920(a919)),x45471),f154(f927(x45471,a919),a919)),f857(f9(f927(x45471,a919),x45471,a919),f7(f927(x45471,a919))))),x45472)),f153(x45471,x45472))
% 15.02/14.79 [4568]E(f857(f857(f85(a1,a919),f857(f103(a1),f857(f857(f79(a1),x45681),a97))),f857(f857(f20(a1,a919,a919),f857(f857(f9(a1,a919,f927(a919,a919)),f857(f857(f10(a915,f927(a919,f927(a919,a919)),a1),f96(a919)),a194)),f2(a919))),f857(f857(f10(a919,a919,a1),a112),f857(f857(f10(a919,a919,a1),f857(f188(a919),x45682)),a104)))),f857(f857(f188(a919),f857(a112,x45682)),f857(f103(a919),x45681)))
% 15.02/14.79 [4569]E(f857(f857(f85(a1,a919),f857(f103(a1),f857(f857(f79(a1),x45691),a97))),f857(f857(f20(a1,a919,a919),f857(f857(f9(a1,a919,f927(a919,a919)),f857(f857(f10(a915,f927(a919,f927(a919,a919)),a1),f96(a919)),a194)),f857(a112,x45692))),f857(f857(f10(a919,a919,a1),a112),f857(f857(f10(a919,a919,a1),f857(f233(a919),x45692)),a104)))),f857(f857(f233(a919),f857(a112,x45692)),f857(f103(a919),x45691)))
% 15.02/14.79 [4589]E(f857(f142(f920(x45891),f920(x45891),f134(x45891),f113(x45891)),f857(f857(f154(f920(x45891),f920(x45891)),f156(f920(x45891),x45891,f113(x45891),f857(f857(f10(f920(x45891),f927(f920(x45891),f920(x45891)),x45891),f18(f920(x45891),f920(x45891))),f857(f857(f9(x45891,f920(x45891),f920(x45891)),f151(x45891)),f113(x45891))))),x45892)),f857(f857(f154(f920(x45891),x45891),f141(x45891)),f857(f136(f920(x45891),f857(f857(f10(a915,a915,f920(x45891)),a321),f857(f857(f9(f920(x45891),f920(x45891),a915),a324),f113(x45891)))),x45892)))
% 15.02/14.79 [4651]E(f857(f256(a1,a1,a915),f857(f857(f9(a1,f927(a1,a915),f927(a1,a915)),f857(f857(f10(f927(a1,f927(a915,a915)),f927(f927(a1,a915),f927(a1,a915)),a1),f20(a1,a915,a915)),f857(f857(f10(f927(a1,a915),f927(a1,f927(a915,a915)),a1),f857(f10(a915,f927(a915,a915),a1),a325)),f857(f857(f10(f927(a1,a1),f927(a1,a915),a1),f857(f10(a1,a915,a1),f857(a324,x46511))),f857(f857(f10(a1,f927(a1,a1),a1),f79(a1)),f857(f80(a1),x46512)))))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),f857(a329,f857(f857(f235(a1),f2(a1)),x46512))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),f857(f857(f9(a1,a1,a915),f235(a1)),x46512))))),f857(f857(f10(a915,a915,a1),f857(a329,f857(a321,f857(f857(f235(a1),f2(a1)),x46512)))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f235(a1),x46512))),f857(f857(f9(a1,a1,a915),f234(a1)),f2(a1))))))),f48(x46511,x46512))
% 15.02/14.79 [4654]E(f857(f261(x46541),f857(f857(f10(f927(a919,a915),a915,x46541),f86(a919)),f857(f857(f9(x46541,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),x46541),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),x46541),f857(f10(a915,f927(a915,a915),a919),a325)),f857(f857(f9(x46541,f927(a919,x46541),f927(a919,a915)),f857(f857(f10(f927(x46541,a915),f927(f927(a919,x46541),f927(a919,a915)),x46541),f10(x46541,a915,a919)),a324)),f857(f164(x46541),x46542))))),f857(f857(f9(a919,a919,a915),f235(a919)),f857(f190(f920(x46541)),x46542))))),f857(f172(x46541),x46542))
% 15.02/14.79 [4460]E(f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),x44601),a97)),x44602)),f857(f857(f3(a1),f857(f857(f79(a1),x44601),a97)),x44602))),a97),f857(f857(f3(a1),f857(f857(f79(a1),x44601),x44601)),f857(f857(f3(a1),f857(f857(f79(a1),x44602),x44602)),a97)))
% 15.02/14.79 [4584]E(f857(f142(f920(f920(x45841)),f920(f920(x45841)),f134(f920(x45841)),f113(f920(x45841))),f857(f857(f154(f920(x45841),f920(f920(x45841))),f156(f920(f920(x45841)),x45841,f113(f920(x45841)),f857(f18(f927(f920(x45841),f920(f920(x45841))),x45841),f857(f857(f9(f920(x45841),f920(f920(x45841)),f920(f920(x45841))),f151(f920(x45841))),f113(f920(x45841)))))),x45842)),f857(f857(f154(f920(x45841),f920(x45841)),f171(x45841)),f857(f136(f920(x45841),f857(f857(f10(a915,a915,f920(x45841)),a321),f857(f857(f9(f920(x45841),f920(x45841),a915),a324),f113(x45841)))),x45842)))
% 15.02/14.79 [4594]E(f857(f857(f85(a1,a919),f857(f103(a1),f857(f857(f79(a1),x45941),a97))),f857(f857(f20(a1,a919,a919),f857(f857(f9(a1,a919,f927(a919,a919)),f857(f857(f10(a915,f927(a919,f927(a919,a919)),a1),f96(a919)),a194)),f2(a919))),f857(f857(f10(a919,a919,a1),a112),f857(f857(f9(a1,a919,a919),f857(f857(f10(a919,f927(a919,a919),a1),f188(a919)),a104)),x45942)))),f857(f857(f188(a919),f857(f103(a919),x45941)),f857(a112,x45942)))
% 15.02/14.79 [4595]E(f857(f857(f85(a1,a919),f857(f103(a1),f857(f857(f79(a1),x45951),a97))),f857(f857(f20(a1,a919,a919),f857(f857(f9(a1,a919,f927(a919,a919)),f857(f857(f10(a915,f927(a919,f927(a919,a919)),a1),f96(a919)),a194)),f857(a112,x45952))),f857(f857(f10(a919,a919,a1),a112),f857(f857(f9(a1,a919,a919),f857(f857(f10(a919,f927(a919,a919),a1),f233(a919)),a104)),x45952)))),f857(f857(f233(a919),f857(f103(a919),x45951)),f857(a112,x45952)))
% 15.02/14.79 [4583]E(f857(f256(x45831,x45831,a915),f857(f857(f20(x45831,a915,f927(x45831,a915)),f857(f857(f10(f927(x45831,f927(a915,a915)),f927(a915,f927(x45831,a915)),x45831),f9(x45831,a915,a915)),f857(f857(f10(f927(x45831,a915),f927(x45831,f927(a915,a915)),x45831),f857(f10(a915,f927(a915,a915),x45831),a325)),a324))),x45832)),f262(x45831,x45832))
% 15.02/14.79 [4628]E(f857(f857(f35(a919),x46281),f857(f857(f79(a919),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),x46282)),f857(f857(f35(a919),x46281),f857(a112,f857(a112,f857(a112,x46282)))))
% 15.02/14.79 [4629]E(f44(a919,x46291,f857(f857(f79(a919),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),x46292)),f44(a919,x46291,f857(a112,f857(a112,f857(a112,x46292)))))
% 15.02/14.79 [4630]E(f44(a919,f857(f857(f79(a919),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),x46301),x46302),f44(a919,f857(a112,f857(a112,f857(a112,x46301))),x46302))
% 15.02/14.79 [4642]E(f123(f857(x46421,f857(f857(f80(a99),f857(f103(a99),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),x46422))),f857(f201(x46421),x46422))
% 15.02/14.79 [4643]E(f857(f857(f35(a919),f857(f857(f79(a919),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),x46431)),x46432),f857(f857(f35(a919),f857(a112,f857(a112,f857(a112,x46431)))),x46432))
% 15.02/14.79 [4701]~E(f27(x47011,x47012,x47013),a25)
% 15.02/14.79 [4702]~E(f26(x47021,x47022,x47023),a25)
% 15.02/14.79 [4706]~E(f126(x47061,x47062,x47063),f119(x47061))
% 15.02/14.79 [3436]E(f857(f193(x34361,x34362),x34363),f121(x34361,x34362))
% 15.02/14.79 [3455]E(f857(f200(x34551,x34552),x34553),f857(f129(x34551),x34552))
% 15.02/14.79 [3531]E(f857(f857(f154(x35311,x35312),x35313),f113(x35311)),f113(x35312))
% 15.02/14.79 [3571]E(f857(f184(x35711,x35712,x35713),f2(a919)),x35712)
% 15.02/14.79 [3573]E(f857(f857(f181(x35731,x35732),x35733),f113(x35732)),f113(f926(x35731,x35732)))
% 15.02/14.79 [3588]E(f857(f190(f920(x35881)),f169(x35881,x35882,x35883)),x35882)
% 15.02/14.79 [3607]E(f84(x36071,f61(x36071,x36072,x36073)),f857(f62(x36071,x36072),x36073))
% 15.02/14.79 [3611]E(f242(x36111,x36112,f242(x36112,x36111,x36113)),x36113)
% 15.02/14.79 [3631]E(f857(f168(x36311),f169(x36311,x36312,x36313)),f169(x36311,x36312,x36313))
% 15.02/14.79 [3658]E(f140(x36581,x36582,f152(x36581,x36583)),f152(x36581,f140(x36581,x36582,x36583)))
% 15.02/14.79 [3677]E(f857(f250(f920(x36771),f920(x36771)),f166(x36771,x36772,x36773)),f857(f136(x36771,x36772),x36773))
% 15.02/14.79 [3720]E(f857(f857(f151(x37201),x37202),f169(x37201,x37203,x37202)),f169(x37201,f857(a112,x37203),x37202))
% 15.02/14.79 [3752]E(f19(x37521,x37522,x37523,f2(a99)),x37522)
% 15.02/14.79 [3753]E(f185(x37531,x37532,x37533,f2(a919)),x37532)
% 15.02/14.79 [3754]E(f21(x37541,x37542,x37543,f2(a99)),x37542)
% 15.02/14.79 [3761]E(f163(x37611,x37612,x37613,f113(x37611)),f113(x37612))
% 15.02/14.79 [3762]E(f130(x37621,x37622,x37623,f119(x37621)),f119(x37622))
% 15.02/14.79 [3768]E(f857(f857(f164(x37681),f857(f857(f151(x37681),x37682),x37683)),f2(a919)),x37682)
% 15.02/14.79 [3798]E(f58(x37981,x37982,f113(x37981),x37983),f113(f926(x37981,x37982)))
% 15.02/14.79 [3819]P26(x38191,x38192,x38193,f189(f927(x38191,a915)))
% 15.02/14.79 [3922]E(f264(x39221,x39222,x39223),f857(f251(f927(a99,f927(a915,f923(f921(x39221)))),f926(a99,a99)),f40(x39221)))
% 15.02/14.79 [3980]E(f857(f72(x39801,x39802,x39801,x39803),f31(x39801)),x39803)
% 15.02/14.79 [4159]P106(f857(f857(f328(f926(x41591,x41591)),f857(f857(f251(x41591,x41591),x41592),x41592)),f306(x41591,x41593)))
% 15.02/14.79 [4759]~P106(f857(f857(f328(f926(f920(x47591),f920(x47591))),f857(f857(f251(f920(x47591),f920(x47591)),x47592),f113(x47591))),f145(x47591,x47593)))
% 15.02/14.79 [4760]~P106(f857(f857(f328(f926(f920(x47601),f920(x47601))),f857(f857(f251(f920(x47601),f920(x47601)),x47602),f113(x47601))),f147(x47601,x47603)))
% 15.02/14.79 [4761]~P106(f857(f857(f328(f926(f920(x47611),f920(x47611))),f857(f857(f251(f920(x47611),f920(x47611)),x47612),f113(x47611))),f157(x47611,x47613)))
% 15.02/14.79 [4762]~P106(f857(f857(f328(f926(f920(x47621),f920(x47621))),f857(f857(f251(f920(x47621),f920(x47621)),f113(x47621)),x47622)),f145(x47621,x47623)))
% 15.02/14.79 [4763]~P106(f857(f857(f328(f926(f920(x47631),f920(x47631))),f857(f857(f251(f920(x47631),f920(x47631)),f113(x47631)),x47632)),f157(x47631,x47633)))
% 15.02/14.79 [3506]E(f857(f857(f202(x35061),x35062),x35063),f203(x35061,f216(x35062,x35063)))
% 15.02/14.79 [3560]E(f857(f285(x35601,x35602),f857(f285(x35602,x35601),x35603)),x35603)
% 15.02/14.79 [3583]E(f857(f857(f181(x35831,x35832),f113(x35831)),x35833),f113(f926(x35831,x35832)))
% 15.02/14.79 [3586]E(f176(x35861,x35862,f857(f281(a919),x35863)),f857(f857(f175(x35861),x35863),x35862))
% 15.02/14.79 [3604]E(f152(x36041,f857(f136(x36041,x36042),x36043)),f857(f136(x36041,x36042),f152(x36041,x36043)))
% 15.02/14.79 [3605]E(f857(f283(x36051,x36052),f857(f285(x36052,x36051),x36053)),f857(f263(x36052,x36051),x36053))
% 15.02/14.79 [3606]E(f857(f263(x36061,x36062),f857(f285(x36062,x36061),x36063)),f857(f283(x36062,x36061),x36063))
% 15.02/14.79 [3624]E(f857(f136(x36241,x36242),f857(f168(x36241),x36243)),f857(f168(x36241),f857(f136(x36241,x36242),x36243)))
% 15.02/14.79 [3637]E(f857(f857(f138(x36371),x36372),f857(f171(x36371),x36373)),f857(f857(f138(x36371),f857(a112,x36372)),x36373))
% 15.02/14.79 [3653]E(f28(f26(x36531,x36532,x36533)),f857(f857(f79(a919),f28(x36533)),f857(a112,f2(a919))))
% 15.02/14.79 [3654]E(f857(f310(x36541,x36542,x36543),f189(f927(x36542,a915))),f189(f927(x36541,a915)))
% 15.02/14.79 [3655]E(f857(f310(x36551,x36552,x36553),f241(f927(x36552,a915))),f241(f927(x36551,a915)))
% 15.02/14.79 [3656]E(f857(f284(x36561,x36562,x36563),f189(f927(x36561,a915))),f189(f927(x36562,a915)))
% 15.02/14.79 [3657]E(f857(f309(x36571,x36572,x36573),f189(f927(x36571,a915))),f189(f927(x36572,a915)))
% 15.02/14.79 [3683]E(f120(x36831,f126(f921(x36831),x36832,x36833)),f116(x36831,x36832,f120(x36831,x36833)))
% 15.02/14.79 [3685]E(f857(f857(f308(x36851),x36852),f857(f172(x36851),x36853)),f857(f172(x36851),f140(x36851,x36852,x36853)))
% 15.02/14.79 [3772]E(f857(f190(a916),f26(x37721,x37722,x37723)),f857(f857(f79(a919),f857(f190(a916),x37723)),f857(a112,f2(a919))))
% 15.02/14.79 [3773]E(f857(f309(f926(x37731,x37732),x37732,f255(x37731,x37732)),x37733),f857(f283(x37731,x37732),x37733))
% 15.02/14.79 [3774]E(f857(f309(f926(x37741,x37742),x37741,f250(x37741,x37742)),x37743),f857(f263(x37741,x37742),x37743))
% 15.02/14.79 [3790]E(f857(f172(x37901),f169(x37901,f857(a112,x37902),x37903)),f857(f857(f308(x37901),x37903),f189(f927(x37901,a915))))
% 15.02/14.79 [3848]E(f857(f857(f251(x38481,x38482),f857(f250(x38481,x38482),x38483)),f857(f255(x38481,x38482),x38483)),x38483)
% 15.02/14.79 [3855]E(f857(f190(f921(x38551)),f126(x38551,x38552,x38553)),f857(f857(f79(a919),f857(f190(f921(x38551)),x38553)),f857(a112,f2(a919))))
% 15.02/14.79 [3857]E(f857(f857(f256(x38571,x38572,x38571),f18(x38571,x38572)),x38573),f857(f250(x38571,x38572),x38573))
% 15.02/14.79 [3935]E(f28(f27(x39351,x39352,x39353)),f857(f857(f79(a919),f857(f857(f79(a919),f28(x39352)),f28(x39353))),f857(a112,f2(a919))))
% 15.02/14.79 [3985]E(f857(f72(x39851,x39851,x39852,f31(x39851)),x39853),x39853)
% 15.02/14.79 [3992]E(f857(f857(f134(x39921),f169(x39921,x39922,x39923)),f857(f857(f151(x39921),x39923),f113(x39921))),f857(f857(f151(x39921),x39923),f169(x39921,x39922,x39923)))
% 15.02/14.79 [4094]E(f857(f190(a916),f27(x40941,x40942,x40943)),f857(f857(f79(a919),f857(f857(f79(a919),f857(f190(a916),x40942)),f857(f190(a916),x40943))),f857(a112,f2(a919))))
% 15.02/14.79 [4168]P106(f857(f857(f234(f927(x41681,a915)),f857(f172(x41681),f857(f136(x41681,x41682),x41683))),f857(f172(x41681),x41683)))
% 15.02/14.79 [4212]P106(f857(f857(f234(f927(x42121,a915)),f857(f172(x42121),f857(f857(f175(x42121),x42122),x42123))),f857(f172(x42121),x42123)))
% 15.02/14.79 [4213]P106(f857(f857(f234(f927(x42131,a915)),f857(f172(x42131),f857(f857(f138(x42131),x42132),x42133))),f857(f172(x42131),x42133)))
% 15.02/14.79 [4217]P106(f857(f857(f234(f927(x42171,a915)),f857(f172(x42171),f176(x42171,x42172,x42173))),f857(f172(x42171),x42172)))
% 15.02/14.79 [4218]P106(f857(f857(f234(f927(x42181,a915)),f857(f172(x42181),f170(x42181,x42182,x42183))),f857(f172(x42181),x42183)))
% 15.02/14.79 [4239]P26(f926(x42391,x42392),f926(x42392,x42391),f857(f256(x42391,x42392,f926(x42392,x42391)),f857(f9(x42392,x42391,f926(x42392,x42391)),f251(x42392,x42391))),x42393)
% 15.02/14.79 [4250]E(f857(f857(f857(f183(f920(x42501),f920(x42501)),f44(a919,x42502,f857(f190(f920(x42501)),x42503))),f167(x42501)),x42503),f857(f857(f857(f183(f920(x42501),f920(x42501)),x42502),f167(x42501)),x42503))
% 15.02/14.79 [4294]P106(f857(f857(f328(f926(f920(x42941),f920(x42941))),f857(f857(f251(f920(x42941),f920(x42941)),x42942),x42942)),f158(x42941,f306(x42941,x42943))))
% 15.02/14.79 [4433]E(f84(f926(x44331,x44332),f857(f857(f20(f926(x44331,x44332),x44332,a915),f857(f857(f10(x44331,f927(x44332,a915),f926(x44331,x44332)),x44333),f250(x44331,x44332))),f255(x44331,x44332))),f84(f926(x44331,x44332),f857(f256(x44331,x44332,a915),x44333)))
% 15.02/14.79 [4434]E(f89(f926(x44341,x44342),f857(f857(f20(f926(x44341,x44342),x44342,a915),f857(f857(f10(x44341,f927(x44342,a915),f926(x44341,x44342)),x44343),f250(x44341,x44342))),f255(x44341,x44342))),f89(f926(x44341,x44342),f857(f256(x44341,x44342,a915),x44343)))
% 15.02/14.79 [4467]E(f857(f857(f287(f926(a919,x44671),x44671),f318(a919,x44671,a239,x44672)),f857(f857(f20(x44671,x44671,f926(a919,x44671)),f857(f857(f10(a919,f927(x44671,f926(a919,x44671)),x44671),f251(a919,x44671)),x44673)),f7(x44671))),f320(x44671,x44673,x44672))
% 15.02/14.79 [4530]E(f857(f257(x45301,x45301,x45302,x45302,f7(x45301),f7(x45302)),x45303),x45303)
% 15.02/14.79 [4603]E(f857(f142(f920(f920(x46031)),f920(f920(x46031)),f134(f920(x46031)),f113(f920(x46031))),f857(f857(f154(f920(x46031),f920(f920(x46031))),f857(f857(f9(f920(x46031),f920(x46031),f920(f920(x46031))),f857(f857(f10(f927(x46031,f920(x46031)),f927(f920(x46031),f920(f920(x46031))),f920(x46031)),f154(x46031,f920(x46031))),f857(f9(x46031,f920(x46031),f920(x46031)),f151(x46031)))),x46032)),f54(x46031,x46033,x46032))),f54(x46031,f857(a112,x46033),x46032))
% 15.02/14.79 [4659]E(f224(a919,f926(x46591,f921(x46591)),f2(a919),f857(f256(x46591,f921(x46591),a919),f857(f857(f9(x46591,a919,f927(f921(x46591),a919)),f857(f857(f10(f927(f921(x46591),f927(a919,a919)),f927(a919,f927(f921(x46591),a919)),x46591),f9(f921(x46591),a919,a919)),f857(f857(f10(f927(f921(x46591),a919),f927(f921(x46591),f927(a919,a919)),x46591),f857(f10(a919,f927(a919,a919),f921(x46591)),f79(a919))),f857(f857(f9(x46591,f927(f921(x46591),a919),f927(f921(x46591),a919)),f857(f857(f10(f927(a919,a919),f927(f927(f921(x46591),a919),f927(f921(x46591),a919)),x46591),f10(a919,a919,f921(x46591))),f857(f857(f10(a919,f927(a919,a919),x46591),f79(a919)),x46592))),f125(x46591,x46592))))),f77(a919))),f857(f135(x46591),x46593)),f857(f125(x46591,x46592),x46593))
% 15.02/14.79 [4668]E(f857(f857(f85(a1,x46681),f219(f857(f857(f72(f926(a1,a1),a1,x46681,f255(a1,a1)),f213(x46681)),x46682),f857(f857(f72(f926(a1,a1),a1,x46681,f255(a1,a1)),f213(x46681)),x46683))),f857(f857(f20(a1,a1,x46681),f857(f857(f10(a1,f927(a1,x46681),a1),f202(x46681)),f857(f857(f20(a1,a1,a1),f857(f857(f10(a1,f927(a1,a1),a1),f79(a1)),f857(f857(f10(a1,a1,a1),f857(f80(a1),f857(f857(f72(f926(a1,a1),a1,x46681,f250(a1,a1)),f213(x46681)),x46682))),f857(f857(f9(a1,a1,a1),f35(a1)),f857(f857(f72(f926(a1,a1),a1,x46681,f255(a1,a1)),f213(x46681)),x46682))))),f857(f857(f10(a1,a1,a1),f857(f80(a1),f857(f857(f72(f926(a1,a1),a1,x46681,f250(a1,a1)),f213(x46681)),x46683))),f857(f857(f9(a1,a1,a1),f35(a1)),f857(f857(f72(f926(a1,a1),a1,x46681,f255(a1,a1)),f213(x46681)),x46683)))))),f7(a1))),f231(x46681,x46682,x46683))
% 15.02/14.79 [4697]~E(f857(f857(f151(x46971),x46972),x46973),x46973)
% 15.02/14.79 [4704]~E(f857(f857(f151(x47041),x47042),x47043),f113(x47041))
% 15.02/14.79 [4718]~E(f857(f857(f308(x47181),x47182),x47183),f189(f927(x47181,a915)))
% 15.02/14.79 [4740]~E(f857(f309(x47401,f927(x47401,a915),x47402),x47403),f857(f307(x47401),x47403))
% 15.02/14.79 [3565]E(f857(f857(f159(x35651,f113(x35651)),x35652),x35653),f113(x35651))
% 15.02/14.79 [3566]E(f857(f141(x35661),f857(f857(f151(x35661),x35662),x35663)),x35662)
% 15.02/14.79 [3567]E(f857(f171(x35671),f857(f857(f151(x35671),x35672),x35673)),x35673)
% 15.02/14.79 [3610]E(f857(f857(f138(x36101),f77(a919)),f857(f857(f151(x36101),x36102),x36103)),x36103)
% 15.02/14.79 [3644]E(f114(x36441,f857(f857(f138(x36441),x36442),x36443)),f857(f857(f138(x36441),x36442),f114(x36441,x36443)))
% 15.02/14.79 [3646]E(f857(f857(f159(x36461,x36462),x36463),f857(f857(f164(x36461),x36462),x36463)),x36462)
% 15.02/14.79 [3667]E(f857(f857(f308(x36671),x36672),f857(f857(f308(x36671),x36672),x36673)),f857(f857(f308(x36671),x36672),x36673))
% 15.02/14.79 [3680]E(f857(f857(f308(x36801),x36802),f857(f172(x36801),x36803)),f857(f172(x36801),f857(f857(f151(x36801),x36802),x36803)))
% 15.02/14.79 [3682]E(f857(f857(f138(x36821),x36822),f857(f171(x36821),x36823)),f857(f171(x36821),f857(f857(f138(x36821),x36822),x36823)))
% 15.02/14.79 [3694]E(f857(f857(f175(x36941),f77(a919)),f857(f857(f151(x36941),x36942),x36943)),f857(f857(f151(x36941),x36942),f113(x36941)))
% 15.02/14.79 [3737]E(f857(f62(x37371,x37372),f857(f857(f308(x37371),x37373),f189(f927(x37371,a915)))),x37373)
% 15.02/14.79 [3780]E(f857(f857(f79(a919),x37801),f857(f857(f79(a919),x37802),x37803)),f857(f857(f79(a919),x37802),f857(f857(f79(a919),x37801),x37803)))
% 15.02/14.79 [3781]E(f857(f857(f79(a1),x37811),f857(f857(f79(a1),x37812),x37813)),f857(f857(f79(a1),x37812),f857(f857(f79(a1),x37811),x37813)))
% 15.02/14.79 [3786]E(f857(f857(f253(x37861,x37862),f189(f927(x37861,a915))),x37863),f189(f927(f926(x37861,x37862),a915)))
% 15.02/14.79 [3811]E(f857(f857(f110(f927(x38111,a915)),x38112),x38113),f857(f857(f110(f927(x38111,a915)),x38113),x38112))
% 15.02/14.79 [3812]E(f857(f857(f101(f927(x38121,a915)),x38122),x38123),f857(f857(f101(f927(x38121,a915)),x38123),x38122))
% 15.02/14.79 [3814]E(f857(f857(f134(x38141),x38142),f857(f857(f151(x38141),x38143),f113(x38141))),f857(f167(x38141),f857(f857(f151(x38141),x38143),x38142)))
% 15.02/14.79 [3815]E(f857(f857(f134(x38151),f857(f168(x38151),x38152)),f857(f168(x38151),x38153)),f857(f168(x38151),f857(f857(f134(x38151),x38153),x38152)))
% 15.02/14.79 [3825]E(f857(f171(x38251),f857(f857(f175(x38251),f857(a112,x38252)),x38253)),f857(f857(f175(x38251),x38252),f857(f171(x38251),x38253)))
% 15.02/14.79 [3833]P106(f857(f857(f328(x38331),x38332),f857(f857(f308(x38331),x38332),x38333)))
% 15.02/14.79 [3837]E(f857(f857(f38(x38371,f927(x38372,a915)),f189(f927(x38371,a915))),x38373),f241(f927(x38372,a915)))
% 15.02/14.79 [3840]E(f857(f284(x38401,x38401,f262(x38401,x38402)),x38403),f857(f857(f101(f927(x38401,a915)),x38402),x38403))
% 15.02/14.79 [3854]E(f857(f190(f920(x38541)),f857(f857(f151(x38541),x38542),x38543)),f857(f857(f79(a919),f857(f190(f920(x38541)),x38543)),f857(a112,f2(a919))))
% 15.02/14.79 [3859]E(f114(x38591,f857(f857(f134(x38591),x38592),f857(f857(f151(x38591),x38593),f113(x38591)))),x38592)
% 15.02/14.79 [3860]E(f144(x38601,f857(f857(f134(x38601),x38602),f857(f857(f151(x38601),x38603),f113(x38601)))),x38603)
% 15.02/14.79 [3869]E(f857(f857(f134(x38691),f857(f857(f175(x38691),x38692),x38693)),f857(f857(f138(x38691),x38692),x38693)),x38693)
% 15.02/14.79 [3878]E(f857(f857(f3(a919),f857(f857(f79(a919),x38781),x38782)),f857(f857(f79(a919),x38783),x38782)),f857(f857(f3(a919),x38781),x38783))
% 15.02/14.79 [3879]E(f857(f857(f3(a919),f857(f857(f79(a919),x38791),x38792)),f857(f857(f79(a919),x38791),x38793)),f857(f857(f3(a919),x38792),x38793))
% 15.02/14.79 [3885]E(f857(f857(f134(x38851),f857(f168(x38851),x38852)),f857(f857(f151(x38851),x38853),f113(x38851))),f857(f168(x38851),f857(f857(f151(x38851),x38853),x38852)))
% 15.02/14.79 [3887]E(f857(f857(f79(a919),f857(f190(f920(x38871)),x38872)),f857(f190(f920(x38871)),x38873)),f857(f190(f920(x38871)),f857(f857(f134(x38871),x38872),x38873)))
% 15.02/14.79 [3890]E(f857(f857(f79(a919),f857(f190(f920(x38901)),x38902)),f857(f190(f920(x38901)),x38903)),f857(f190(f920(x38901)),f173(x38901,x38902,x38903)))
% 15.02/14.79 [3897]E(f857(f857(f110(f927(x38971,a915)),f857(f172(x38971),x38972)),f857(f172(x38971),x38973)),f857(f172(x38971),f857(f857(f134(x38971),x38972),x38973)))
% 15.02/14.79 [3898]E(f44(a919,f857(f857(f80(a919),x38981),x38982),f857(f857(f80(a919),x38981),x38983)),f857(f857(f80(a919),x38981),f44(a919,x38982,x38983)))
% 15.02/14.79 [3910]E(f857(f857(f175(x39101),f857(f857(f3(a919),x39102),f77(a919))),f857(f171(x39101),x39103)),f857(f171(x39101),f857(f857(f175(x39101),x39102),x39103)))
% 15.02/14.79 [3915]E(f857(f857(f101(f927(x39151,a915)),x39152),f857(f78(f927(x39151,a915)),x39153)),f857(f857(f3(f927(x39151,a915)),x39152),x39153))
% 15.02/14.79 [3916]E(f857(f857(f3(f927(x39161,a915)),x39162),f857(f78(f927(x39161,a915)),x39163)),f857(f857(f101(f927(x39161,a915)),x39162),x39163))
% 15.02/14.79 [3939]E(f857(f857(f253(x39391,x39392),x39393),f857(f18(f927(x39392,a915),x39391),f189(f927(x39392,a915)))),f189(f927(f926(x39391,x39392),a915)))
% 15.02/14.79 [3941]E(f857(f857(f3(a919),f857(f857(f80(a919),x39411),x39412)),f857(f857(f80(a919),x39411),x39413)),f857(f857(f80(a919),x39411),f857(f857(f3(a919),x39412),x39413)))
% 15.02/14.79 [3942]E(f857(f857(f79(a919),f857(f857(f80(a919),x39421),x39422)),f857(f857(f80(a919),x39421),x39423)),f857(f857(f80(a919),x39421),f857(f857(f79(a919),x39422),x39423)))
% 15.02/14.79 [3943]E(f857(f857(f3(a1),f857(f857(f80(a1),x39431),x39432)),f857(f857(f80(a1),x39431),x39433)),f857(f857(f80(a1),x39431),f857(f857(f3(a1),x39432),x39433)))
% 15.02/14.79 [3944]E(f857(f857(f79(a1),f857(f857(f80(a1),x39441),x39442)),f857(f857(f80(a1),x39441),x39443)),f857(f857(f80(a1),x39441),f857(f857(f79(a1),x39442),x39443)))
% 15.02/14.79 [3945]E(f857(f857(f80(a1),f857(f857(f243(a1),x39451),x39452)),f857(f857(f243(a1),x39451),x39453)),f857(f857(f243(a1),x39451),f857(f857(f79(a919),x39452),x39453)))
% 15.02/14.79 [3959]E(f857(f857(f39(x39591,f927(x39592,a915)),x39593),f857(f18(f927(x39592,a915),x39591),f189(f927(x39592,a915)))),f189(f927(x39592,a915)))
% 15.02/14.79 [3961]E(f44(a919,f857(f857(f80(a919),x39611),x39612),f857(f857(f80(a919),x39613),x39612)),f857(f857(f80(a919),f44(a919,x39611,x39613)),x39612))
% 15.02/14.79 [3966]E(f44(a1,f857(f857(f3(a1),x39661),f44(a1,x39662,x39663)),x39663),f44(a1,f857(f857(f3(a1),x39661),x39662),x39663))
% 15.02/14.79 [3967]E(f44(a1,f857(f857(f80(a1),x39671),f44(a1,x39672,x39673)),x39673),f44(a1,f857(f857(f80(a1),x39671),x39672),x39673))
% 15.02/14.79 [3968]P106(f857(f857(f234(f927(x39681,a915)),x39682),f857(f857(f308(x39681),x39683),x39682)))
% 15.02/14.79 [4045]E(f857(f857(f38(f927(x40451,a915),f927(x40451,a915)),x40452),f857(f110(f927(x40451,a915)),x40453)),f857(f857(f110(f927(x40451,a915)),x40453),f37(f927(x40451,a915),x40452)))
% 15.02/14.79 [4046]E(f857(f857(f39(f927(x40461,a915),f927(x40461,a915)),x40462),f857(f101(f927(x40461,a915)),x40463)),f857(f857(f101(f927(x40461,a915)),x40463),f36(f927(x40461,a915),x40462)))
% 15.02/14.79 [4058]E(f857(f172(x40581),f857(f857(f857(f183(f920(x40581),f920(x40581)),x40582),f167(x40581)),x40583)),f857(f172(x40581),x40583))
% 15.02/14.79 [4062]E(f857(f857(f175(x40621),f857(f190(f920(x40621)),f177(x40621,x40622,x40623))),x40623),f177(x40621,x40622,x40623))
% 15.02/14.79 [4066]E(f857(f190(f920(x40661)),f857(f857(f857(f183(f920(x40661),f920(x40661)),x40662),f167(x40661)),x40663)),f857(f190(f920(x40661)),x40663))
% 15.02/14.79 [4069]E(f857(f857(f256(x40691,x40692,x40692),f857(f18(f927(x40692,x40692),x40691),f7(x40692))),x40693),f857(f255(x40691,x40692),x40693))
% 15.02/14.79 [4076]E(f44(a1,f857(f857(f3(a1),f44(a1,x40761,x40762)),x40763),x40762),f44(a1,f857(f857(f3(a1),x40761),x40763),x40762))
% 15.02/14.79 [4077]E(f44(a1,f857(f857(f243(a1),f44(a1,x40771,x40772)),x40773),x40772),f44(a1,f857(f857(f243(a1),x40771),x40773),x40772))
% 15.02/14.79 [4080]E(f857(f857(f39(f927(f926(x40801,x40802),a915),f927(x40802,a915)),x40803),f283(x40801,x40802)),f857(f283(x40801,x40802),f36(f927(f926(x40801,x40802),a915),x40803)))
% 15.02/14.79 [4081]E(f857(f857(f39(f927(f926(x40811,x40812),a915),f927(x40811,a915)),x40813),f263(x40811,x40812)),f857(f263(x40811,x40812),f36(f927(f926(x40811,x40812),a915),x40813)))
% 15.02/14.79 [4105]E(f857(f72(x41051,x41051,x41051,x41052),f857(f857(f183(x41051,x41051),x41053),x41052)),f857(f857(f183(x41051,x41051),f857(a112,x41053)),x41052))
% 15.02/14.79 [4123]E(f857(f857(f138(x41231),f857(f857(f3(a919),f857(f190(f920(x41231)),x41232)),x41233)),f857(f168(x41231),x41232)),f857(f168(x41231),f857(f857(f175(x41231),x41233),x41232)))
% 15.02/14.79 [4124]E(f857(f857(f175(x41241),f857(f857(f3(a919),f857(f190(f920(x41241)),x41242)),x41243)),f857(f168(x41241),x41242)),f857(f168(x41241),f857(f857(f138(x41241),x41243),x41242)))
% 15.02/14.79 [4126]E(f857(f857(f79(a919),f857(f165(a919),f857(f857(f154(x41261,a919),x41262),x41263))),f857(f190(f920(x41261)),x41263)),f155(x41261,x41262,x41263))
% 15.02/14.79 [4146]E(f857(f167(x41461),f857(f857(f857(f183(f920(x41461),f920(x41461)),x41462),f167(x41461)),x41463)),f857(f857(f857(f183(f920(x41461),f920(x41461)),f857(a112,x41462)),f167(x41461)),x41463))
% 15.02/14.79 [4160]P106(f857(f857(f234(a919),f857(f190(f920(x41601)),f857(f136(x41601,x41602),x41603))),f857(f190(f920(x41601)),x41603)))
% 15.02/14.79 [4176]E(f857(f857(f110(f927(f927(x41761,a915),a915)),f857(f307(x41761),x41762)),f857(f309(f927(x41761,a915),f927(x41761,a915),f857(f308(x41761),x41763)),f857(f307(x41761),x41762))),f857(f307(x41761),f857(f857(f308(x41761),x41763),x41762)))
% 15.02/14.79 [4195]P25(x41951,x41952,f857(f857(f308(f918(x41951)),f857(f857(f857(f90(x41951),x41953),a25),x41953)),f189(f927(f918(x41951),a915))))
% 15.02/14.79 [4209]P106(f857(f857(f234(a919),f857(f190(f920(x42091)),f177(x42091,x42092,x42093))),f857(f190(f920(x42091)),x42093)))
% 15.02/14.79 [4216]E(f857(f263(x42161,x42162),f857(f261(f926(x42161,x42162)),f857(f256(x42161,x42162,a915),x42163))),f857(f261(x42161),f857(f857(f10(f927(x42162,a915),a915,x42161),f86(x42162)),x42163)))
% 15.02/14.79 [4228]E(f857(f309(a919,a919,f857(f857(f9(a919,a919,a919),f79(a919)),x42281)),f302(a919,x42282,x42283)),f302(a919,f857(f857(f79(a919),x42282),x42281),f857(f857(f79(a919),x42283),x42281)))
% 15.02/14.79 [4242]E(f857(f309(a919,a919,f857(f857(f9(a919,a919,a919),f79(a919)),x42421)),f857(f301(a919,x42422),x42423)),f857(f301(a919,f857(f857(f79(a919),x42422),x42421)),f857(f857(f79(a919),x42423),x42421)))
% 15.02/14.79 [4260]E(f857(f857(f181(x42601,x42602),f857(f857(f154(f926(x42601,x42602),x42601),f250(x42601,x42602)),x42603)),f857(f857(f154(f926(x42601,x42602),x42602),f255(x42601,x42602)),x42603)),x42603)
% 15.02/14.79 [4265]E(f857(f857(f79(a919),f857(f857(f80(a919),x42651),f44(a919,f857(f857(f35(a919),x42652),x42651),x42653))),f44(a919,x42652,x42651)),f44(a919,x42652,f857(f857(f80(a919),x42651),x42653)))
% 15.02/14.79 [4278]E(f857(f857(f134(x42781),x42782),f857(f142(f920(x42781),f920(x42781),f134(x42781),f113(x42781)),x42783)),f857(f142(f920(x42781),f920(x42781),f134(x42781),x42782),x42783))
% 15.02/14.79 [4299]P106(f857(f857(f328(f926(x42991,x42991)),f857(f857(f251(x42991,x42991),x42992),x42992)),f857(f857(f183(f926(x42991,x42991),a915),f2(a919)),x42993)))
% 15.02/14.79 [4304]E(f857(f261(x43041),f857(f857(f10(f927(x43042,a915),a915,x43041),f86(x43042)),f857(f9(x43042,x43041,a915),x43043))),f857(f283(x43042,x43041),f857(f261(f926(x43042,x43041)),f857(f256(x43042,x43041,a915),x43043))))
% 15.02/14.79 [4321]E(f857(f857(f110(f927(x43211,a915)),f857(f857(f39(a919,f927(x43211,a915)),f302(a919,f77(a919),x43212)),x43213)),f857(x43213,f2(a919))),f857(f857(f39(a919,f927(x43211,a915)),f857(f300(a919),x43212)),x43213))
% 15.02/14.79 [4336]E(f857(f142(f920(x43361),f920(x43361),f134(x43361),f113(x43361)),f857(f857(f154(f920(x43361),f920(x43361)),f136(x43361,x43362)),x43363)),f857(f136(x43361,x43362),f857(f142(f920(x43361),f920(x43361),f134(x43361),f113(x43361)),x43363)))
% 15.02/14.79 [4340]E(f857(f255(f920(x43401),f920(x43401)),f166(x43401,x43402,x43403)),f857(f136(x43401,f857(f72(a915,a915,x43401,a321),x43402)),x43403))
% 15.02/14.79 [4385]E(f857(f857(f79(a1),f857(f857(f79(a1),f857(f857(f80(a1),x43851),f857(f857(f35(a1),x43852),x43851))),f44(a1,x43852,x43851))),x43853),f857(f857(f79(a1),x43852),x43853))
% 15.02/14.79 [4422]E(f857(f857(f79(a1),f857(f857(f79(a1),f857(f857(f80(a1),f857(f857(f35(a1),x44221),x44222)),x44222)),f44(a1,x44221,x44222))),x44223),f857(f857(f79(a1),x44221),x44223))
% 15.02/14.79 [4448]E(f84(f926(x44481,x44482),f857(f256(x44481,x44482,a915),f857(f857(f10(f927(x44482,f926(x44481,x44482)),f927(x44482,a915),x44481),f857(f10(f926(x44481,x44482),a915,x44482),x44483)),f251(x44481,x44482)))),f84(f926(x44481,x44482),x44483))
% 15.02/14.79 [4449]E(f89(f926(x44491,x44492),f857(f256(x44491,x44492,a915),f857(f857(f10(f927(x44492,f926(x44491,x44492)),f927(x44492,a915),x44491),f857(f10(f926(x44491,x44492),a915,x44492),x44493)),f251(x44491,x44492)))),f89(f926(x44491,x44492),x44493))
% 15.02/14.79 [4476]P106(f857(f857(f234(f927(x44761,a915)),f36(f927(x44761,a915),f857(f857(f101(f927(f927(x44761,a915),a915)),x44762),x44763))),f857(f857(f101(f927(x44761,a915)),f36(f927(x44761,a915),x44762)),f36(f927(x44761,a915),x44763))))
% 15.02/14.79 [4477]E(f857(f168(x44771),f857(f857(f857(f183(f920(x44771),f920(x44771)),f857(f857(f3(a919),f857(f190(f920(x44771)),x44772)),f44(a919,x44773,f857(f190(f920(x44771)),x44772)))),f167(x44771)),x44772)),f857(f857(f857(f183(f920(x44771),f920(x44771)),x44773),f167(x44771)),f857(f168(x44771),x44772)))
% 15.02/14.79 [4514]P106(f857(f857(f234(a919),f857(f190(f920(x45141)),f857(f857(f138(x45141),f857(f190(f920(x45141)),f177(x45141,x45142,x45143))),x45143))),f857(f190(f920(x45141)),x45143)))
% 15.02/14.79 [4752]~P106(f857(f61(x47521,x47522,f189(f927(x47521,a915))),x47523))
% 15.02/14.79 [4758]~P106(f857(f857(f328(f926(x47581,x47581)),f857(f857(f251(x47581,x47581),x47582),x47583)),f153(x47581,f113(f927(x47581,a919)))))
% 15.02/14.79 [3826]E(f857(f190(f920(x38261)),f857(f857(f175(x38261),x38262),x38263)),f857(f857(f188(a919),f857(f190(f920(x38261)),x38263)),x38262))
% 15.02/14.79 [3827]E(f857(f190(f920(x38271)),f857(f857(f138(x38271),x38272),x38273)),f857(f857(f3(a919),f857(f190(f920(x38271)),x38273)),x38272))
% 15.02/14.79 [3853]E(f857(f190(f920(f920(x38531))),f54(x38531,x38532,x38533)),f857(f857(f243(a919),f857(f190(f920(x38531)),x38533)),x38532))
% 15.02/14.79 [3871]E(f857(f857(f35(a919),f857(f857(f35(a919),x38711),x38712)),x38713),f857(f857(f35(a919),x38711),f857(f857(f80(a919),x38712),x38713)))
% 15.02/14.79 [3872]E(f857(f857(f3(a919),f857(f857(f3(a919),x38721),x38722)),x38723),f857(f857(f3(a919),x38721),f857(f857(f79(a919),x38722),x38723)))
% 15.02/14.79 [3873]E(f857(f857(f80(a919),f857(f857(f80(a919),x38731),x38732)),x38733),f857(f857(f80(a919),x38731),f857(f857(f80(a919),x38732),x38733)))
% 15.02/14.79 [3874]E(f857(f857(f80(a1),f857(f857(f80(a1),x38741),x38742)),x38743),f857(f857(f80(a1),x38741),f857(f857(f80(a1),x38742),x38743)))
% 15.02/14.79 [3875]E(f857(f857(f79(a919),f857(f857(f79(a919),x38751),x38752)),x38753),f857(f857(f79(a919),x38751),f857(f857(f79(a919),x38752),x38753)))
% 15.02/14.79 [3876]E(f857(f857(f79(a1),f857(f857(f79(a1),x38761),x38762)),x38763),f857(f857(f79(a1),x38761),f857(f857(f79(a1),x38762),x38763)))
% 15.02/14.79 [3877]E(f857(f857(f243(a1),f857(f857(f243(a1),x38771),x38772)),x38773),f857(f857(f243(a1),x38771),f857(f857(f80(a919),x38772),x38773)))
% 15.02/14.79 [3896]E(f162(x38961,f857(f857(f151(f927(x38961,a915)),x38962),x38963)),f174(x38961,x38962,f162(x38961,x38963)))
% 15.02/14.79 [3940]E(f857(f857(f3(a919),f857(f857(f3(a919),x39401),x39402)),x39403),f857(f857(f3(a919),f857(f857(f3(a919),x39401),x39403)),x39402))
% 15.02/14.79 [3948]E(f857(f857(f101(f927(x39481,a915)),x39482),f857(f857(f3(f927(x39481,a915)),x39483),x39482)),f189(f927(x39481,a915)))
% 15.02/14.79 [3952]E(f857(f857(f154(a919,x39521),f857(f18(x39521,a919),x39522)),f139(a919,f857(f301(a919,f2(a919)),x39523))),f169(x39521,x39523,x39522))
% 15.02/14.79 [3990]E(f36(f927(x39901,a915),f857(f857(f308(f927(x39901,a915)),x39902),x39903)),f857(f857(f110(f927(x39901,a915)),x39902),f36(f927(x39901,a915),x39903)))
% 15.02/14.79 [3991]E(f37(f927(x39911,a915),f857(f857(f308(f927(x39911,a915)),x39912),x39913)),f857(f857(f101(f927(x39911,a915)),x39912),f37(f927(x39911,a915),x39913)))
% 15.02/14.79 [3993]E(f169(x39931,f857(f190(f920(x39931)),f857(f136(x39931,f857(a324,x39932)),x39933)),x39932),f857(f136(x39931,f857(a324,x39932)),x39933))
% 15.02/14.79 [3995]E(f857(f857(f3(a919),f857(f857(f80(a919),x39951),x39952)),f857(f857(f80(a919),x39953),x39952)),f857(f857(f80(a919),f857(f857(f3(a919),x39951),x39953)),x39952))
% 15.02/14.79 [3996]E(f857(f857(f79(a919),f857(f857(f80(a919),x39961),x39962)),f857(f857(f80(a919),x39963),x39962)),f857(f857(f80(a919),f857(f857(f79(a919),x39961),x39963)),x39962))
% 15.02/14.79 [3997]E(f857(f857(f3(a1),f857(f857(f80(a1),x39971),x39972)),f857(f857(f80(a1),x39973),x39972)),f857(f857(f80(a1),f857(f857(f3(a1),x39971),x39973)),x39972))
% 15.02/14.79 [3998]E(f857(f857(f79(a1),f857(f857(f80(a1),x39981),x39982)),f857(f857(f80(a1),x39983),x39982)),f857(f857(f80(a1),f857(f857(f79(a1),x39981),x39983)),x39982))
% 15.02/14.79 [4000]E(f857(f857(f188(a919),f857(f857(f3(a919),x40001),x40002)),f857(f857(f3(a919),x40003),x40002)),f857(f857(f3(a919),f857(f857(f188(a919),x40001),x40003)),x40002))
% 15.02/14.79 [4022]E(f857(f857(f101(f927(f920(x40221),a915)),f160(x40221,x40222)),f160(x40221,x40223)),f160(x40221,f857(f857(f101(f927(x40221,a915)),x40222),x40223)))
% 15.02/14.79 [4025]E(f857(f857(f110(f927(x40251,a915)),x40252),f857(f857(f110(f927(x40251,a915)),x40252),x40253)),f857(f857(f110(f927(x40251,a915)),x40252),x40253))
% 15.02/14.79 [4026]E(f857(f857(f110(f927(x40261,a915)),x40262),f857(f857(f3(f927(x40261,a915)),x40263),x40262)),f857(f857(f110(f927(x40261,a915)),x40262),x40263))
% 15.02/14.79 [4027]E(f857(f857(f101(f927(x40271,a915)),x40272),f857(f857(f101(f927(x40271,a915)),x40272),x40273)),f857(f857(f101(f927(x40271,a915)),x40272),x40273))
% 15.02/14.79 [4039]E(f857(f857(f288(x40391,x40392,x40392),x40393),f306(x40392,f189(f927(f926(x40392,x40392),a915)))),x40393)
% 15.02/14.79 [4042]E(f857(f857(f110(f927(x40421,a915)),f857(f857(f308(x40421),x40422),f189(f927(x40421,a915)))),x40423),f857(f857(f308(x40421),x40422),x40423))
% 15.02/14.79 [4061]E(f857(f857(f3(a919),f857(f857(f3(a919),f857(a112,x40611)),x40612)),f857(a112,x40613)),f857(f857(f3(a919),f857(f857(f3(a919),x40611),x40612)),x40613))
% 15.02/14.79 [4089]E(f857(f857(f101(f927(f927(x40891,a915),a915)),f857(f307(x40891),x40892)),f857(f307(x40891),x40893)),f857(f307(x40891),f857(f857(f101(f927(x40891,a915)),x40892),x40893)))
% 15.02/14.79 [4092]E(f857(f857(f110(f927(x40921,a915)),f857(f78(f927(x40921,a915)),x40922)),x40923),f857(f78(f927(x40921,a915)),f857(f857(f3(f927(x40921,a915)),x40922),x40923)))
% 15.02/14.79 [4102]E(f857(f857(f308(x41021),x41022),f857(f857(f3(f927(x41021,a915)),x41023),f857(f857(f308(x41021),x41022),f189(f927(x41021,a915))))),f857(f857(f308(x41021),x41022),x41023))
% 15.02/14.79 [4112]P106(f857(f857(f234(f927(x41121,a915)),x41122),f857(f857(f110(f927(x41121,a915)),x41123),x41122)))
% 15.02/14.79 [4113]P106(f857(f857(f234(f927(x41131,a915)),x41132),f857(f857(f110(f927(x41131,a915)),x41132),x41133)))
% 15.02/14.79 [4117]E(f857(f857(f101(f927(x41171,a915)),f857(f78(f927(x41171,a915)),x41172)),f857(f78(f927(x41171,a915)),x41173)),f857(f78(f927(x41171,a915)),f857(f857(f110(f927(x41171,a915)),x41172),x41173)))
% 15.02/14.79 [4118]E(f857(f857(f110(f927(x41181,a915)),f857(f78(f927(x41181,a915)),x41182)),f857(f78(f927(x41181,a915)),x41183)),f857(f78(f927(x41181,a915)),f857(f857(f101(f927(x41181,a915)),x41182),x41183)))
% 15.02/14.79 [4132]P106(f857(f857(f234(f927(x41321,a915)),f857(f172(x41321),x41322)),f857(f172(x41321),f857(f857(f151(x41321),x41323),x41322))))
% 15.02/14.79 [4144]E(f857(f857(f110(f927(x41441,a915)),f857(f857(f3(f927(x41441,a915)),x41442),x41443)),f857(f857(f101(f927(x41441,a915)),x41442),x41443)),x41442)
% 15.02/14.79 [4196]E(f857(f857(f8(x41961,a1),f857(f857(f10(a919,a1,x41961),f100(a1)),x41962)),x41963),f857(f100(a1),f857(f857(f8(x41961,a919),x41962),x41963)))
% 15.02/14.79 [4197]E(f857(f857(f11(x41971,a1),f857(f857(f10(a919,a1,x41971),f100(a1)),x41972)),x41973),f857(f100(a1),f857(f857(f11(x41971,a919),x41972),x41973)))
% 15.02/14.79 [4244]E(f857(f857(f134(x42441),f177(x42441,x42442,x42443)),f857(f857(f138(x42441),f857(f190(f920(x42441)),f177(x42441,x42442,x42443))),x42443)),x42443)
% 15.02/14.79 [4248]E(f857(f78(f927(f926(x42481,x42482),a915)),f857(f857(f253(x42481,x42482),x42483),f857(f18(f927(x42482,a915),x42481),f241(f927(x42482,a915))))),f857(f857(f253(x42481,x42482),f857(f78(f927(x42481,a915)),x42483)),f857(f18(f927(x42482,a915),x42481),f241(f927(x42482,a915)))))
% 15.02/14.79 [4249]E(f857(f78(f927(f926(x42491,x42492),a915)),f857(f857(f253(x42491,x42492),f241(f927(x42491,a915))),f857(f18(f927(x42492,a915),x42491),x42493))),f857(f857(f253(x42491,x42492),f241(f927(x42491,a915))),f857(f18(f927(x42492,a915),x42491),f857(f78(f927(x42492,a915)),x42493))))
% 15.02/14.79 [4300]E(f857(f857(f39(f927(x43001,a915),f927(x43001,a915)),x43002),f857(f857(f9(f927(x43001,a915),f927(x43001,a915),f927(x43001,a915)),f101(f927(x43001,a915))),x43003)),f857(f857(f101(f927(x43001,a915)),f36(f927(x43001,a915),x43002)),x43003))
% 15.02/14.79 [4306]E(f857(f142(f920(x43061),f920(x43061),f134(x43061),f113(x43061)),f857(f857(f151(f920(x43061)),x43062),x43063)),f857(f857(f134(x43061),x43062),f857(f142(f920(x43061),f920(x43061),f134(x43061),f113(x43061)),x43063)))
% 15.02/14.79 [4327]E(f857(f857(f308(f927(x43271,a915)),f857(f284(x43271,x43271,x43272),f857(f857(f308(x43271),x43273),f189(f927(x43271,a915))))),f189(f927(f927(x43271,a915),a915))),f857(f857(f59(x43271),f857(f857(f308(x43271),x43273),f189(f927(x43271,a915)))),x43272))
% 15.02/14.79 [4337]E(f857(f857(f79(a919),f857(f857(f80(a919),x43371),f857(f857(f35(a919),x43372),x43373))),f857(f857(f35(a919),f857(f857(f80(a919),x43371),f44(a919,x43372,x43373))),x43373)),f857(f857(f35(a919),f857(f857(f80(a919),x43371),x43372)),x43373))
% 15.02/14.79 [4338]E(f857(f857(f79(a1),f857(f857(f80(a1),x43381),f857(f857(f35(a1),x43382),x43383))),f857(f857(f35(a1),f857(f857(f80(a1),x43381),f44(a1,x43382,x43383))),x43383)),f857(f857(f35(a1),f857(f857(f80(a1),x43381),x43382)),x43383))
% 15.02/14.79 [4370]E(f857(f857(f3(f927(x43701,a915)),f857(f172(x43701),x43702)),f857(f857(f308(x43701),x43703),f189(f927(x43701,a915)))),f857(f172(x43701),f857(f136(x43701,f857(f857(f10(a915,a915,x43701),a321),f857(a324,x43703))),x43702)))
% 15.02/14.79 [4420]E(f857(f857(f134(x44201),f857(f142(f920(x44201),f920(x44201),f134(x44201),f113(x44201)),x44202)),f857(f142(f920(x44201),f920(x44201),f134(x44201),f113(x44201)),x44203)),f857(f142(f920(x44201),f920(x44201),f134(x44201),f113(x44201)),f857(f857(f134(f920(x44201)),x44202),x44203)))
% 15.02/14.79 [4423]E(f857(f857(f251(f920(x44231),f920(x44231)),f857(f136(x44231,x44232),x44233)),f857(f136(x44231,f857(f72(a915,a915,x44231,a321),x44232)),x44233)),f166(x44231,x44232,x44233))
% 15.02/14.79 [4426]E(f857(f857(f79(a919),f857(f857(f79(a919),f857(f857(f35(a919),x44261),x44262)),f857(f857(f35(a919),x44263),x44262))),f857(f857(f35(a919),f857(f857(f79(a919),f44(a919,x44261,x44262)),f44(a919,x44263,x44262))),x44262)),f857(f857(f35(a919),f857(f857(f79(a919),x44261),x44263)),x44262))
% 15.02/14.79 [4427]E(f857(f857(f79(a1),f857(f857(f79(a1),f857(f857(f35(a1),x44271),x44272)),f857(f857(f35(a1),x44273),x44272))),f857(f857(f35(a1),f857(f857(f79(a1),f44(a1,x44271,x44272)),f44(a1,x44273,x44272))),x44272)),f857(f857(f35(a1),f857(f857(f79(a1),x44271),x44273)),x44272))
% 15.02/14.79 [4480]E(f857(f857(f101(f927(f920(x44801),a915)),f857(f857(f9(f920(x44801),f927(f920(x44801),a915),a915),f328(f920(x44801))),f161(x44801,x44802))),f857(f857(f9(f920(x44801),f927(f920(x44801),a915),a915),f328(f920(x44801))),f161(x44801,x44803))),f160(x44801,f857(f857(f101(f927(x44801,a915)),f857(f857(f9(x44801,f927(x44801,a915),a915),f328(x44801)),x44802)),f857(f857(f9(x44801,f927(x44801,a915),a915),f328(x44801)),x44803))))
% 15.02/14.79 [4492]E(f857(f261(x44921),f857(f857(f20(x44921,a915,a915),f857(f857(f10(a915,f927(a915,a915),x44921),a326),f857(f857(f9(x44921,x44921,a915),a324),x44922))),f857(f857(f9(x44921,f927(x44921,a915),a915),f328(x44921)),x44923))),f857(f857(f308(x44921),x44922),x44923))
% 15.02/14.79 [4512]E(f857(f857(f85(f920(f920(x45121)),f920(f920(x45121))),f53(x45121,x45122)),f857(f857(f20(f920(f920(x45121)),f920(f920(x45121)),f920(f920(x45121))),f857(f857(f10(f920(f920(x45121)),f927(f920(f920(x45121)),f920(f920(x45121))),f920(f920(x45121))),f134(f920(x45121))),f857(f154(f920(x45121),f920(x45121)),f857(f151(x45121),x45123)))),f7(f920(f920(x45121))))),f53(x45121,f857(f857(f151(x45121),x45123),x45122)))
% 15.02/14.79 [4515]E(f857(f261(x45151),f857(f857(f20(x45151,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45151),a326),f857(f857(f9(x45151,f927(x45151,a915),a915),f328(x45151)),x45152))),f857(f857(f9(x45151,f927(x45151,a915),a915),f328(x45151)),x45153))),f857(f857(f110(f927(x45151,a915)),x45152),x45153))
% 15.02/14.79 [4516]E(f857(f261(x45161),f857(f857(f20(x45161,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45161),a325),f857(f857(f9(x45161,f927(x45161,a915),a915),f328(x45161)),x45162))),f857(f857(f9(x45161,f927(x45161,a915),a915),f328(x45161)),x45163))),f857(f857(f101(f927(x45161,a915)),x45162),x45163))
% 15.02/14.79 [4606]E(f857(f857(f39(x46061,f927(f927(x46061,a915),a915)),x46062),f857(f857(f9(x46061,f927(f927(x46061,a915),a915),f927(f927(x46061,a915),a915)),f857(f857(f10(f927(x46061,a915),f927(f927(f927(x46061,a915),a915),f927(f927(x46061,a915),a915)),x46061),f308(f927(x46061,a915))),f857(f857(f10(f927(x46061,a915),f927(x46061,a915),x46061),f284(x46061,x46061,x46063)),f857(f857(f9(x46061,f927(x46061,a915),f927(x46061,a915)),f308(x46061)),f189(f927(x46061,a915)))))),f189(f927(f927(x46061,a915),a915)))),f857(f857(f59(x46061),x46062),x46063))
% 15.02/14.79 [4608]E(f857(f857(f202(x46081),f857(f857(f80(a1),f857(f857(f72(f926(a1,a1),a1,x46081,f250(a1,a1)),f213(x46081)),x46082)),f857(f857(f72(f926(a1,a1),a1,x46081,f250(a1,a1)),f213(x46081)),x46083))),f857(f857(f80(a1),f857(f857(f72(f926(a1,a1),a1,x46081,f255(a1,a1)),f213(x46081)),x46082)),f857(f857(f72(f926(a1,a1),a1,x46081,f255(a1,a1)),f213(x46081)),x46083))),f229(x46081,x46082,x46083))
% 15.02/14.79 [4611]E(f857(f261(f920(x46111)),f857(f857(f20(f920(x46111),a915,a915),f857(f857(f10(a915,f927(a915,a915),f920(x46111)),a325),f857(f857(f9(f920(x46111),a919,a915),f857(f857(f10(a919,f927(a919,a915),f920(x46111)),a324),f190(f920(x46111)))),x46112))),f857(f857(f9(f920(x46111),f927(x46111,a915),a915),f857(f857(f10(f927(x46111,a915),f927(f927(x46111,a915),a915),f920(x46111)),f234(f927(x46111,a915))),f172(x46111))),f857(f172(x46111),x46113)))),f857(f172(f920(x46111)),f54(x46111,x46112,x46113)))
% 15.02/14.79 [4013]E(f44(a919,f857(f857(f79(a919),f857(f857(f80(a919),x40131),x40132)),x40133),x40132),f44(a919,x40133,x40132))
% 15.02/14.79 [4060]E(f139(a919,f857(f301(a919,f857(f857(f79(a919),x40601),x40602)),x40603)),f857(f857(f138(a919),x40602),f139(a919,f857(f301(a919,x40601),x40603))))
% 15.02/14.79 [4101]E(f857(f857(f79(a1),f857(f100(a1),x41011)),f857(f857(f79(a1),f857(f100(a1),x41012)),x41013)),f857(f857(f79(a1),f857(f100(a1),f857(f857(f79(a919),x41011),x41012))),x41013))
% 15.02/14.79 [4108]E(f857(f857(f110(f927(x41081,a915)),f857(f857(f3(f927(x41081,a915)),x41082),x41083)),x41083),f857(f857(f110(f927(x41081,a915)),x41082),x41083))
% 15.02/14.79 [4109]E(f857(f857(f3(f927(x41091,a915)),f857(f857(f3(f927(x41091,a915)),x41092),x41093)),x41093),f857(f857(f3(f927(x41091,a915)),x41092),x41093))
% 15.02/14.79 [4133]E(f857(f857(f288(x41331,x41331,x41332),f306(x41331,f189(f927(f926(x41331,x41331),a915)))),x41333),x41333)
% 15.02/14.79 [4141]E(f857(f857(f110(f927(x41411,a915)),f857(f280(x41411),x41412)),f857(f280(x41411),x41413)),f857(f280(x41411),f857(f857(f110(f927(f926(x41411,x41411),a915)),x41412),x41413)))
% 15.02/14.79 [4151]E(f265(x41511,f857(f857(f151(f926(a99,x41511)),f857(f857(f251(a99,x41511),f2(a99)),x41512)),x41513)),f265(x41511,x41513))
% 15.02/14.79 [4153]E(f857(f857(f110(f927(x41531,a915)),f36(f927(x41531,a915),x41532)),f36(f927(x41531,a915),x41533)),f36(f927(x41531,a915),f857(f857(f110(f927(f927(x41531,a915),a915)),x41532),x41533)))
% 15.02/14.79 [4154]E(f857(f857(f101(f927(x41541,a915)),f37(f927(x41541,a915),x41542)),f37(f927(x41541,a915),x41543)),f37(f927(x41541,a915),f857(f857(f110(f927(f927(x41541,a915),a915)),x41542),x41543)))
% 15.02/14.79 [4191]E(f857(f857(f288(x41911,x41911,x41911),f857(f857(f183(f926(x41911,x41911),a915),x41912),x41913)),x41913),f857(f857(f183(f926(x41911,x41911),a915),f857(a112,x41912)),x41913))
% 15.02/14.79 [4236]P106(f857(f857(f234(f927(x42361,a915)),f857(f857(f3(f927(x42361,a915)),x42362),x42363)),x42362))
% 15.02/14.79 [4237]P106(f857(f857(f234(f927(x42371,a915)),f857(f857(f101(f927(x42371,a915)),x42372),x42373)),x42373))
% 15.02/14.79 [4238]P106(f857(f857(f234(f927(x42381,a915)),f857(f857(f101(f927(x42381,a915)),x42382),x42383)),x42382))
% 15.02/14.79 [4262]E(f306(x42621,f857(f857(f110(f927(f926(x42621,x42621),a915)),f306(x42621,x42622)),f306(x42621,x42623))),f306(x42621,f857(f857(f110(f927(f926(x42621,x42621),a915)),x42622),x42623)))
% 15.02/14.79 [4266]E(f36(f927(x42661,a915),f857(f857(f308(f927(x42661,a915)),x42662),f857(f857(f308(f927(x42661,a915)),x42663),f189(f927(f927(x42661,a915),a915))))),f857(f857(f110(f927(x42661,a915)),x42662),x42663))
% 15.02/14.79 [4267]E(f37(f927(x42671,a915),f857(f857(f308(f927(x42671,a915)),x42672),f857(f857(f308(f927(x42671,a915)),x42673),f189(f927(f927(x42671,a915),a915))))),f857(f857(f101(f927(x42671,a915)),x42672),x42673))
% 15.02/14.79 [4272]E(f857(f857(f288(x42721,x42721,x42721),f857(f857(f183(f926(x42721,x42721),a915),x42722),x42723)),x42723),f857(f857(f288(x42721,x42721,x42721),x42723),f857(f857(f183(f926(x42721,x42721),a915),x42722),x42723)))
% 15.02/14.79 [4341]E(f857(f857(f110(f927(x43411,a915)),f857(f261(x43411),f857(f857(f9(x43411,x43411,a915),a324),x43412))),x43413),f857(f857(f308(x43411),x43412),x43413))
% 15.02/14.79 [4343]E(f857(a104,f857(f857(f8(x43431,a1),f857(f857(f10(a919,a1,x43431),f100(a1)),x43432)),x43433)),f857(f857(f8(x43431,a919),x43432),x43433))
% 15.02/14.79 [4344]E(f857(a104,f857(f857(f11(x43441,a1),f857(f857(f10(a919,a1,x43441),f100(a1)),x43442)),x43443)),f857(f857(f11(x43441,a919),x43442),x43443))
% 15.02/14.79 [4417]E(f857(f156(f920(x44171),x44171,f857(f171(x44171),x44172),f857(f18(f927(f920(x44171),f920(x44171)),x44171),f857(f857(f9(f920(x44171),f920(x44171),f920(x44171)),f134(x44171)),x44172))),x44173),f857(f171(x44171),f857(f857(f134(x44171),x44173),x44172)))
% 15.02/14.79 [4445]P106(f857(f857(f234(f927(f927(x44451,a915),a915)),f857(f857(f110(f927(f927(x44451,a915),a915)),f857(f307(x44451),x44452)),f857(f307(x44451),x44453))),f857(f307(x44451),f857(f857(f110(f927(x44451,a915)),x44452),x44453))))
% 15.02/14.79 [4535]E(f857(f261(x45351),f857(f857(f20(x45351,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45351),a325),f857(f857(f9(x45351,f927(x45351,a915),a915),f328(x45351)),x45352))),f857(f857(f10(a915,a915,x45351),a321),f857(f857(f9(x45351,f927(x45351,a915),a915),f328(x45351)),x45353)))),f857(f857(f3(f927(x45351,a915)),x45352),x45353))
% 15.02/14.79 [4559]E(f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,a919,a915),f235(a919)),f857(f190(f920(x45591)),x45592)))),f857(f857(f10(x45591,a915,a919),x45593),f857(f164(x45591),x45592))))),f857(f190(f920(x45591)),f857(f136(x45591,x45593),x45592)))
% 15.02/14.79 [4561]E(f857(f190(f920(x45611)),f176(x45611,x45612,x45613)),f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,a919,a915),f235(a919)),f857(f190(f920(x45611)),x45612)))),f857(f857(f9(a919,f927(a919,a915),a915),f328(a919)),x45613)))))
% 15.02/14.79 [4657]E(f857(f857(f101(f927(f926(f920(x46571),f920(x46571)),a915)),f857(f309(f926(f926(x46571,f920(x46571)),f926(x46571,f920(x46571))),f926(f920(x46571),f920(x46571)),f257(f926(x46571,f920(x46571)),f920(x46571),f926(x46571,f920(x46571)),f920(x46571),f857(f256(x46571,f920(x46571),f920(x46571)),f151(x46571)),f857(f256(x46571,f920(x46571),f920(x46571)),f151(x46571)))),f318(x46571,f920(x46571),x46572,f857(f143(x46571,x46572),x46573)))),f857(f261(f926(f920(x46571),f920(x46571))),f857(f256(f920(x46571),f920(x46571),a915),f857(f857(f9(f920(x46571),f927(f920(x46571),a915),f927(f920(x46571),a915)),f857(f857(f10(f927(a915,a915),f927(f927(f920(x46571),a915),f927(f920(x46571),a915)),f920(x46571)),f10(a915,a915,f920(x46571))),f857(f857(f10(a915,f927(a915,a915),f920(x46571)),a325),f857(f857(f9(f920(x46571),a919,a915),f857(f857(f10(a919,f927(a919,a915),f920(x46571)),a324),f190(f920(x46571)))),f857(a112,x46573))))),f857(f857(f9(f920(x46571),a919,a915),f857(f857(f10(a919,f927(a919,a915),f920(x46571)),a324),f190(f920(x46571)))),f857(a112,x46573)))))),f857(f143(x46571,x46572),f857(a112,x46573)))
% 15.02/14.79 [4155]E(f44(a919,f857(a112,f857(f857(f79(a919),f857(f857(f80(a919),x41551),x41552)),x41553)),x41552),f44(a919,f857(a112,x41553),x41552))
% 15.02/14.79 [4403]E(f857(f261(x44031),f857(f857(f20(x44031,a915,a915),f857(f857(f10(a915,f927(a915,a915),x44031),a325),x44032)),x44033)),f857(f857(f101(f927(x44031,a915)),f857(f261(x44031),x44032)),f857(f261(x44031),x44033)))
% 15.02/14.79 [4404]E(f857(f261(x44041),f857(f857(f20(x44041,a915,a915),f857(f857(f10(a915,f927(a915,a915),x44041),a326),x44042)),x44043)),f857(f857(f110(f927(x44041,a915)),f857(f261(x44041),x44042)),f857(f261(x44041),x44043)))
% 15.02/14.79 [4406]E(f857(f857(f134(x44061),f857(f857(f138(x44061),f44(a919,x44062,f857(f190(f920(x44061)),x44063))),x44063)),f857(f857(f175(x44061),f44(a919,x44062,f857(f190(f920(x44061)),x44063))),x44063)),f857(f857(f857(f183(f920(x44061),f920(x44061)),x44062),f167(x44061)),x44063))
% 15.02/14.79 [4412]E(f857(f261(x44121),f857(f857(f20(x44121,a915,a915),f857(f857(f10(a915,f927(a915,a915),x44121),a329),x44122)),x44123)),f857(f857(f110(f927(x44121,a915)),f857(f78(f927(x44121,a915)),f857(f261(x44121),x44122))),f857(f261(x44121),x44123)))
% 15.02/14.79 [4428]E(f857(f857(f79(a919),f857(f190(f920(x44281)),f857(f136(x44281,x44282),x44283))),f857(f190(f920(x44281)),f857(f136(x44281,f857(f857(f10(a915,a915,x44281),a321),x44282)),x44283))),f857(f190(f920(x44281)),x44283))
% 15.02/14.79 [4451]P106(f857(f857(f234(f927(x44511,a915)),f857(f857(f110(f927(x44511,a915)),f37(f927(x44511,a915),x44512)),f37(f927(x44511,a915),x44513))),f37(f927(x44511,a915),f857(f857(f101(f927(f927(x44511,a915),a915)),x44512),x44513))))
% 15.02/14.79 [4465]E(f857(f172(x44651),f857(f136(x44651,f857(f857(f10(a915,a915,x44651),a321),f857(f857(f9(x44651,x44651,a915),a324),x44652))),x44653)),f857(f857(f3(f927(x44651,a915)),f857(f172(x44651),x44653)),f857(f857(f308(x44651),x44652),f189(f927(x44651,a915)))))
% 15.02/14.79 [4474]P106(f857(f857(f234(f927(f926(x44741,x44741),a915)),f857(f857(f110(f927(f926(x44741,x44741),a915)),f306(x44741,x44742)),f306(x44741,x44743))),f306(x44741,f857(f857(f110(f927(f926(x44741,x44741),a915)),x44742),x44743))))
% 15.02/14.79 [4497]E(f857(f857(f80(a919),f857(a112,f857(a112,f2(a919)))),f857(f857(f8(a919,a919),f857(f857(f10(a919,a919,a919),f857(f79(a919),x44971)),f857(f857(f9(a919,a919,a919),f80(a919)),x44972))),f857(f281(a919),x44973))),f857(f857(f80(a919),x44973),f857(f857(f79(a919),x44971),f857(f857(f79(a919),x44971),f857(f857(f80(a919),f857(f857(f3(a919),x44973),f77(a919))),x44972)))))
% 15.02/14.79 [4507]E(f857(f261(x45071),f857(f857(f20(x45071,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45071),a325),f857(f857(f9(x45071,f927(x45071,a915),a915),f328(x45071)),f857(f172(x45071),x45072)))),x45073)),f857(f172(x45071),f857(f136(x45071,x45073),x45072)))
% 15.02/14.79 [4656]E(f857(f261(x46561),f857(f857(f10(f927(a919,a915),a915,x46561),f86(a919)),f857(f857(f9(x46561,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),x46561),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),x46561),f857(f10(a915,f927(a915,a915),a919),a325)),f857(f857(f9(x46561,f927(a919,x46561),f927(a919,a915)),f857(f857(f10(f927(x46561,a915),f927(f927(a919,x46561),f927(a919,a915)),x46561),f10(x46561,a915,a919)),a324)),f857(f164(x46561),x46562))))),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,a919,a915),f235(a919)),f857(f190(f920(x46561)),x46562)))),f857(f857(f9(a919,f927(a919,a915),a915),f328(a919)),x46563))))),f857(f172(x46561),f176(x46561,x46562,x46563)))
% 15.02/14.79 [4548]E(f857(f261(x45481),f857(f857(f20(x45481,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45481),a329),f857(f857(f10(a915,a915,x45481),a321),f857(f857(f9(x45481,x45481,a915),a324),x45482)))),x45483)),f857(f857(f308(x45481),x45482),f857(f261(x45481),x45483)))
% 15.02/14.79 [4580]E(f857(f857(f154(f926(x45801,a919),x45801),f250(x45801,a919)),f857(f136(f926(x45801,a919),f857(f857(f9(f926(x45801,a919),f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),f926(x45801,a919)),f328(a919)),f255(x45801,a919))),x45802)),f857(f857(f181(x45801,a919),x45803),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(x45801)),x45803)))))),f176(x45801,x45803,x45802))
% 15.02/14.79 [4607]E(f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f8(a919,a1),f857(f857(f10(a1,a1,a919),f857(f79(a1),x46071)),f857(f857(f9(a919,a1,a1),f857(f857(f10(a1,f927(a1,a1),a919),f80(a1)),f100(a1))),x46072))),f857(f281(a919),x46073))),f857(f857(f80(a1),f857(f100(a1),x46073)),f857(f857(f79(a1),x46071),f857(f857(f79(a1),x46071),f857(f857(f80(a1),f857(f100(a1),f857(f857(f3(a919),x46073),f77(a919)))),x46072)))))
% 15.02/14.79 [4649]E(f857(f261(f926(x46491,x46492)),f857(f256(x46491,x46492,a915),f857(f857(f9(x46491,f927(f926(x46492,x46491),a915),f927(x46492,a915)),f857(f857(f10(f927(x46492,f927(f927(f926(x46492,x46491),a915),a915)),f927(f927(f926(x46492,x46491),a915),f927(x46492,a915)),x46491),f9(x46492,f927(f926(x46492,x46491),a915),a915)),f857(f857(f10(f927(x46492,f926(x46492,x46491)),f927(x46492,f927(f927(f926(x46492,x46491),a915),a915)),x46491),f857(f10(f926(x46492,x46491),f927(f927(f926(x46492,x46491),a915),a915),x46492),f328(f926(x46492,x46491)))),f857(f9(x46492,x46491,f926(x46492,x46491)),f251(x46492,x46491))))),x46493))),f857(f285(x46492,x46491),x46493))
% 15.02/14.79 [4670]E(f857(f261(f920(x46701)),f857(f857(f10(f927(x46701,a915),a915,f920(x46701)),f86(x46701)),f857(f857(f10(f927(x46701,f927(f920(x46701),a915)),f927(x46701,a915),f920(x46701)),f857(f10(f927(f920(x46701),a915),a915,x46701),f86(f920(x46701)))),f857(f857(f9(f920(x46701),f927(x46701,f927(f920(x46701),a915)),f927(x46701,f927(f920(x46701),a915))),f857(f857(f10(f927(x46701,f927(f927(f920(x46701),a915),f927(f920(x46701),a915))),f927(f927(x46701,f927(f920(x46701),a915)),f927(x46701,f927(f920(x46701),a915))),f920(x46701)),f20(x46701,f927(f920(x46701),a915),f927(f920(x46701),a915))),f857(f857(f10(f927(x46701,f927(f920(x46701),f927(a915,a915))),f927(x46701,f927(f927(f920(x46701),a915),f927(f920(x46701),a915))),f920(x46701)),f857(f10(f927(f920(x46701),f927(a915,a915)),f927(f927(f920(x46701),a915),f927(f920(x46701),a915)),x46701),f20(f920(x46701),a915,a915))),f857(f857(f10(f927(x46701,f927(f920(x46701),a915)),f927(x46701,f927(f920(x46701),f927(a915,a915))),f920(x46701)),f857(f10(f927(f920(x46701),a915),f927(f920(x46701),f927(a915,a915)),x46701),f857(f10(a915,f927(a915,a915),f920(x46701)),a325))),f857(f857(f9(f920(x46701),f927(x46701,f927(f920(x46701),f920(x46701))),f927(x46701,f927(f920(x46701),a915))),f857(f857(f10(f927(f927(f920(x46701),f920(x46701)),f927(f920(x46701),a915)),f927(f927(x46701,f927(f920(x46701),f920(x46701))),f927(x46701,f927(f920(x46701),a915))),f920(x46701)),f10(f927(f920(x46701),f920(x46701)),f927(f920(x46701),a915),x46701)),f857(f857(f10(f927(f920(x46701),a915),f927(f927(f920(x46701),f920(x46701)),f927(f920(x46701),a915)),f920(x46701)),f10(f920(x46701),a915,f920(x46701))),a324))),f151(x46701)))))),f857(f857(f9(x46701,f927(f920(x46701),a915),f927(f920(x46701),a915)),f857(f857(f10(f927(a915,a915),f927(f927(f920(x46701),a915),f927(f920(x46701),a915)),x46701),f10(a915,a915,f920(x46701))),f857(f857(f10(a915,f927(a915,a915),x46701),a325),f857(f857(f9(x46701,f927(x46701,a915),a915),f328(x46701)),x46702)))),f857(f857(f9(f920(x46701),f927(f920(x46701),a915),a915),f328(f920(x46701))),x46703)))))),f174(x46701,x46702,x46703))
% 15.02/14.79 [4667]E(f857(f857(f85(a1,f926(a1,a1)),f857(f857(f3(a1),x46671),x46672)),f857(f857(f9(a1,f926(a1,a1),f926(a1,a1)),f857(f857(f20(a1,f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),f857(f857(f10(a915,f927(f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),a1),f96(f926(a1,a1))),f857(f234(a1),f2(a1)))),f857(f251(a1,a1),f857(f857(f79(a1),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x46673)),f77(a1))))),f857(f857(f251(a1,a1),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x46673)),x46671))),f857(f42(x46672),f857(f857(f251(a1,a1),x46673),x46671)))
% 15.02/14.79 [4690]~E(f29(x46901,x46902),f30(x46903,x46904))
% 15.02/14.79 [3710]E(f116(x37101,f857(x37102,x37103),f857(x37104,x37103)),f857(f204(x37101,x37102,x37104),x37103))
% 15.02/14.79 [3763]E(f857(f857(f244(x37631,x37632,x37633),x37634),f2(a919)),x37632)
% 15.02/14.79 [3803]E(f185(x38031,x38032,x38033,f857(a112,x38034)),f857(x38033,x38034))
% 15.02/14.79 [3845]E(f170(x38451,x38452,f170(x38451,x38453,x38454)),f170(x38451,x38453,f170(x38451,x38452,x38454)))
% 15.02/14.79 [3846]E(f126(x38461,x38462,f116(x38461,x38463,x38464)),f116(x38461,f126(x38461,x38462,x38463),x38464))
% 15.02/14.79 [3981]E(f857(f156(x39811,x39812,x39813,x39814),f113(x39812)),x39813)
% 15.02/14.79 [3982]E(f857(f142(x39821,x39822,x39823,x39824),f113(x39822)),x39824)
% 15.02/14.79 [4019]E(f857(f190(f924(x40191,x40192)),f221(x40191,x40192,x40193,x40194)),f2(a919))
% 15.02/14.79 [4044]E(f857(f256(x40441,x40442,x40443),f254(x40441,x40442,x40443,x40444)),x40444)
% 15.02/14.79 [4088]E(f857(f857(f134(x40881),f169(x40881,x40882,x40883)),f169(x40881,x40884,x40883)),f857(f857(f134(x40881),f169(x40881,x40884,x40883)),f169(x40881,x40882,x40883)))
% 15.02/14.79 [4174]E(f857(f857(f258(x41741,x41742,x41743,f926(x41742,x41743)),x41744),f251(x41742,x41743)),x41744)
% 15.02/14.79 [4184]E(f127(x41841,x41842,x41843,x41844,f119(x41842)),x41843)
% 15.02/14.79 [4190]E(f74(x41901,x41902,x41903,x41904,f857(x41903,x41904)),x41903)
% 15.02/14.79 [4458]P44(x44581,x44582,x44583,x44584,f189(f927(x44581,a915)),x44584)
% 15.02/14.79 [3512]E(f857(f857(f18(x35121,x35122),x35123),x35124),x35123)
% 15.02/14.79 [3793]E(f170(x37931,x37932,f857(f136(x37931,x37933),x37934)),f857(f136(x37931,x37933),f170(x37931,x37932,x37934)))
% 15.02/14.79 [3828]E(f857(f857(f63(x38281,x38282,x38283),x38284),f189(f927(x38281,a915))),x38284)
% 15.02/14.79 [3852]E(f857(f857(f164(x38521),f857(f857(f151(x38521),x38522),x38523)),f857(a112,x38524)),f857(f857(f164(x38521),x38523),x38524))
% 15.02/14.79 [3920]E(f857(f857(x39201,x39202),f857(f184(x39203,x39204,x39201),x39202)),f857(f184(x39203,x39204,x39201),f857(a112,x39202)))
% 15.02/14.79 [3962]E(f254(x39621,x39622,x39623,f857(f256(x39621,x39622,x39623),x39624)),x39624)
% 15.02/14.79 [4017]E(f857(f857(f159(x40171,f857(f857(f151(x40171),x40172),x40173)),f2(a919)),x40174),f857(f857(f151(x40171),x40174),x40173))
% 15.02/14.79 [4029]E(f857(f857(f39(f927(x40291,a915),f927(x40292,a915)),x40293),f310(x40292,x40291,x40294)),f857(f310(x40292,x40291,x40294),f36(f927(x40291,a915),x40293)))
% 15.02/14.79 [4030]E(f857(f857(f39(f927(x40301,a915),f927(x40302,a915)),x40303),f309(x40301,x40302,x40304)),f857(f309(x40301,x40302,x40304),f36(f927(x40301,a915),x40303)))
% 15.02/14.79 [4055]E(f120(x40551,f130(x40552,f921(x40551),x40553,x40554)),f857(f118(x40552,x40551,x40554),x40553))
% 15.02/14.79 [4129]E(f857(f125(x41291,x41292),f126(x41291,x41293,x41294)),f857(f857(f79(a919),f857(f857(f79(a919),f857(x41292,x41293)),f857(f125(x41291,x41292),x41294))),f857(a112,f2(a919))))
% 15.02/14.79 [4150]E(f857(f142(x41501,x41502,f857(f9(x41502,x41501,x41501),x41503),x41504),f857(f168(x41502),f113(x41502))),x41504)
% 15.02/14.79 [4256]E(f224(x42561,f926(x42562,f921(x42562)),x42563,f857(f256(x42562,f921(x42562),x42561),x42564),f857(f135(x42562),f119(x42562))),x42563)
% 15.02/14.79 [4388]E(f857(f256(x43881,x43882,x43883),f857(f857(f10(f927(x43882,f926(x43881,x43882)),f927(x43882,x43883),x43881),f857(f10(f926(x43881,x43882),x43883,x43882),x43884)),f251(x43881,x43882))),x43884)
% 15.02/14.79 [3701]E(f857(f255(x37011,x37012),f857(f857(f251(x37011,x37012),x37013),x37014)),x37014)
% 15.02/14.79 [3702]E(f857(f250(x37021,x37022),f857(f857(f251(x37021,x37022),x37023),x37024)),x37023)
% 15.02/14.79 [3735]E(f857(f190(f920(x37351)),f857(f857(f159(x37351,x37352),x37353),x37354)),f857(f190(f920(x37351)),x37352))
% 15.02/14.79 [3736]E(f857(f190(f920(x37361)),f857(f857(f154(x37362,x37361),x37363),x37364)),f857(f190(f920(x37362)),x37364))
% 15.02/14.79 [3757]E(f857(f857(f138(x37571),f857(a112,x37572)),f857(f857(f151(x37571),x37573),x37574)),f857(f857(f138(x37571),x37572),x37574))
% 15.02/14.79 [3823]E(f857(f857(f175(x38231),x38232),f169(x38231,x38233,x38234)),f169(x38231,f857(f857(f188(a919),x38232),x38233),x38234))
% 15.02/14.79 [3824]E(f857(f857(f138(x38241),x38242),f169(x38241,x38243,x38244)),f169(x38241,f857(f857(f3(a919),x38243),x38242),x38244))
% 15.02/14.79 [3830]E(f857(f857(f308(x38301),x38302),f857(f857(f308(x38301),x38303),x38304)),f857(f857(f308(x38301),x38303),f857(f857(f308(x38301),x38302),x38304)))
% 15.02/14.79 [3834]E(f857(f857(f154(x38341,x38342),x38343),f114(x38341,x38344)),f114(x38342,f857(f857(f154(x38341,x38342),x38343),x38344)))
% 15.02/14.79 [3850]E(f857(f168(x38501),f857(f857(f154(x38502,x38501),x38503),x38504)),f857(f857(f154(x38502,x38501),x38503),f857(f168(x38502),x38504)))
% 15.02/14.79 [3851]E(f857(f857(f154(x38511,x38512),x38513),f857(f171(x38511),x38514)),f857(f171(x38512),f857(f857(f154(x38511,x38512),x38513),x38514)))
% 15.02/14.79 [3866]E(f857(f857(f175(x38661),f857(a112,x38662)),f857(f857(f151(x38661),x38663),x38664)),f857(f857(f151(x38661),x38663),f857(f857(f175(x38661),x38662),x38664)))
% 15.02/14.79 [3870]E(f857(f172(x38701),f857(f857(f154(x38702,x38701),x38703),x38704)),f857(f309(x38702,x38701,x38703),f857(f172(x38702),x38704)))
% 15.02/14.79 [3883]E(f857(f857(f154(x38831,x38832),f857(f18(x38832,x38831),x38833)),x38834),f169(x38832,f857(f190(f920(x38831)),x38834),x38833))
% 15.02/14.79 [3919]E(f19(x39191,x39192,x39193,f857(a5,f857(a112,f857(a22,x39194)))),f857(x39193,x39194))
% 15.02/14.79 [3923]E(f857(f857(f134(x39231),f857(f136(x39231,x39232),x39233)),f857(f136(x39231,x39232),x39234)),f857(f136(x39231,x39232),f857(f857(f134(x39231),x39233),x39234)))
% 15.02/14.79 [3936]E(f152(x39361,f857(f857(f154(x39362,x39361),x39363),f152(x39362,x39364))),f152(x39361,f857(f857(f154(x39362,x39361),x39363),x39364)))
% 15.02/14.79 [3951]E(f857(f285(x39511,x39511),f857(f857(f287(x39512,x39511),x39513),x39514)),f857(f857(f287(x39512,x39511),f857(f285(x39512,x39512),x39513)),x39514))
% 15.02/14.79 [3963]E(f857(f857(f288(x39631,x39632,x39633),x39634),f189(f927(f926(x39632,x39633),a915))),f189(f927(f926(x39631,x39633),a915)))
% 15.02/14.79 [3964]E(f857(f857(f175(x39641),f857(f857(f3(a919),x39642),x39643)),f857(f857(f138(x39641),x39643),x39644)),f857(f857(f138(x39641),x39643),f857(f857(f175(x39641),x39642),x39644)))
% 15.02/14.79 [3983]E(f857(f857(f134(x39831),f169(x39831,x39832,x39833)),f169(x39831,x39834,x39833)),f169(x39831,f857(f857(f79(a919),x39832),x39834),x39833))
% 15.02/14.79 [3984]E(f857(f857(f857(f277(x39841),x39842),x39843),x39844),f857(f251(f927(a99,f927(a915,f923(f921(x39841)))),f926(a99,a99)),f857(f41(x39841),x39842)))
% 15.02/14.79 [4010]E(f36(f927(x40101,a915),f857(f309(x40102,f927(x40101,a915),x40103),x40104)),f857(f857(f39(x40102,f927(x40101,a915)),x40104),x40103))
% 15.02/14.79 [4011]E(f37(f927(x40111,a915),f857(f309(x40112,f927(x40111,a915),x40113),x40114)),f857(f857(f38(x40112,f927(x40111,a915)),x40114),x40113))
% 15.02/14.79 [4012]E(f857(f190(f920(f926(x40121,x40122))),f857(f857(f181(x40121,x40122),x40123),x40124)),f857(f857(f188(a919),f857(f190(f920(x40121)),x40123)),f857(f190(f920(x40122)),x40124)))
% 15.02/14.79 [4014]E(f857(f310(x40141,x40142,x40143),f857(f78(f927(x40142,a915)),x40144)),f857(f78(f927(x40141,a915)),f857(f310(x40141,x40142,x40143),x40144)))
% 15.02/14.79 [4065]E(f857(f310(x40651,x40652,x40653),f857(f261(x40652),x40654)),f857(f261(x40651),f857(f857(f10(x40652,a915,x40651),x40654),x40653)))
% 15.02/14.79 [4083]E(f857(f857(f164(x40831),f857(f857(f134(x40831),x40832),f857(f857(f151(x40831),x40833),x40834))),f857(f190(f920(x40831)),x40832)),x40833)
% 15.02/14.79 [4106]E(f857(f309(x41061,x41062,x41063),f857(f310(x41061,x41062,x41063),x41064)),f857(f857(f101(f927(x41062,a915)),x41064),f857(f309(x41061,x41062,x41063),f241(f927(x41061,a915)))))
% 15.02/14.79 [4125]P106(f857(f857(f328(x41251),f857(x41252,x41253)),f857(f309(x41254,x41251,x41252),f241(f927(x41254,a915)))))
% 15.02/14.79 [4134]E(f21(x41341,x41342,x41343,f857(a5,f857(a112,f857(a22,x41344)))),f857(f857(x41343,x41344),f21(x41341,x41342,x41343,x41344)))
% 15.02/14.79 [4138]E(f857(f857(f134(x41381),f169(x41381,x41382,x41383)),f857(f857(f151(x41381),x41383),x41384)),f857(f857(f151(x41381),x41383),f857(f857(f134(x41381),f169(x41381,x41382,x41383)),x41384)))
% 15.02/14.79 [4140]E(f857(f857(f253(x41401,x41402),f857(f172(x41401),x41403)),f857(f18(f927(x41402,a915),x41401),f857(f172(x41402),x41404))),f857(f172(f926(x41401,x41402)),f58(x41401,x41402,x41403,x41404)))
% 15.02/14.79 [4152]E(f155(x41521,x41522,f857(f857(f151(x41521),x41523),x41524)),f857(f857(f79(a919),f857(f857(f79(a919),f857(x41522,x41523)),f155(x41521,x41522,x41524))),f857(a112,f2(a919))))
% 15.02/14.79 [4165]E(f185(f920(x41651),f857(f857(f151(x41651),x41652),x41653),f857(f857(f9(a919,f920(x41651),f920(x41651)),f138(x41651)),x41653),x41654),f857(f857(f138(x41651),x41654),f857(f857(f151(x41651),x41652),x41653)))
% 15.02/14.79 [4166]P26(x41661,f926(x41662,x41661),f330(x41663,x41664,x41662,x41661),f857(f857(f39(x41662,f927(x41661,a915)),x41664),x41663))
% 15.02/14.79 [4175]E(f857(f857(f3(f927(x41751,a915)),f857(f857(f3(f927(x41751,a915)),x41752),x41753)),f857(f857(f308(x41751),x41754),f189(f927(x41751,a915)))),f857(f857(f3(f927(x41751,a915)),x41752),f857(f857(f308(x41751),x41754),x41753)))
% 15.02/14.79 [4188]E(f857(f857(f183(f927(x41881,x41882),f927(x41881,x41882)),x41883),f72(x41882,x41882,x41881,x41884)),f72(x41882,x41882,x41881,f857(f857(f183(x41882,x41882),x41883),x41884)))
% 15.02/14.79 [4261]E(f857(f857(f857(f183(f920(x42611),f920(x42611)),x42612),f167(x42611)),f857(f857(f857(f183(f920(x42611),f920(x42611)),x42613),f167(x42611)),x42614)),f857(f857(f857(f183(f920(x42611),f920(x42611)),f857(f857(f79(a919),x42612),x42613)),f167(x42611)),x42614))
% 15.02/14.79 [4346]P106(f857(f857(f234(f927(x43461,a915)),f857(f172(x43461),f857(f857(f159(x43461,x43462),x43463),x43464))),f857(f857(f308(x43461),x43464),f857(f172(x43461),x43462))))
% 15.02/14.79 [4378]E(f857(f857(f39(f927(x43781,a915),f927(f926(x43781,x43782),a915)),x43783),f857(f857(f9(f927(x43781,a915),f927(x43781,f927(x43782,a915)),f927(f926(x43781,x43782),a915)),f253(x43781,x43782)),x43784)),f857(f857(f253(x43781,x43782),f36(f927(x43781,a915),x43783)),x43784))
% 15.02/14.79 [4416]E(f210(x44161,x44162,x44163,f857(f72(x44162,f927(a99,f927(a99,f927(f926(a99,a99),f927(a99,f921(x44162))))),x44161,f209(x44162)),x44164)),f211(x44161,x44162,x44164,x44163))
% 15.02/14.79 [4431]E(f206(x44311,x44312,x44313,f857(f72(x44312,f927(a99,f927(a99,f927(f926(a99,a99),f927(a99,f921(f923(x44312)))))),x44311,f205(x44312)),x44314)),f207(x44311,x44312,x44314,x44313))
% 15.02/14.79 [4436]P106(f857(f65(x44361,x44362,x44363,x44364,f189(f927(x44361,a915))),x44364))
% 15.02/14.79 [4475]E(f857(f857(f39(x44751,f927(x44752,a915)),x44753),f857(f857(f9(x44751,f927(x44752,a915),f927(x44752,a915)),f857(f857(f10(x44752,f927(f927(x44752,a915),f927(x44752,a915)),x44751),f308(x44752)),x44754)),f189(f927(x44752,a915)))),f857(f309(x44751,x44752,x44754),x44753))
% 15.02/14.79 [4482]P106(f857(f857(f234(f927(x44821,a915)),f857(f283(x44822,x44821),f857(f857(f101(f927(f926(x44822,x44821),a915)),x44823),x44824))),f857(f857(f101(f927(x44821,a915)),f857(f283(x44822,x44821),x44823)),f857(f283(x44822,x44821),x44824))))
% 15.02/14.79 [4483]P106(f857(f857(f234(f927(x44831,a915)),f857(f263(x44831,x44832),f857(f857(f101(f927(f926(x44831,x44832),a915)),x44833),x44834))),f857(f857(f101(f927(x44831,a915)),f857(f263(x44831,x44832),x44833)),f857(f263(x44831,x44832),x44834))))
% 15.02/14.79 [4517]P25(x45171,x45172,f857(f857(f308(f918(x45171)),f857(f857(f857(f90(x45171),f857(f18(f927(a917,a915),x45171),f857(f18(a915,a917),a238))),x45173),x45174)),f189(f927(f918(x45171),a915))))
% 15.02/14.79 [4544]P106(f857(f857(f234(f927(f926(x45441,x45442),a915)),f857(f309(x45442,f926(x45441,x45442),f330(x45443,x45444,x45441,x45442)),f857(f857(f39(x45441,f927(x45442,a915)),x45444),x45443))),f857(f857(f253(x45441,x45442),x45444),x45443)))
% 15.02/14.79 [4545]E(f857(f118(x45451,f926(x45451,x45452),x45453),f857(f857(f10(f927(x45452,f921(f926(x45451,x45452))),f921(f926(x45451,x45452)),x45451),f118(x45452,f926(x45451,x45452),x45454)),f857(f857(f10(f927(x45452,f926(x45451,x45452)),f927(x45452,f921(f926(x45451,x45452))),x45451),f857(f10(f926(x45451,x45452),f921(f926(x45451,x45452)),x45452),f129(f926(x45451,x45452)))),f251(x45451,x45452)))),f131(x45451,x45452,x45453,x45454))
% 15.02/14.79 [4546]E(f275(x45461,x45462,x45463,f857(f72(x45462,f927(a99,f927(a99,f927(f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x45462)))),f926(a99,a99))))),x45461,f277(x45462)),x45464)),f278(x45461,x45462,x45464,x45463))
% 15.02/14.79 [4586]E(f84(f926(x45861,x45862),f857(f256(x45861,x45862,a915),f857(f857(f9(x45861,f927(x45862,a915),f927(x45862,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x45862,a915),f927(x45862,a915)),x45861),f10(a915,a915,x45862)),f857(f857(f10(a915,f927(a915,a915),x45861),a325),f857(a324,x45863)))),f857(a324,x45864)))),f857(f857(f251(x45861,x45862),x45863),x45864))
% 15.02/14.79 [4587]E(f89(f926(x45871,x45872),f857(f256(x45871,x45872,a915),f857(f857(f9(x45871,f927(x45872,a915),f927(x45872,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x45872,a915),f927(x45872,a915)),x45871),f10(a915,a915,x45872)),f857(f857(f10(a915,f927(a915,a915),x45871),a325),f857(a324,x45873)))),f857(a324,x45874)))),f857(f857(f251(x45871,x45872),x45873),x45874))
% 15.02/14.79 [4658]E(f857(f857(f256(f920(x46581),f920(x46581),f926(f920(x46581),f920(x46581))),f857(f857(f20(f920(x46581),f927(f920(x46581),f926(f920(x46581),f920(x46581))),f927(f920(x46581),f926(f920(x46581),f920(x46581)))),f857(f857(f10(f927(f920(x46581),f927(f926(f920(x46581),f920(x46581)),f926(f920(x46581),f920(x46581)))),f927(f927(f920(x46581),f926(f920(x46581),f920(x46581))),f927(f920(x46581),f926(f920(x46581),f920(x46581)))),f920(x46581)),f20(f920(x46581),f926(f920(x46581),f920(x46581)),f926(f920(x46581),f920(x46581)))),f857(f857(f10(f927(f920(x46581),f926(f920(x46581),f920(x46581))),f927(f920(x46581),f927(f926(f920(x46581),f920(x46581)),f926(f920(x46581),f920(x46581)))),f920(x46581)),f857(f10(f926(f920(x46581),f920(x46581)),f927(f926(f920(x46581),f920(x46581)),f926(f920(x46581),f920(x46581))),f920(x46581)),f857(f96(f926(f920(x46581),f920(x46581))),f857(x46582,x46583)))),f857(f857(f10(f920(x46581),f927(f920(x46581),f926(f920(x46581),f920(x46581))),f920(x46581)),f251(f920(x46581),f920(x46581))),f857(f151(x46581),x46583))))),f857(f857(f9(f920(x46581),f927(f920(x46581),f920(x46581)),f927(f920(x46581),f926(f920(x46581),f920(x46581)))),f857(f857(f10(f927(f920(x46581),f926(f920(x46581),f920(x46581))),f927(f927(f920(x46581),f920(x46581)),f927(f920(x46581),f926(f920(x46581),f920(x46581)))),f920(x46581)),f10(f920(x46581),f926(f920(x46581),f920(x46581)),f920(x46581))),f251(f920(x46581),f920(x46581)))),f857(f151(x46581),x46583)))),f166(x46581,x46582,x46584)),f166(x46581,x46582,f857(f857(f151(x46581),x46583),x46584)))
% 15.02/14.79 [3775]E(f857(f190(f918(x37751)),f857(f857(f857(f90(x37751),x37752),x37753),x37754)),f2(a919))
% 15.02/14.79 [3899]E(f857(f857(f175(x38991),x38992),f857(f857(f175(x38991),x38993),x38994)),f857(f857(f175(x38991),f857(f857(f188(a919),x38992),x38993)),x38994))
% 15.02/14.79 [3900]E(f857(f857(f138(x39001),x39002),f857(f857(f138(x39001),x39003),x39004)),f857(f857(f138(x39001),f857(f857(f79(a919),x39002),x39003)),x39004))
% 15.02/14.79 [3911]E(f857(f857(f134(x39111),f857(f857(f151(x39111),x39112),x39113)),x39114),f857(f857(f151(x39111),x39112),f857(f857(f134(x39111),x39113),x39114)))
% 15.02/14.79 [3912]E(f857(f857(f134(x39121),f857(f857(f134(x39121),x39122),x39123)),x39124),f857(f857(f134(x39121),x39122),f857(f857(f134(x39121),x39123),x39124)))
% 15.02/14.79 [3994]E(f857(f857(f164(x39941),f857(f857(f151(x39941),x39942),x39943)),x39944),f185(x39941,x39942,f857(f164(x39941),x39943),x39944))
% 15.02/14.79 [4003]E(f857(f857(f183(x40031,x40031),x40032),f857(f857(f183(x40031,x40031),x40033),x40034)),f857(f857(f183(x40031,x40031),f857(f857(f80(a919),x40033),x40032)),x40034))
% 15.02/14.79 [4032]E(f857(f857(f110(f927(x40321,a915)),x40322),f857(f857(f308(x40321),x40323),x40324)),f857(f857(f308(x40321),x40323),f857(f857(f110(f927(x40321,a915)),x40322),x40324)))
% 15.02/14.79 [4047]E(f857(f857(f857(f183(x40471,x40471),x40472),x40473),f857(x40473,x40474)),f857(x40473,f857(f857(f857(f183(x40471,x40471),x40472),x40473),x40474)))
% 15.02/14.79 [4056]E(f857(f857(f288(x40561,x40562,x40563),f189(f927(f926(x40561,x40562),a915))),x40564),f189(f927(f926(x40561,x40563),a915)))
% 15.02/14.79 [4071]E(f857(f857(f110(f927(x40711,a915)),f857(f857(f308(x40711),x40712),x40713)),x40714),f857(f857(f308(x40711),x40712),f857(f857(f110(f927(x40711,a915)),x40713),x40714)))
% 15.02/14.79 [4090]E(f857(f34(f926(x40901,x40902)),f857(f857(f253(x40901,x40902),x40903),f857(f18(f927(x40902,a915),x40901),x40904))),f857(f857(f80(a919),f857(f34(x40901),x40903)),f857(f34(x40902),x40904)))
% 15.02/14.79 [4097]E(f857(f857(f101(f927(x40971,a915)),f857(f857(f308(x40971),x40972),x40973)),f857(f857(f308(x40971),x40972),x40974)),f857(f857(f308(x40971),x40972),f857(f857(f101(f927(x40971,a915)),x40973),x40974)))
% 15.02/14.79 [4110]E(f857(f857(f110(f927(x41101,a915)),x41102),f857(f857(f110(f927(x41101,a915)),x41103),x41104)),f857(f857(f110(f927(x41101,a915)),x41103),f857(f857(f110(f927(x41101,a915)),x41102),x41104)))
% 15.02/14.79 [4111]E(f857(f857(f101(f927(x41111,a915)),x41112),f857(f857(f101(f927(x41111,a915)),x41113),x41114)),f857(f857(f101(f927(x41111,a915)),x41113),f857(f857(f101(f927(x41111,a915)),x41112),x41114)))
% 15.02/14.79 [4121]E(f63(x41211,x41212,f857(f857(f10(x41212,f927(x41212,x41212),x41211),x41213),x41214)),f857(f64(x41212,x41211,x41213),x41214))
% 15.02/14.79 [4130]E(f179(x41301,f857(f857(f154(f920(x41302),f920(x41301)),f857(f154(x41302,x41301),x41303)),x41304)),f857(f857(f154(f920(x41302),f920(x41301)),f857(f154(x41302,x41301),x41303)),f179(x41302,x41304)))
% 15.02/14.79 [4149]E(f857(f142(f920(x41491),f920(x41491),f134(x41491),f113(x41491)),f857(f857(f154(x41492,f920(x41491)),x41493),x41494)),f163(x41492,x41491,x41493,x41494))
% 15.02/14.79 [4208]E(f857(f72(x42081,x42081,x42081,f857(f857(f183(x42081,x42081),x42082),x42083)),f857(f857(f183(x42081,x42081),x42084),x42083)),f857(f857(f183(x42081,x42081),f857(f857(f79(a919),x42082),x42084)),x42083))
% 15.02/14.79 [4231]E(f857(f857(f101(f927(x42311,a915)),f857(f857(f110(f927(x42311,a915)),x42312),x42313)),f857(f857(f110(f927(x42311,a915)),x42312),x42314)),f857(f857(f110(f927(x42311,a915)),x42312),f857(f857(f101(f927(x42311,a915)),x42313),x42314)))
% 15.02/14.79 [4232]E(f857(f857(f101(f927(x42321,a915)),f857(f857(f3(f927(x42321,a915)),x42322),x42323)),f857(f857(f3(f927(x42321,a915)),x42322),x42324)),f857(f857(f3(f927(x42321,a915)),x42322),f857(f857(f110(f927(x42321,a915)),x42323),x42324)))
% 15.02/14.79 [4233]E(f857(f857(f110(f927(x42331,a915)),f857(f857(f3(f927(x42331,a915)),x42332),x42333)),f857(f857(f3(f927(x42331,a915)),x42332),x42334)),f857(f857(f3(f927(x42331,a915)),x42332),f857(f857(f101(f927(x42331,a915)),x42333),x42334)))
% 15.02/14.79 [4234]E(f857(f857(f110(f927(x42341,a915)),f857(f857(f101(f927(x42341,a915)),x42342),x42343)),f857(f857(f101(f927(x42341,a915)),x42342),x42344)),f857(f857(f101(f927(x42341,a915)),x42342),f857(f857(f110(f927(x42341,a915)),x42343),x42344)))
% 15.02/14.79 [4235]E(f857(f857(f3(f927(x42351,a915)),f857(f857(f101(f927(x42351,a915)),x42352),x42353)),f857(f857(f101(f927(x42351,a915)),x42352),x42354)),f857(f857(f101(f927(x42351,a915)),x42352),f857(f857(f3(f927(x42351,a915)),x42353),x42354)))
% 15.02/14.79 [4240]E(f857(f34(f926(x42401,x42402)),f857(f857(f253(x42401,x42402),f857(f857(f308(x42401),x42403),f189(f927(x42401,a915)))),f857(f18(f927(x42402,a915),x42401),x42404))),f857(f34(x42402),x42404))
% 15.02/14.79 [4275]E(f857(f857(f39(x42751,f927(x42752,a915)),x42753),f857(f857(f10(f927(x42752,a915),f927(x42752,a915),x42751),f78(f927(x42752,a915))),x42754)),f857(f78(f927(x42752,a915)),f857(f857(f38(x42751,f927(x42752,a915)),x42753),x42754)))
% 15.02/14.79 [4276]E(f857(f857(f38(x42761,f927(x42762,a915)),x42763),f857(f857(f10(f927(x42762,a915),f927(x42762,a915),x42761),f78(f927(x42762,a915))),x42764)),f857(f78(f927(x42762,a915)),f857(f857(f39(x42761,f927(x42762,a915)),x42763),x42764)))
% 15.02/14.79 [4292]E(f857(f857(f288(x42921,x42921,x42921),f857(f857(f183(f926(x42921,x42921),a915),x42922),x42923)),f857(f857(f183(f926(x42921,x42921),a915),x42924),x42923)),f857(f857(f183(f926(x42921,x42921),a915),f857(f857(f79(a919),x42922),x42924)),x42923))
% 15.02/14.79 [4322]E(f857(f857(f38(x43221,f927(f927(x43222,a915),a915)),x43223),f857(f857(f10(f927(x43222,a915),f927(f927(x43222,a915),a915),x43221),f307(x43222)),x43224)),f857(f307(x43222),f857(f857(f38(x43221,f927(x43222,a915)),x43223),x43224)))
% 15.02/14.79 [4351]E(f857(f857(f38(f927(x43511,a915),f927(x43512,a915)),x43513),f857(f857(f9(f927(x43511,a915),f927(x43511,f927(x43512,a915)),f927(x43512,a915)),f38(x43511,f927(x43512,a915))),x43514)),f857(f857(f38(x43511,f927(x43512,a915)),f36(f927(x43511,a915),x43513)),x43514))
% 15.02/14.79 [4352]E(f857(f857(f39(f927(x43521,a915),f927(x43522,a915)),x43523),f857(f857(f9(f927(x43521,a915),f927(x43521,f927(x43522,a915)),f927(x43522,a915)),f39(x43521,f927(x43522,a915))),x43524)),f857(f857(f39(x43521,f927(x43522,a915)),f36(f927(x43521,a915),x43523)),x43524))
% 15.02/14.79 [4357]E(f857(f857(f154(x43571,x43572),x43573),f857(f142(f920(x43571),f920(x43571),f134(x43571),f113(x43571)),x43574)),f857(f142(f920(x43572),f920(x43572),f134(x43572),f113(x43572)),f857(f857(f154(f920(x43571),f920(x43572)),f857(f154(x43571,x43572),x43573)),x43574)))
% 15.02/14.79 [4359]E(f185(f920(x43591),f113(x43591),f857(f857(f10(f920(x43591),f920(x43591),a919),f857(f151(x43591),x43592)),f857(f857(f9(a919,f920(x43591),f920(x43591)),f175(x43591)),x43593)),x43594),f857(f857(f175(x43591),x43594),f857(f857(f151(x43591),x43592),x43593)))
% 15.02/14.79 [4397]P106(f857(f857(f234(f927(x43971,a915)),f857(f309(x43972,x43971,x43973),f857(f310(x43972,x43971,x43973),x43974))),x43974))
% 15.02/14.79 [4399]E(f857(f309(f926(x43991,x43992),f926(x43992,x43991),f857(f256(x43991,x43992,f926(x43992,x43991)),f857(f9(x43992,x43991,f926(x43992,x43991)),f251(x43992,x43991)))),f857(f857(f253(x43991,x43992),x43993),f857(f18(f927(x43992,a915),x43991),x43994))),f857(f857(f253(x43992,x43991),x43994),f857(f18(f927(x43991,a915),x43992),x43993)))
% 15.02/14.79 [4408]E(f857(f857(f39(x44081,f927(x44082,a915)),x44083),f857(f857(f10(f927(x44081,a915),f927(x44082,a915),x44081),f310(x44082,x44081,x44084)),f857(f857(f9(x44081,f927(x44081,a915),f927(x44081,a915)),f308(x44081)),f189(f927(x44081,a915))))),f857(f310(x44082,x44081,x44084),x44083))
% 15.02/14.79 [4409]E(f857(f857(f39(x44091,f927(x44092,a915)),x44093),f857(f857(f10(f927(x44091,a915),f927(x44092,a915),x44091),f284(x44091,x44092,x44094)),f857(f857(f9(x44091,f927(x44091,a915),f927(x44091,a915)),f308(x44091)),f189(f927(x44091,a915))))),f857(f284(x44091,x44092,x44094),x44093))
% 15.02/14.79 [4496]E(f857(f857(f110(f927(x44961,a915)),f857(f857(f110(f927(x44961,a915)),f857(f857(f101(f927(x44961,a915)),x44962),x44963)),f857(f857(f101(f927(x44961,a915)),x44963),x44964))),f857(f857(f101(f927(x44961,a915)),x44964),x44962)),f857(f857(f101(f927(x44961,a915)),f857(f857(f101(f927(x44961,a915)),f857(f857(f110(f927(x44961,a915)),x44962),x44963)),f857(f857(f110(f927(x44961,a915)),x44963),x44964))),f857(f857(f110(f927(x44961,a915)),x44964),x44962)))
% 15.02/14.79 [4560]E(f857(f142(f920(x45601),f920(x45601),f134(x45601),f113(x45601)),f857(f857(f154(x45602,f920(x45601)),f857(f857(f9(x45602,f920(x45601),f920(x45601)),f857(f857(f10(x45601,f927(f920(x45601),f920(x45601)),x45602),f151(x45601)),x45603)),f113(x45601))),x45604)),f857(f857(f154(x45602,x45601),x45603),x45604))
% 15.02/14.79 [4570]E(f857(f857(f85(a1,x45701),f857(f103(a1),f857(f857(f79(a1),x45702),a97))),f857(f857(f20(a1,x45701,x45701),f857(f857(f9(a1,x45701,f927(x45701,x45701)),f857(f857(f10(a915,f927(x45701,f927(x45701,x45701)),a1),f96(x45701)),a194)),x45703)),f857(f857(f10(a919,x45701,a1),x45704),a104))),f185(x45701,x45703,x45704,f857(f103(a919),x45702)))
% 15.02/14.79 [4601]E(f857(f261(x46011),f857(f857(f10(f927(x46012,a915),a915,x46011),f86(x46012)),f857(f857(f10(f927(x46012,a915),f927(x46012,a915),x46011),f857(f20(x46012,a915,a915),f857(f857(f10(a915,f927(a915,a915),x46012),a325),f857(f857(f9(x46012,f927(x46012,a915),a915),f328(x46012)),x46013)))),f857(f9(x46012,x46011,a915),x46014)))),f857(f284(x46012,x46011,f857(f261(f926(x46012,x46011)),f857(f256(x46012,x46011,a915),x46014))),x46013))
% 15.02/14.79 [4756]~P106(f857(f857(f189(f927(x47561,f927(x47562,a915))),x47563),x47564))
% 15.02/14.79 [4059]E(f857(f857(f164(x40591),f857(f857(f134(x40591),x40592),x40593)),f857(f857(f79(a919),f857(f190(f920(x40591)),x40592)),x40594)),f857(f857(f164(x40591),x40593),x40594))
% 15.02/14.79 [4064]E(f857(f857(f138(x40641),x40642),f857(f857(f175(x40641),f857(f857(f79(a919),x40643),x40642)),x40644)),f857(f857(f175(x40641),x40643),f857(f857(f138(x40641),x40642),x40644)))
% 15.02/14.79 [4163]E(f857(f857(f110(f927(x41631,a915)),f857(f283(x41632,x41631),x41633)),f857(f283(x41632,x41631),x41634)),f857(f283(x41632,x41631),f857(f857(f110(f927(f926(x41632,x41631),a915)),x41633),x41634)))
% 15.02/14.79 [4164]E(f857(f857(f110(f927(x41641,a915)),f857(f263(x41641,x41642),x41643)),f857(f263(x41641,x41642),x41644)),f857(f263(x41641,x41642),f857(f857(f110(f927(f926(x41641,x41642),a915)),x41643),x41644)))
% 15.02/14.79 [4169]E(f857(f857(f110(f927(x41691,a915)),f857(f857(f110(f927(x41691,a915)),x41692),x41693)),x41694),f857(f857(f110(f927(x41691,a915)),x41692),f857(f857(f110(f927(x41691,a915)),x41693),x41694)))
% 15.02/14.79 [4170]E(f857(f857(f3(f927(x41701,a915)),f857(f857(f101(f927(x41701,a915)),x41702),x41703)),x41704),f857(f857(f101(f927(x41701,a915)),x41702),f857(f857(f3(f927(x41701,a915)),x41703),x41704)))
% 15.02/14.79 [4171]E(f857(f857(f101(f927(x41711,a915)),f857(f857(f101(f927(x41711,a915)),x41712),x41713)),x41714),f857(f857(f101(f927(x41711,a915)),x41712),f857(f857(f101(f927(x41711,a915)),x41713),x41714)))
% 15.02/14.79 [4210]E(f857(f857(f110(f927(f926(x42101,x42102),a915)),f857(f285(x42102,x42101),x42103)),f857(f285(x42102,x42101),x42104)),f857(f285(x42102,x42101),f857(f857(f110(f927(f926(x42102,x42101),a915)),x42103),x42104)))
% 15.02/14.79 [4211]E(f857(f857(f101(f927(f926(x42111,x42112),a915)),f857(f285(x42112,x42111),x42113)),f857(f285(x42112,x42111),x42114)),f857(f285(x42112,x42111),f857(f857(f101(f927(f926(x42112,x42111),a915)),x42113),x42114)))
% 15.02/14.79 [4224]E(f857(f857(f110(f927(x42241,f927(x42242,a915))),f242(x42242,x42241,x42243)),f242(x42242,x42241,x42244)),f242(x42242,x42241,f857(f857(f110(f927(x42242,f927(x42241,a915))),x42243),x42244)))
% 15.02/14.79 [4225]E(f857(f857(f101(f927(x42251,f927(x42252,a915))),f242(x42252,x42251,x42253)),f242(x42252,x42251,x42254)),f242(x42252,x42251,f857(f857(f101(f927(x42252,f927(x42251,a915))),x42253),x42254)))
% 15.02/14.79 [4279]E(f857(f857(f101(f927(x42791,a915)),f857(f857(f110(f927(x42791,a915)),x42792),x42793)),f857(f857(f110(f927(x42791,a915)),x42794),x42793)),f857(f857(f110(f927(x42791,a915)),f857(f857(f101(f927(x42791,a915)),x42792),x42794)),x42793))
% 15.02/14.79 [4280]E(f857(f857(f110(f927(x42801,a915)),f857(f857(f3(f927(x42801,a915)),x42802),x42803)),f857(f857(f3(f927(x42801,a915)),x42804),x42803)),f857(f857(f3(f927(x42801,a915)),f857(f857(f110(f927(x42801,a915)),x42802),x42804)),x42803))
% 15.02/14.79 [4281]E(f857(f857(f110(f927(x42811,a915)),f857(f857(f101(f927(x42811,a915)),x42812),x42813)),f857(f857(f101(f927(x42811,a915)),x42814),x42813)),f857(f857(f101(f927(x42811,a915)),f857(f857(f110(f927(x42811,a915)),x42812),x42814)),x42813))
% 15.02/14.79 [4282]E(f857(f857(f3(f927(x42821,a915)),f857(f857(f101(f927(x42821,a915)),x42822),x42823)),f857(f857(f101(f927(x42821,a915)),x42824),x42823)),f857(f857(f101(f927(x42821,a915)),f857(f857(f3(f927(x42821,a915)),x42822),x42824)),x42823))
% 15.02/14.79 [4283]E(f857(f857(f3(f927(x42831,a915)),f857(f857(f101(f927(x42831,a915)),x42832),x42833)),f857(f857(f101(f927(x42831,a915)),x42834),x42833)),f857(f857(f3(f927(x42831,a915)),f857(f857(f101(f927(x42831,a915)),x42832),x42833)),x42834))
% 15.02/14.79 [4295]E(f857(f857(f3(f927(x42951,a915)),f857(f857(f3(f927(x42951,a915)),x42952),f857(f857(f308(x42951),x42953),f189(f927(x42951,a915))))),x42954),f857(f857(f3(f927(x42951,a915)),x42952),f857(f857(f308(x42951),x42953),x42954)))
% 15.02/14.79 [4348]E(f857(f857(f110(f927(x43481,a915)),f857(f857(f308(x43481),x43482),f857(f857(f308(x43481),x43483),f189(f927(x43481,a915))))),f857(f280(x43481),x43484)),f857(f280(x43481),f857(f857(f308(f926(x43481,x43481)),f857(f857(f251(x43481,x43481),x43482),x43483)),x43484)))
% 15.02/14.79 [4373]E(f857(f857(f39(a919,f927(x43731,a915)),f857(f300(a919),x43732)),f857(f857(f10(a919,f927(x43731,a915),a919),x43733),f857(f857(f9(a919,a919,a919),f79(a919)),x43734))),f857(f857(f39(a919,f927(x43731,a915)),f302(a919,x43734,f857(f857(f79(a919),x43732),x43734))),x43733))
% 15.02/14.79 [4374]E(f174(x43741,f857(f284(x43741,x43741,x43742),f857(f857(f308(x43741),x43743),f189(f927(x43741,a915)))),f857(f284(f920(x43741),f920(x43741),f158(x43741,x43742)),f857(f857(f308(f920(x43741)),x43744),f189(f927(f920(x43741),a915))))),f857(f284(f920(x43741),f920(x43741),f158(x43741,x43742)),f857(f857(f308(f920(x43741)),f857(f857(f151(x43741),x43743),x43744)),f189(f927(f920(x43741),a915)))))
% 15.02/14.79 [4438]E(f857(f261(x44381),f857(f857(f9(x44381,f927(x44382,a915),a915),f857(f857(f10(x44382,f927(f927(x44382,a915),a915),x44381),f328(x44382)),x44383)),x44384)),f857(f310(x44381,x44382,x44383),x44384))
% 15.02/14.79 [4529]E(f857(f261(x45291),f857(f857(f9(x45291,f927(f926(x45292,x45291),a915),a915),f857(f857(f10(f926(x45292,x45291),f927(f927(f926(x45292,x45291),a915),a915),x45291),f328(f926(x45292,x45291))),f857(f251(x45292,x45291),x45293))),x45294)),f857(f284(x45292,x45291,x45294),f857(f857(f308(x45292),x45293),f189(f927(x45292,a915)))))
% 15.02/14.79 [4543]E(f857(f857(f154(f926(x45431,a919),x45431),f250(x45431,a919)),f857(f136(f926(x45431,a919),f857(f857(f10(a919,a915,f926(x45431,a919)),x45432),f857(f857(f10(a919,a919,f926(x45431,a919)),a112),f255(x45431,a919)))),f857(f857(f181(x45431,a919),x45433),x45434))),f857(f857(f154(f926(x45431,a919),x45431),f250(x45431,a919)),f857(f136(f926(x45431,a919),f857(f857(f10(a919,a915,f926(x45431,a919)),x45432),f255(x45431,a919))),f857(f857(f181(x45431,a919),x45433),f857(f857(f154(a919,a919),a112),x45434)))))
% 15.02/14.79 [4552]P106(f857(f857(f234(f927(f927(x45521,a915),a915)),f857(f857(f39(x45522,f927(f927(x45521,a915),a915)),x45523),f857(f857(f10(f927(x45521,a915),f927(f927(x45521,a915),a915),x45522),f307(x45521)),x45524))),f857(f307(x45521),f857(f857(f39(x45522,f927(x45521,a915)),x45523),x45524))))
% 15.02/14.79 [4593]E(f857(f857(f85(a1,x45931),f857(f103(a1),f857(f857(f79(a1),x45932),a97))),f857(f857(f20(a1,x45931,x45931),f857(f857(f9(a1,x45931,f927(x45931,x45931)),f857(f857(f10(a915,f927(x45931,f927(x45931,x45931)),a1),f96(x45931)),a194)),x45933)),f857(f857(f20(a1,x45931,x45931),f857(f857(f10(a919,f927(x45931,x45931),a1),x45934),a104)),f857(f857(f10(a919,x45931,a1),f184(x45931,x45933,x45934)),a104)))),f857(f184(x45931,x45933,x45934),f857(f103(a919),x45932)))
% 15.02/14.79 [4617]E(f857(f261(f926(x46171,x46172)),f857(f256(x46171,x46172,a915),f857(f857(f9(x46171,f927(x46172,a915),f927(x46172,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x46172,a915),f927(x46172,a915)),x46171),f10(a915,a915,x46172)),f857(f857(f10(a915,f927(a915,a915),x46171),a325),f857(f857(f9(x46171,f927(x46171,a915),a915),f328(x46171)),x46173)))),f857(f857(f9(x46172,f927(x46172,a915),a915),f328(x46172)),x46174)))),f230(x46171,x46172,x46173,x46174))
% 15.02/14.79 [4653]E(f857(f857(f39(x46531,f927(f926(x46531,x46532),a915)),x46533),f857(f857(f20(x46531,f927(x46532,f927(f926(x46531,x46532),a915)),f927(f926(x46531,x46532),a915)),f857(f857(f10(f927(x46532,a915),f927(f927(x46532,f927(f926(x46531,x46532),a915)),f927(f926(x46531,x46532),a915)),x46531),f39(x46532,f927(f926(x46531,x46532),a915))),x46534)),f857(f857(f9(x46531,f927(f926(x46531,x46532),a915),f927(x46532,f927(f926(x46531,x46532),a915))),f857(f857(f10(f927(x46532,f927(f927(f926(x46531,x46532),a915),f927(f926(x46531,x46532),a915))),f927(f927(f926(x46531,x46532),a915),f927(x46532,f927(f926(x46531,x46532),a915))),x46531),f9(x46532,f927(f926(x46531,x46532),a915),f927(f926(x46531,x46532),a915))),f857(f857(f10(f927(x46532,f926(x46531,x46532)),f927(x46532,f927(f927(f926(x46531,x46532),a915),f927(f926(x46531,x46532),a915))),x46531),f857(f10(f926(x46531,x46532),f927(f927(f926(x46531,x46532),a915),f927(f926(x46531,x46532),a915)),x46532),f308(f926(x46531,x46532)))),f251(x46531,x46532)))),f189(f927(f926(x46531,x46532),a915))))),f857(f857(f253(x46531,x46532),x46533),x46534))
% 15.02/14.79 [4219]E(f857(f857(f134(x42191),f857(f857(f175(x42191),x42192),x42193)),f857(f857(f175(x42191),f857(f857(f3(a919),x42192),f857(f190(f920(x42191)),x42193))),x42194)),f857(f857(f175(x42191),x42192),f857(f857(f134(x42191),x42193),x42194)))
% 15.02/14.79 [4220]E(f857(f857(f134(x42201),f857(f857(f138(x42201),x42202),x42203)),f857(f857(f138(x42201),f857(f857(f3(a919),x42202),f857(f190(f920(x42201)),x42203))),x42204)),f857(f857(f138(x42201),x42202),f857(f857(f134(x42201),x42203),x42204)))
% 15.02/14.79 [4269]E(f857(f857(f79(a919),f857(f857(f80(a919),x42691),x42692)),f857(f857(f79(a919),f857(f857(f80(a919),x42693),x42692)),x42694)),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f79(a919),x42691),x42693)),x42692)),x42694))
% 15.02/14.79 [4414]E(f89(x44141,f857(f857(f9(x44141,x44142,a915),f857(f857(f10(x44142,f927(x44142,a915),x44141),a324),x44143)),x44144)),f857(f91(x44141,x44142,f241(f927(x44141,a915)),x44143),x44144))
% 15.02/14.79 [4462]P106(f857(f857(f234(f927(x44621,a915)),f857(f857(f3(f927(x44621,a915)),f857(f283(x44622,x44621),x44623)),f857(f283(x44622,x44621),x44624))),f857(f283(x44622,x44621),f857(f857(f3(f927(f926(x44622,x44621),a915)),x44623),x44624))))
% 15.02/14.79 [4463]P106(f857(f857(f234(f927(x44631,a915)),f857(f857(f3(f927(x44631,a915)),f857(f263(x44631,x44632),x44633)),f857(f263(x44631,x44632),x44634))),f857(f263(x44631,x44632),f857(f857(f3(f927(f926(x44631,x44632),a915)),x44633),x44634))))
% 15.02/14.79 [4572]E(f857(f857(f79(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x45721),x45722)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x45723),x45724)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),f857(f857(f79(a919),x45721),x45723)),f857(f857(f79(a919),x45722),x45724))),f189(f927(f926(a919,a919),a915))))))
% 15.02/14.79 [4612]E(f857(f857(f80(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x46121),x46122)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x46123),x46124)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),f857(f857(f79(a919),f857(f857(f80(a919),x46121),x46123)),f857(f857(f80(a919),x46122),x46124))),f857(f857(f79(a919),f857(f857(f80(a919),x46121),x46124)),f857(f857(f80(a919),x46122),x46123)))),f189(f927(f926(a919,a919),a915))))))
% 15.02/14.79 [4633]E(f857(f261(x46331),f857(f857(f10(f927(x46332,a915),a915,x46331),f87(x46332)),f857(f857(f10(f927(x46332,a915),f927(x46332,a915),x46331),f857(f20(x46332,a915,a915),f857(f857(f10(a915,f927(a915,a915),x46332),a329),f857(f857(f9(x46332,f927(x46332,a915),a915),f328(x46332)),x46333)))),f857(f857(f9(x46331,f927(x46332,f927(x46331,a915)),f927(x46332,a915)),f857(f857(f10(f927(f927(x46331,a915),a915),f927(f927(x46332,f927(x46331,a915)),f927(x46332,a915)),x46331),f10(f927(x46331,a915),a915,x46332)),f328(x46331))),x46334)))),f857(f857(f38(x46332,f927(x46331,a915)),x46333),x46334))
% 15.02/14.79 [4666]E(f857(f857(f288(x46661,x46661,x46661),f857(f857(f308(f926(x46661,x46661)),f857(f857(f251(x46661,x46661),x46662),x46663)),x46664)),f306(x46661,f857(f857(f308(f926(x46661,x46661)),f857(f857(f251(x46661,x46661),x46662),x46663)),x46664))),f857(f857(f110(f927(f926(x46661,x46661),a915)),f857(f857(f288(x46661,x46661,x46661),x46664),f306(x46661,x46664))),f857(f261(f926(x46661,x46661)),f857(f256(x46661,x46661,a915),f857(f857(f9(x46661,f927(x46661,a915),f927(x46661,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x46661,a915),f927(x46661,a915)),x46661),f10(a915,a915,x46661)),f857(f857(f10(a915,f927(a915,a915),x46661),a325),f857(f857(f9(x46661,f927(f926(x46661,x46661),a915),a915),f857(f857(f10(f926(x46661,x46661),f927(f927(f926(x46661,x46661),a915),a915),x46661),f328(f926(x46661,x46661))),f857(f857(f9(x46661,x46661,f926(x46661,x46661)),f251(x46661,x46661)),x46662))),f306(x46661,x46664))))),f857(f857(f9(x46661,f927(f926(x46661,x46661),a915),a915),f857(f857(f10(f926(x46661,x46661),f927(f927(f926(x46661,x46661),a915),a915),x46661),f328(f926(x46661,x46661))),f857(f251(x46661,x46661),x46663))),f306(x46661,x46664)))))))
% 15.02/14.79 [4464]E(f857(f136(x44641,f857(f857(f20(x44641,a915,a915),f857(f857(f10(a915,f927(a915,a915),x44641),a325),x44642)),x44643)),x44644),f857(f136(x44641,x44643),f857(f136(x44641,x44642),x44644)))
% 15.02/14.79 [4566]E(f857(f857(f134(x45661),f857(f857(f857(f96(f920(x45661)),f857(f857(f328(a919),f2(a919)),x45662)),f857(f857(f151(x45661),x45663),f113(x45661))),f113(x45661))),f176(x45661,x45664,f857(f261(a919),f857(f857(f9(a919,f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),a919),f328(a919)),a112)),x45662)))),f176(x45661,f857(f857(f151(x45661),x45663),x45664),x45662))
% 15.02/14.79 [4662]E(f857(f261(f926(x46621,x46622)),f857(f857(f10(f927(a919,a915),a915,f926(x46621,x46622)),f86(a919)),f857(f857(f9(f926(x46621,x46622),f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),f926(x46621,x46622)),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),f926(x46621,x46622)),f857(f10(a915,f927(a915,a915),a919),a325)),f857(f857(f9(f926(x46621,x46622),f927(a919,f926(x46621,x46622)),f927(a919,a915)),f857(f857(f10(f927(f926(x46621,x46622),a915),f927(f927(a919,f926(x46621,x46622)),f927(a919,a915)),f926(x46621,x46622)),f10(f926(x46621,x46622),a915,a919)),a324)),f857(f857(f20(a919,x46622,f926(x46621,x46622)),f857(f857(f10(x46621,f927(x46622,f926(x46621,x46622)),a919),f251(x46621,x46622)),f857(f164(x46621),x46623))),f857(f164(x46622),x46624)))))),f857(f857(f9(a919,a919,a915),f235(a919)),f857(f857(f188(a919),f857(f190(f920(x46621)),x46623)),f857(f190(f920(x46622)),x46624)))))),f857(f172(f926(x46621,x46622)),f857(f857(f181(x46621,x46622),x46623),x46624)))
% 15.02/14.79 [4585]E(f857(f261(f926(x45851,x45852)),f857(f256(x45851,x45852,a915),f857(f857(f9(x45851,f927(x45852,a915),f927(x45852,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x45852,a915),f927(x45852,a915)),x45851),f10(a915,a915,x45852)),f857(f857(f10(a915,f927(a915,a915),x45851),a325),x45853))),x45854))),f857(f857(f253(x45851,x45852),f857(f261(x45851),x45853)),f857(f18(f927(x45852,a915),x45851),f857(f261(x45852),x45854))))
% 15.02/14.79 [4588]E(f857(f261(f926(x45881,x45882)),f857(f256(x45881,x45882,a915),f857(f857(f20(x45881,f927(x45882,a915),f927(x45882,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x45882,a915),f927(x45882,a915)),x45881),f10(a915,a915,x45882)),f857(f857(f10(a915,f927(a915,a915),x45881),a325),x45883))),x45884))),f857(f857(f253(x45881,x45882),f857(f261(x45881),x45883)),f857(f857(f10(f927(x45882,a915),f927(x45882,a915),x45881),f261(x45882)),x45884)))
% 15.02/14.79 [4600]E(f857(f261(x46001),f857(f857(f10(f927(x46002,a915),a915,x46001),f87(x46002)),f857(f857(f10(f927(x46002,a915),f927(x46002,a915),x46001),f857(f20(x46002,a915,a915),f857(f857(f10(a915,f927(a915,a915),x46002),a329),f857(f857(f9(x46002,f927(x46002,a915),a915),f328(x46002)),x46003)))),x46004))),f857(f857(f38(x46002,f927(x46001,a915)),x46003),f857(f857(f10(f927(x46001,a915),f927(x46001,a915),x46002),f261(x46001)),f857(f9(x46001,x46002,a915),x46004))))
% 15.02/14.79 [4645]E(f857(f857(f154(f926(x46451,a919),x46451),f250(x46451,a919)),f857(f136(f926(x46451,a919),f857(f857(f9(f926(x46451,a919),f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),f926(x46451,a919)),f328(a919)),f255(x46451,a919))),x46452)),f857(f857(f181(x46451,a919),x46453),f139(a919,f857(f301(a919,x46454),f857(f857(f79(a919),x46454),f857(f190(f920(x46451)),x46453))))))),f857(f857(f154(f926(x46451,a919),x46451),f250(x46451,a919)),f857(f136(f926(x46451,a919),f857(f857(f9(f926(x46451,a919),f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),f926(x46451,a919)),f328(a919)),f857(f857(f9(f926(x46451,a919),a919,a919),f857(f857(f10(a919,f927(a919,a919),f926(x46451,a919)),f79(a919)),f255(x46451,a919))),x46454))),x46452)),f857(f857(f181(x46451,a919),x46453),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(x46451)),x46453)))))))
% 15.02/14.79 [4646]E(f857(a112,f857(f857(f233(a919),f857(f190(f920(x46461)),x46462)),f857(f142(a919,f920(x46463),f857(f9(f920(x46463),a919,a919),f857(f857(f10(a919,f927(a919,a919),f920(x46463)),f233(a919)),f857(f857(f9(f920(x46463),a919,a919),f857(f857(f10(a919,f927(a919,a919),f920(x46463)),f3(a919)),f190(f920(x46463)))),f857(a112,f2(a919))))),f2(a919)),f857(f168(f920(x46463)),f857(f136(f920(x46463),f857(f857(f10(a915,a915,f920(x46463)),a321),f857(f857(f9(f920(x46463),f920(x46463),a915),a324),f113(x46463)))),x46464))))),f857(f857(f233(a919),f857(a112,f857(f190(f920(x46461)),x46462))),f857(f142(a919,f920(x46463),f857(f9(f920(x46463),a919,a919),f857(f857(f10(a919,f927(a919,a919),f920(x46463)),f233(a919)),f190(f920(x46463)))),f2(a919)),f857(f168(f920(x46463)),x46464))))
% 15.02/14.79 [4599]E(f857(f857(f134(x45991),f176(x45991,x45992,x45993)),f176(x45991,x45994,f857(f261(a919),f857(f857(f9(a919,f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),a919),f328(a919)),f857(f857(f9(a919,a919,a919),f79(a919)),f857(f190(f920(x45991)),x45992)))),x45993)))),f176(x45991,f857(f857(f134(x45991),x45992),x45994),x45993))
% 15.02/14.79 [4647]E(f37(f927(x46471,a915),f857(f261(f927(x46471,a915)),f857(f857(f10(f927(x46472,a915),a915,f927(x46471,a915)),f86(x46472)),f857(f857(f10(f927(x46472,a915),f927(x46472,a915),f927(x46471,a915)),f857(f20(x46472,a915,a915),f857(f857(f10(a915,f927(a915,a915),x46472),a325),f857(f857(f9(x46472,f927(x46472,a915),a915),f328(x46472)),x46473)))),f857(f857(f9(f927(x46471,a915),f927(x46472,f927(x46471,a915)),f927(x46472,a915)),f857(f857(f10(f927(f927(x46471,a915),a915),f927(f927(x46472,f927(x46471,a915)),f927(x46472,a915)),f927(x46471,a915)),f10(f927(x46471,a915),a915,x46472)),a324)),x46474))))),f857(f857(f38(x46472,f927(x46471,a915)),x46473),x46474))
% 15.02/14.79 [4648]E(f36(f927(x46481,a915),f857(f261(f927(x46481,a915)),f857(f857(f10(f927(x46482,a915),a915,f927(x46481,a915)),f86(x46482)),f857(f857(f10(f927(x46482,a915),f927(x46482,a915),f927(x46481,a915)),f857(f20(x46482,a915,a915),f857(f857(f10(a915,f927(a915,a915),x46482),a325),f857(f857(f9(x46482,f927(x46482,a915),a915),f328(x46482)),x46483)))),f857(f857(f9(f927(x46481,a915),f927(x46482,f927(x46481,a915)),f927(x46482,a915)),f857(f857(f10(f927(f927(x46481,a915),a915),f927(f927(x46482,f927(x46481,a915)),f927(x46482,a915)),f927(x46481,a915)),f10(f927(x46481,a915),a915,x46482)),a324)),x46484))))),f857(f857(f39(x46482,f927(x46481,a915)),x46483),x46484))
% 15.02/14.79 [4655]E(f857(f857(f151(f920(x46551)),f857(f857(f151(x46551),x46552),f857(f142(f920(x46551),f920(x46551),f134(x46551),f113(x46551)),f857(f857(f154(f920(x46551),f920(x46551)),f156(f920(x46551),x46551,f113(x46551),f857(f857(f10(f920(x46551),f927(f920(x46551),f920(x46551)),x46551),f18(f920(x46551),f920(x46551))),f857(f857(f9(x46551,f920(x46551),f920(x46551)),f151(x46551)),f113(x46551))))),x46553)))),f179(x46551,f857(f857(f151(f920(x46551)),x46554),f857(f142(f920(f920(x46551)),f920(f920(x46551)),f134(f920(x46551)),f113(f920(x46551))),f857(f857(f154(f920(x46551),f920(f920(x46551))),f156(f920(f920(x46551)),x46551,f113(f920(x46551)),f857(f18(f927(f920(x46551),f920(f920(x46551))),x46551),f857(f857(f9(f920(x46551),f920(f920(x46551)),f920(f920(x46551))),f151(f920(x46551))),f113(f920(x46551)))))),x46553))))),f179(x46551,f857(f857(f151(f920(x46551)),f857(f857(f151(x46551),x46552),x46554)),x46553)))
% 15.02/14.79 [4663]E(f857(f261(f926(x46631,x46631)),f857(f256(x46631,x46631,a915),f857(f857(f9(x46631,f927(f926(x46632,x46632),a915),f927(x46631,a915)),f857(f857(f10(f927(x46631,f927(f927(f926(x46632,x46632),a915),a915)),f927(f927(f926(x46632,x46632),a915),f927(x46631,a915)),x46631),f9(x46631,f927(f926(x46632,x46632),a915),a915)),f857(f857(f10(f927(x46631,f926(x46632,x46632)),f927(x46631,f927(f927(f926(x46632,x46632),a915),a915)),x46631),f857(f10(f926(x46632,x46632),f927(f927(f926(x46632,x46632),a915),a915),x46631),f328(f926(x46632,x46632)))),f857(f857(f9(x46631,f927(x46631,x46632),f927(x46631,f926(x46632,x46632))),f857(f857(f10(f927(x46632,f926(x46632,x46632)),f927(f927(x46631,x46632),f927(x46631,f926(x46632,x46632))),x46631),f10(x46632,f926(x46632,x46632),x46631)),f857(f857(f10(x46632,f927(x46632,f926(x46632,x46632)),x46631),f251(x46632,x46632)),x46633))),x46633)))),x46634))),f857(f857(f287(x46632,x46631),x46634),x46633))
% 15.02/14.79 [4709]~E(f30(x47091,x47092),f27(x47093,x47094,x47095))
% 15.02/14.79 [4710]~E(f30(x47101,x47102),f26(x47103,x47104,x47105))
% 15.02/14.79 [4711]~E(f29(x47111,x47112),f27(x47113,x47114,x47115))
% 15.02/14.79 [4712]~E(f29(x47121,x47122),f26(x47123,x47124,x47125))
% 15.02/14.79 [4713]~E(f27(x47131,x47132,x47133),f30(x47134,x47135))
% 15.02/14.79 [4714]~E(f27(x47141,x47142,x47143),f29(x47144,x47145))
% 15.02/14.79 [4715]~E(f26(x47151,x47152,x47153),f30(x47154,x47155))
% 15.02/14.79 [4716]~E(f26(x47161,x47162,x47163),f29(x47164,x47165))
% 15.02/14.79 [3794]E(f857(f857(f154(x37941,x37942),x37943),f169(x37941,x37944,x37945)),f169(x37942,x37944,f857(x37943,x37945)))
% 15.02/14.79 [4131]E(f130(x41311,x41312,x41313,f126(x41311,x41314,x41315)),f126(x41312,f857(x41313,x41314),f130(x41311,x41312,x41313,x41315)))
% 15.02/14.79 [4363]E(f857(f74(x43631,x43632,x43633,x43634,x43635),x43634),x43635)
% 15.02/14.79 [4415]E(f252(x44151,x44152,x44153,f242(x44152,x44151,x44154),f242(x44153,x44152,x44155)),f242(x44153,x44151,f252(x44153,x44152,x44151,x44155,x44154)))
% 15.02/14.79 [3988]E(f857(f857(f256(x39881,x39882,x39883),x39884),x39885),f857(f857(x39884,f857(f250(x39881,x39882),x39885)),f857(f255(x39881,x39882),x39885)))
% 15.02/14.79 [4024]E(f857(f857(f857(f64(x40241,x40242,x40243),x40244),x40245),f189(f927(x40242,a915))),x40245)
% 15.02/14.79 [4303]E(f857(f72(f920(x43031),f920(x43032),f920(x43033),f857(f154(x43031,x43032),x43034)),f857(f154(x43033,x43031),x43035)),f857(f154(x43033,x43032),f857(f72(x43031,x43032,x43033,x43034),x43035)))
% 15.02/14.79 [4377]E(f84(x43771,f65(x43772,x43771,x43773,x43774,x43775)),f857(f857(f63(x43772,x43771,x43773),x43774),x43775))
% 15.02/14.79 [4411]E(f857(f857(f79(a919),f857(f857(f79(a919),f857(x44111,f857(f250(x44112,x44113),x44114))),f857(x44115,f857(f255(x44112,x44113),x44114)))),f857(a112,f2(a919))),f260(x44112,x44113,x44111,x44115,x44114))
% 15.02/14.79 [3924]E(f857(f857(f175(x39241),x39242),f857(f857(f154(x39243,x39241),x39244),x39245)),f857(f857(f154(x39243,x39241),x39244),f857(f857(f175(x39243),x39242),x39245)))
% 15.02/14.79 [3925]E(f857(f857(f138(x39251),x39252),f857(f857(f154(x39253,x39251),x39254),x39255)),f857(f857(f154(x39253,x39251),x39254),f857(f857(f138(x39253),x39252),x39255)))
% 15.02/14.79 [3957]E(f857(f857(f154(x39571,x39572),x39573),f857(f857(f151(x39571),x39574),x39575)),f857(f857(f151(x39572),f857(x39573,x39574)),f857(f857(f154(x39571,x39572),x39573),x39575)))
% 15.02/14.79 [4018]E(f857(f309(x40181,x40182,x40183),f857(f857(f308(x40181),x40184),x40185)),f857(f857(f308(x40182),f857(x40183,x40184)),f857(f309(x40181,x40182,x40183),x40185)))
% 15.02/14.79 [4048]E(f173(x40481,f857(f857(f151(x40481),x40482),x40483),f857(f857(f151(x40481),x40484),x40485)),f857(f857(f151(x40481),x40482),f857(f857(f151(x40481),x40484),f173(x40481,x40483,x40485))))
% 15.02/14.79 [4085]E(f857(f857(f181(x40851,x40852),f857(f857(f175(x40851),x40853),x40854)),f857(f857(f175(x40852),x40853),x40855)),f857(f857(f175(f926(x40851,x40852)),x40853),f857(f857(f181(x40851,x40852),x40854),x40855)))
% 15.02/14.79 [4086]E(f857(f857(f181(x40861,x40862),f857(f857(f138(x40861),x40863),x40864)),f857(f857(f138(x40862),x40863),x40865)),f857(f857(f138(f926(x40861,x40862)),x40863),f857(f857(f181(x40861,x40862),x40864),x40865)))
% 15.02/14.79 [4096]E(f857(f857(f159(x40961,f857(f857(f151(x40961),x40962),x40963)),f857(a112,x40964)),x40965),f857(f857(f151(x40961),x40962),f857(f857(f159(x40961,x40963),x40964),x40965)))
% 15.02/14.79 [4099]E(f857(f857(f134(x40991),f857(f857(f154(x40992,x40991),x40993),x40994)),f857(f857(f154(x40992,x40991),x40993),x40995)),f857(f857(f154(x40992,x40991),x40993),f857(f857(f134(x40992),x40994),x40995)))
% 15.02/14.79 [4103]E(f857(f857(x41031,x41032),f857(f857(f244(x41033,x41034,x41031),x41032),x41035)),f857(f857(f244(x41033,x41034,x41031),x41032),f857(a112,x41035)))
% 15.02/14.79 [4135]E(f163(x41351,x41352,x41353,f857(f857(f151(x41351),x41354),x41355)),f857(f857(f134(x41352),f857(x41353,x41354)),f163(x41351,x41352,x41353,x41355)))
% 15.02/14.79 [4147]E(f857(f857(f288(x41471,x41472,x41473),f857(f285(x41472,x41471),x41474)),f857(f285(x41473,x41472),x41475)),f857(f285(x41473,x41471),f857(f857(f288(x41473,x41472,x41471),x41475),x41474)))
% 15.02/14.79 [4179]E(f857(f857(f857(f183(f920(x41791),f920(x41791)),x41792),f167(x41791)),f857(f857(f154(x41793,x41791),x41794),x41795)),f857(f857(f154(x41793,x41791),x41794),f857(f857(f857(f183(f920(x41793),f920(x41793)),x41792),f167(x41793)),x41795)))
% 15.02/14.79 [4180]E(f857(f857(f258(x41801,x41802,x41801,x41803),f857(f251(x41802,x41801),x41804)),x41805),f857(x41805,x41804))
% 15.02/14.79 [4205]E(f155(x42051,x42052,f857(f857(f154(x42053,x42051),x42054),x42055)),f155(x42053,f857(f72(x42051,a919,x42053,x42052),x42054),x42055))
% 15.02/14.79 [4268]E(f177(f926(x42681,x42682),f857(f72(x42682,a915,f926(x42681,x42682),x42683),f255(x42681,x42682)),f857(f857(f181(x42681,x42682),x42684),x42685)),f857(f857(f181(x42681,x42682),x42684),f177(x42682,x42683,x42685)))
% 15.02/14.79 [4273]E(f857(f309(x42731,x42732,f857(f857(f10(x42733,x42732,x42731),x42734),x42735)),f241(f927(x42731,a915))),f857(f309(x42733,x42732,x42734),f857(f309(x42731,x42733,x42735),f241(f927(x42731,a915)))))
% 15.02/14.79 [4286]E(f177(f926(x42861,x42862),f857(f72(x42861,a915,f926(x42861,x42862),x42863),f250(x42861,x42862)),f857(f857(f181(x42861,x42862),x42864),x42865)),f857(f857(f181(x42861,x42862),f177(x42861,x42863,x42864)),x42865))
% 15.02/14.79 [4307]E(f857(f857(f110(f927(x43071,a915)),f857(f310(x43071,x43072,x43073),f857(f857(f308(x43072),x43074),f189(f927(x43072,a915))))),f857(f310(x43071,x43072,x43073),x43075)),f857(f310(x43071,x43072,x43073),f857(f857(f308(x43072),x43074),x43075)))
% 15.02/14.79 [4362]E(f857(f857(f134(f926(x43621,x43622)),f857(f857(f154(x43622,f926(x43621,x43622)),f857(f251(x43621,x43622),x43623)),x43624)),f58(x43621,x43622,x43625,x43624)),f58(x43621,x43622,f857(f857(f151(x43621),x43623),x43625),x43624))
% 15.02/14.79 [4364]E(f857(f857(f154(x43641,x43642),x43643),f177(x43641,f857(f72(x43642,a915,x43641,x43644),x43643),x43645)),f177(x43642,x43644,f857(f857(f154(x43641,x43642),x43643),x43645)))
% 15.02/14.79 [4369]E(f857(f142(x43691,x43692,f857(f9(x43692,x43691,x43691),f857(f9(x43691,x43692,x43691),x43693)),x43694),f857(f168(x43692),f857(f168(x43692),x43695))),f857(f142(x43691,x43692,x43693,x43694),x43695))
% 15.02/14.79 [4472]P106(f857(f857(f234(f927(x44721,a915)),f857(f284(x44722,x44721,x44723),f857(f857(f101(f927(x44722,a915)),x44724),x44725))),f857(f857(f101(f927(x44721,a915)),f857(f284(x44722,x44721,x44723),x44724)),f857(f284(x44722,x44721,x44723),x44725))))
% 15.02/14.79 [4473]P106(f857(f857(f234(f927(x44731,a915)),f857(f309(x44732,x44731,x44733),f857(f857(f101(f927(x44732,a915)),x44734),x44735))),f857(f857(f101(f927(x44731,a915)),f857(f309(x44732,x44731,x44733),x44734)),f857(f309(x44732,x44731,x44733),x44735))))
% 15.02/14.79 [4573]E(f857(f255(x45731,x45732),f857(f257(x45733,x45731,x45732,x45732,x45734,f31(x45732)),x45735)),f857(f255(x45733,x45732),x45735))
% 15.02/14.79 [4574]E(f857(f250(x45741,x45742),f857(f257(x45741,x45741,x45743,x45742,f31(x45741),x45744),x45745)),f857(f250(x45741,x45743),x45745))
% 15.02/14.79 [4661]P25(x46611,x46612,f857(f857(f308(f918(x46611)),f857(f857(f857(f90(x46611),f857(f857(f9(x46611,f927(a917,a915),f927(a917,a915)),f857(f857(f10(f927(a917,f927(a915,a915)),f927(f927(a917,a915),f927(a917,a915)),x46611),f20(a917,a915,a915)),f857(f857(f10(f927(a917,a915),f927(a917,f927(a915,a915)),x46611),f857(f10(a915,f927(a915,a915),a917),a325)),x46613))),f857(f857(f10(a915,a915,a917),a321),x46614))),f29(x46614,x46615)),x46613)),f189(f927(f918(x46611),a915))))
% 15.02/14.79 [3764]E(f857(f857(f857(f857(f205(x37641),x37642),x37643),x37644),x37645),f193(x37641,x37642))
% 15.02/14.79 [3765]E(f857(f857(f857(f857(f209(x37651),x37652),x37653),x37654),x37655),f200(x37651,x37652))
% 15.02/14.79 [3810]E(f93(x38101,x38102,f857(f857(f857(f90(x38101),x38103),x38104),x38105)),f2(a919))
% 15.02/14.79 [4136]E(f857(f857(f38(x41361,f927(x41362,a915)),f857(f857(f308(x41361),x41363),x41364)),x41365),f857(f857(f101(f927(x41362,a915)),f857(x41365,x41363)),f857(f857(f38(x41361,f927(x41362,a915)),x41364),x41365)))
% 15.02/14.79 [4137]E(f857(f857(f39(x41371,f927(x41372,a915)),f857(f857(f308(x41371),x41373),x41374)),x41375),f857(f857(f110(f927(x41372,a915)),f857(x41375,x41373)),f857(f857(f39(x41371,f927(x41372,a915)),x41374),x41375)))
% 15.02/14.79 [4187]E(f857(f118(x41871,x41872,f857(x41873,x41874)),f857(f857(f9(x41871,a99,f921(x41872)),x41875),x41874)),f857(f198(x41871,x41872,x41873,x41875),x41874))
% 15.02/14.79 [4199]E(f857(f857(f110(f927(x41991,a915)),f857(f310(x41991,x41992,x41993),x41994)),f857(f310(x41991,x41992,x41993),x41995)),f857(f310(x41991,x41992,x41993),f857(f857(f110(f927(x41992,a915)),x41994),x41995)))
% 15.02/14.79 [4200]E(f857(f857(f3(f927(x42001,a915)),f857(f310(x42001,x42002,x42003),x42004)),f857(f310(x42001,x42002,x42003),x42005)),f857(f310(x42001,x42002,x42003),f857(f857(f3(f927(x42002,a915)),x42004),x42005)))
% 15.02/14.79 [4201]E(f857(f857(f101(f927(x42011,a915)),f857(f310(x42011,x42012,x42013),x42014)),f857(f310(x42011,x42012,x42013),x42015)),f857(f310(x42011,x42012,x42013),f857(f857(f101(f927(x42012,a915)),x42014),x42015)))
% 15.02/14.79 [4202]E(f857(f857(f110(f927(x42021,a915)),f857(f284(x42022,x42021,x42023),x42024)),f857(f284(x42022,x42021,x42023),x42025)),f857(f284(x42022,x42021,x42023),f857(f857(f110(f927(x42022,a915)),x42024),x42025)))
% 15.02/14.79 [4203]E(f857(f857(f110(f927(x42031,a915)),f857(f309(x42032,x42031,x42033),x42034)),f857(f309(x42032,x42031,x42033),x42035)),f857(f309(x42032,x42031,x42033),f857(f857(f110(f927(x42032,a915)),x42034),x42035)))
% 15.02/14.79 [4264]E(f857(f857(f159(x42641,f857(f857(f134(x42641),x42642),f857(f857(f151(x42641),x42643),x42644))),f857(f190(f920(x42641)),x42642)),x42645),f857(f857(f134(x42641),x42642),f857(f857(f151(x42641),x42645),x42644)))
% 15.02/14.79 [4271]E(f857(f857(f38(x42711,f927(x42712,a915)),x42713),f857(f857(f10(f927(x42712,a915),f927(x42712,a915),x42711),f857(f308(x42712),x42714)),x42715)),f857(f857(f308(x42712),x42714),f857(f857(f38(x42711,f927(x42712,a915)),x42713),x42715)))
% 15.02/14.79 [4424]E(f857(f857(f154(x44241,x44242),x44243),f857(f136(x44241,f857(f72(x44242,a915,x44241,x44244),x44243)),x44245)),f857(f136(x44242,x44244),f857(f857(f154(x44241,x44242),x44243),x44245)))
% 15.02/14.79 [4430]E(f857(f190(f920(x44301)),f857(f136(x44301,x44302),f857(f857(f154(x44303,x44301),x44304),x44305))),f857(f190(f920(x44303)),f857(f136(x44303,f857(f72(x44301,a915,x44303,x44302),x44304)),x44305)))
% 15.02/14.79 [4638]E(f857(f156(f920(f926(x46381,x46382)),x46382,f113(f926(x46381,x46382)),f857(f857(f9(x46382,f927(f920(x46382),f920(f926(x46381,x46382))),f927(f920(x46382),f920(f926(x46381,x46382)))),f857(f857(f10(f927(f920(f926(x46381,x46382)),f920(f926(x46381,x46382))),f927(f927(f920(x46382),f920(f926(x46381,x46382))),f927(f920(x46382),f920(f926(x46381,x46382)))),x46382),f10(f920(f926(x46381,x46382)),f920(f926(x46381,x46382)),f920(x46382))),f857(f857(f10(f926(x46381,x46382),f927(f920(f926(x46381,x46382)),f920(f926(x46381,x46382))),x46382),f151(f926(x46381,x46382))),f857(f251(x46381,x46382),x46383)))),f857(f181(x46381,x46382),x46384))),x46385),f857(f857(f181(x46381,x46382),f857(f857(f151(x46381),x46383),x46384)),x46385))
% 15.02/14.79 [4128]E(f857(f857(f159(x41281,f857(f857(f159(x41281,x41282),x41283),x41284)),x41283),x41285),f857(f857(f159(x41281,x41282),x41283),x41285))
% 15.02/14.79 [4181]E(f857(f283(x41811,x41812),f857(f857(f308(f926(x41811,x41812)),f857(f857(f251(x41811,x41812),x41813),x41814)),x41815)),f857(f857(f308(x41812),x41814),f857(f283(x41811,x41812),x41815)))
% 15.02/14.79 [4182]E(f857(f263(x41821,x41822),f857(f857(f308(f926(x41821,x41822)),f857(f857(f251(x41821,x41822),x41823),x41824)),x41825)),f857(f857(f308(x41821),x41823),f857(f263(x41821,x41822),x41825)))
% 15.02/14.79 [4229]E(f122(x42291,x42292,f857(x42293,x42294),f857(f857(f9(x42291,a99,f921(f923(x42292))),x42295),x42294)),f857(f196(x42291,x42292,x42293,x42295),x42294))
% 15.02/14.79 [4257]E(f857(f857(f110(f927(f926(x42571,x42572),a915)),f857(f857(f253(x42571,x42572),x42573),x42574)),f857(f857(f253(x42571,x42572),x42575),x42574)),f857(f857(f253(x42571,x42572),f857(f857(f110(f927(x42571,a915)),x42573),x42575)),x42574))
% 15.02/14.79 [4258]E(f857(f857(f3(f927(f926(x42581,x42582),a915)),f857(f857(f253(x42581,x42582),x42583),x42584)),f857(f857(f253(x42581,x42582),x42585),x42584)),f857(f857(f253(x42581,x42582),f857(f857(f3(f927(x42581,a915)),x42583),x42585)),x42584))
% 15.02/14.79 [4259]E(f857(f857(f101(f927(f926(x42591,x42592),a915)),f857(f857(f253(x42591,x42592),x42593),x42594)),f857(f857(f253(x42591,x42592),x42595),x42594)),f857(f857(f253(x42591,x42592),f857(f857(f101(f927(x42591,a915)),x42593),x42595)),x42594))
% 15.02/14.79 [4318]E(f857(f857(f101(f927(x43181,a915)),f857(f857(f38(x43182,f927(x43181,a915)),x43183),x43184)),f857(f857(f38(x43182,f927(x43181,a915)),x43185),x43184)),f857(f857(f38(x43182,f927(x43181,a915)),f857(f857(f110(f927(x43182,a915)),x43183),x43185)),x43184))
% 15.02/14.79 [4319]E(f857(f857(f110(f927(x43191,a915)),f857(f857(f39(x43192,f927(x43191,a915)),x43193),x43194)),f857(f857(f39(x43192,f927(x43191,a915)),x43195),x43194)),f857(f857(f39(x43192,f927(x43191,a915)),f857(f857(f110(f927(x43192,a915)),x43193),x43195)),x43194))
% 15.02/14.79 [4333]E(f857(f857(f38(x43331,f927(x43332,a915)),x43333),f857(f857(f10(f927(x43332,a915),f927(x43332,a915),x43331),f857(f110(f927(x43332,a915)),x43334)),x43335)),f857(f857(f110(f927(x43332,a915)),x43334),f857(f857(f38(x43331,f927(x43332,a915)),x43333),x43335)))
% 15.02/14.79 [4334]E(f857(f857(f39(x43341,f927(x43342,a915)),x43343),f857(f857(f10(f927(x43342,a915),f927(x43342,a915),x43341),f857(f3(f927(x43342,a915)),x43344)),x43345)),f857(f857(f3(f927(x43342,a915)),x43344),f857(f857(f38(x43341,f927(x43342,a915)),x43343),x43345)))
% 15.02/14.79 [4335]E(f857(f857(f39(x43351,f927(x43352,a915)),x43353),f857(f857(f10(f927(x43352,a915),f927(x43352,a915),x43351),f857(f101(f927(x43352,a915)),x43354)),x43355)),f857(f857(f101(f927(x43352,a915)),x43354),f857(f857(f39(x43351,f927(x43352,a915)),x43353),x43355)))
% 15.02/14.79 [4389]E(f185(f920(x43891),f857(f857(f151(x43891),x43892),x43893),f857(f857(f10(f920(x43891),f920(x43891),a919),f857(f151(x43891),x43894)),f857(f857(f9(a919,x43891,f920(x43891)),f159(x43891,x43893)),x43892)),x43895),f857(f857(f159(x43891,f857(f857(f151(x43891),x43894),x43893)),x43895),x43892))
% 15.02/14.79 [4393]E(f857(f857(f38(x43931,f927(f926(x43932,x43933),a915)),x43934),f857(f857(f10(f927(f926(x43933,x43932),a915),f927(f926(x43932,x43933),a915),x43931),f285(x43933,x43932)),x43935)),f857(f285(x43933,x43932),f857(f857(f38(x43931,f927(f926(x43933,x43932),a915)),x43934),x43935)))
% 15.02/14.79 [4394]E(f857(f857(f39(x43941,f927(f926(x43942,x43943),a915)),x43944),f857(f857(f10(f927(f926(x43943,x43942),a915),f927(f926(x43942,x43943),a915),x43941),f285(x43943,x43942)),x43945)),f857(f285(x43943,x43942),f857(f857(f39(x43941,f927(f926(x43943,x43942),a915)),x43944),x43945)))
% 15.02/14.79 [4495]P106(f857(f857(f234(f927(x44951,a915)),f857(f857(f3(f927(x44951,a915)),f857(f309(x44952,x44951,x44953),x44954)),f857(f309(x44952,x44951,x44953),x44955))),f857(f309(x44952,x44951,x44953),f857(f857(f3(f927(x44952,a915)),x44954),x44955))))
% 15.02/14.79 [4641]E(f857(f156(f920(f926(x46411,x46412)),x46411,f113(f926(x46411,x46412)),f857(f857(f9(x46411,f927(f920(x46411),f920(f926(x46411,x46412))),f927(f920(x46411),f920(f926(x46411,x46412)))),f857(f857(f10(f927(f920(f926(x46411,x46412)),f920(f926(x46411,x46412))),f927(f927(f920(x46411),f920(f926(x46411,x46412))),f927(f920(x46411),f920(f926(x46411,x46412)))),x46411),f10(f920(f926(x46411,x46412)),f920(f926(x46411,x46412)),f920(x46411))),f857(f857(f10(f926(x46411,x46412),f927(f920(f926(x46411,x46412)),f920(f926(x46411,x46412))),x46411),f151(f926(x46411,x46412))),f857(f857(f9(x46411,x46412,f926(x46411,x46412)),f251(x46411,x46412)),x46413)))),f857(f857(f9(f920(x46411),f920(x46412),f920(f926(x46411,x46412))),f181(x46411,x46412)),x46414))),x46415),f857(f857(f181(x46411,x46412),x46415),f857(f857(f151(x46412),x46413),x46414)))
% 15.02/14.79 [4358]E(f857(f857(f110(f927(x43581,a915)),f857(f284(x43582,x43581,x43583),x43584)),f857(f284(x43582,x43581,x43585),x43584)),f857(f284(x43582,x43581,f857(f857(f110(f927(f926(x43582,x43581),a915)),x43583),x43585)),x43584))
% 15.02/14.79 [4395]E(f857(f857(f134(f926(x43951,x43952)),f857(f857(f181(x43951,x43952),x43953),f857(f857(f175(x43952),f857(f190(f920(x43951)),x43953)),x43954))),f857(f857(f181(x43951,x43952),x43955),f857(f857(f138(x43952),f857(f190(f920(x43951)),x43953)),x43954))),f857(f857(f181(x43951,x43952),f857(f857(f134(x43951),x43953),x43955)),x43954))
% 15.02/14.79 [4498]E(f857(f857(f253(x44981,x44982),x44983),f857(f857(f20(x44981,f927(x44982,a915),f927(x44982,a915)),f857(f857(f10(f927(x44982,a915),f927(f927(x44982,a915),f927(x44982,a915)),x44981),f110(f927(x44982,a915))),x44984)),x44985)),f857(f857(f110(f927(f926(x44981,x44982),a915)),f857(f857(f253(x44981,x44982),x44983),x44984)),f857(f857(f253(x44981,x44982),x44983),x44985)))
% 15.02/14.79 [4499]E(f857(f857(f253(x44991,x44992),x44993),f857(f857(f20(x44991,f927(x44992,a915),f927(x44992,a915)),f857(f857(f10(f927(x44992,a915),f927(f927(x44992,a915),f927(x44992,a915)),x44991),f3(f927(x44992,a915))),x44994)),x44995)),f857(f857(f3(f927(f926(x44991,x44992),a915)),f857(f857(f253(x44991,x44992),x44993),x44994)),f857(f857(f253(x44991,x44992),x44993),x44995)))
% 15.02/14.79 [4500]E(f857(f857(f253(x45001,x45002),x45003),f857(f857(f20(x45001,f927(x45002,a915),f927(x45002,a915)),f857(f857(f10(f927(x45002,a915),f927(f927(x45002,a915),f927(x45002,a915)),x45001),f101(f927(x45002,a915))),x45004)),x45005)),f857(f857(f101(f927(f926(x45001,x45002),a915)),f857(f857(f253(x45001,x45002),x45003),x45004)),f857(f857(f253(x45001,x45002),x45003),x45005)))
% 15.02/14.79 [4504]E(f857(f857(f38(x45041,f927(x45042,a915)),x45043),f857(f857(f9(x45041,f927(x45042,a915),f927(x45042,a915)),f857(f857(f10(f927(x45042,a915),f927(f927(x45042,a915),f927(x45042,a915)),x45041),f110(f927(x45042,a915))),x45044)),x45045)),f857(f857(f110(f927(x45042,a915)),f857(f857(f38(x45041,f927(x45042,a915)),x45043),x45044)),x45045))
% 15.02/14.79 [4505]E(f857(f857(f39(x45051,f927(x45052,a915)),x45053),f857(f857(f9(x45051,f927(x45052,a915),f927(x45052,a915)),f857(f857(f10(f927(x45052,a915),f927(f927(x45052,a915),f927(x45052,a915)),x45051),f3(f927(x45052,a915))),x45054)),x45055)),f857(f857(f3(f927(x45052,a915)),f857(f857(f39(x45051,f927(x45052,a915)),x45053),x45054)),x45055))
% 15.02/14.79 [4506]E(f857(f857(f39(x45061,f927(x45062,a915)),x45063),f857(f857(f9(x45061,f927(x45062,a915),f927(x45062,a915)),f857(f857(f10(f927(x45062,a915),f927(f927(x45062,a915),f927(x45062,a915)),x45061),f101(f927(x45062,a915))),x45064)),x45065)),f857(f857(f101(f927(x45062,a915)),f857(f857(f39(x45061,f927(x45062,a915)),x45063),x45064)),x45065))
% 15.02/14.79 [4510]E(f857(f857(f38(x45101,f927(x45102,a915)),x45103),f857(f857(f20(x45101,f927(x45102,a915),f927(x45102,a915)),f857(f857(f10(f927(x45102,a915),f927(f927(x45102,a915),f927(x45102,a915)),x45101),f101(f927(x45102,a915))),x45104)),x45105)),f857(f857(f101(f927(x45102,a915)),f857(f857(f38(x45101,f927(x45102,a915)),x45103),x45104)),f857(f857(f38(x45101,f927(x45102,a915)),x45103),x45105)))
% 15.02/14.79 [4511]E(f857(f857(f39(x45111,f927(x45112,a915)),x45113),f857(f857(f20(x45111,f927(x45112,a915),f927(x45112,a915)),f857(f857(f10(f927(x45112,a915),f927(f927(x45112,a915),f927(x45112,a915)),x45111),f110(f927(x45112,a915))),x45114)),x45115)),f857(f857(f110(f927(x45112,a915)),f857(f857(f39(x45111,f927(x45112,a915)),x45113),x45114)),f857(f857(f39(x45111,f927(x45112,a915)),x45113),x45115)))
% 15.02/14.79 [4525]E(f857(f857(f38(x45251,f927(x45252,a915)),x45253),f857(f857(f20(x45251,f927(x45252,a915),f927(x45252,a915)),f857(f857(f10(f927(x45252,a915),f927(f927(x45252,a915),f927(x45252,a915)),x45251),f101(f927(x45252,a915))),x45254)),x45255)),f857(f857(f101(f927(x45252,a915)),f37(f927(x45252,a915),f857(f309(x45251,f927(x45252,a915),x45254),x45253))),f37(f927(x45252,a915),f857(f309(x45251,f927(x45252,a915),x45255),x45253))))
% 15.02/14.79 [4526]E(f857(f857(f39(x45261,f927(x45262,a915)),x45263),f857(f857(f20(x45261,f927(x45262,a915),f927(x45262,a915)),f857(f857(f10(f927(x45262,a915),f927(f927(x45262,a915),f927(x45262,a915)),x45261),f110(f927(x45262,a915))),x45264)),x45265)),f857(f857(f110(f927(x45262,a915)),f36(f927(x45262,a915),f857(f309(x45261,f927(x45262,a915),x45264),x45263))),f36(f927(x45262,a915),f857(f309(x45261,f927(x45262,a915),x45265),x45263))))
% 15.02/14.79 [4562]E(f857(f857(f138(x45621),f857(f190(f920(x45621)),f177(x45621,x45622,f857(f857(f154(x45623,x45621),x45624),x45625)))),f857(f857(f154(x45623,x45621),x45624),x45625)),f857(f857(f154(x45623,x45621),x45624),f857(f857(f138(x45623),f857(f190(f920(x45623)),f177(x45623,f857(f72(x45621,a915,x45623,x45622),x45624),x45625))),x45625)))
% 15.02/14.79 [4437]E(f857(f857(f134(f926(x44371,x44372)),f857(f857(f181(x44371,x44372),f857(f857(f175(x44371),f857(f190(f920(x44372)),x44373)),x44374)),x44373)),f857(f857(f181(x44371,x44372),f857(f857(f138(x44371),f857(f190(f920(x44372)),x44373)),x44374)),x44375)),f857(f857(f181(x44371,x44372),x44374),f857(f857(f134(x44372),x44373),x44375)))
% 15.02/14.79 [4553]E(f84(x45531,f857(f857(f20(x45531,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45531),a325),f857(f857(f9(x45531,f927(x45531,a915),a915),f328(x45531)),x45532))),f857(f857(f9(x45531,x45533,a915),f857(f857(f10(x45533,f927(x45533,a915),x45531),a324),x45534)),x45535))),f857(f76(x45531,x45533,x45532,x45534),x45535))
% 15.02/14.79 [4554]E(f89(x45541,f857(f857(f20(x45541,a915,a915),f857(f857(f10(a915,f927(a915,a915),x45541),a325),f857(f857(f9(x45541,f927(x45541,a915),a915),f328(x45541)),x45542))),f857(f857(f9(x45541,x45543,a915),f857(f857(f10(x45543,f927(x45543,a915),x45541),a324),x45544)),x45545))),f857(f91(x45541,x45543,x45542,x45544),x45545))
% 15.02/14.79 [4602]E(f857(f857(f85(a1,x46021),f857(f103(a1),f857(f857(f79(a1),x46022),a97))),f857(f857(f20(a1,x46021,x46021),f857(f857(f9(a1,x46021,f927(x46021,x46021)),f857(f857(f10(a915,f927(x46021,f927(x46021,x46021)),a1),f96(x46021)),a194)),f185(x46021,x46023,x46024,x46025))),f857(f857(f10(a919,x46021,a1),x46024),f857(f857(f9(a1,a919,a919),f857(f857(f10(a919,f927(a919,a919),a1),f79(a919)),a104)),x46025)))),f185(x46021,x46023,x46024,f857(f857(f79(a919),f857(f103(a919),x46022)),x46025)))
% 15.02/14.79 [4637]E(f857(f857(f85(a1,x46371),f857(f103(a1),f857(f857(f79(a1),x46372),a97))),f857(f857(f20(a1,x46371,x46371),f857(f857(f9(a1,x46371,f927(x46371,x46371)),f857(f857(f10(a915,f927(x46371,f927(x46371,x46371)),a1),f96(x46371)),a194)),f857(f184(x46371,x46373,x46374),x46375))),f857(f857(f20(a1,x46371,x46371),f857(f857(f10(a919,f927(x46371,x46371),a1),x46374),f857(f857(f9(a1,a919,a919),f857(f857(f10(a919,f927(a919,a919),a1),f79(a919)),a104)),x46375))),f857(f857(f10(a919,x46371,a1),f184(x46371,x46373,x46374)),f857(f857(f9(a1,a919,a919),f857(f857(f10(a919,f927(a919,a919),a1),f79(a919)),a104)),x46375))))),f857(f184(x46371,x46373,x46374),f857(f857(f79(a919),f857(f103(a919),x46372)),x46375)))
% 15.02/14.79 [4671]E(f857(f261(f926(x46711,x46712)),f857(f256(x46711,x46712,a915),f857(f857(f10(f927(x46712,f927(x46713,a915)),f927(x46712,a915),x46711),f857(f10(f927(x46713,a915),a915,x46712),f86(x46713))),f857(f857(f9(x46711,f927(x46712,f927(x46713,a915)),f927(x46712,f927(x46713,a915))),f857(f857(f10(f927(f927(x46713,a915),f927(x46713,a915)),f927(f927(x46712,f927(x46713,a915)),f927(x46712,f927(x46713,a915))),x46711),f10(f927(x46713,a915),f927(x46713,a915),x46712)),f857(f857(f10(f927(x46713,f927(a915,a915)),f927(f927(x46713,a915),f927(x46713,a915)),x46711),f20(x46713,a915,a915)),f857(f857(f10(f927(x46713,a915),f927(x46713,f927(a915,a915)),x46711),f857(f10(a915,f927(a915,a915),x46713),a325)),f857(f857(f9(x46711,f927(f926(x46711,x46713),a915),f927(x46713,a915)),f857(f857(f10(f927(x46713,f927(f927(f926(x46711,x46713),a915),a915)),f927(f927(f926(x46711,x46713),a915),f927(x46713,a915)),x46711),f9(x46713,f927(f926(x46711,x46713),a915),a915)),f857(f857(f10(f927(x46713,f926(x46711,x46713)),f927(x46713,f927(f927(f926(x46711,x46713),a915),a915)),x46711),f857(f10(f926(x46711,x46713),f927(f927(f926(x46711,x46713),a915),a915),x46713),f328(f926(x46711,x46713)))),f251(x46711,x46713)))),x46714))))),f857(f857(f9(x46712,f927(f926(x46713,x46712),a915),f927(x46713,a915)),f857(f857(f10(f927(x46713,f927(f927(f926(x46713,x46712),a915),a915)),f927(f927(f926(x46713,x46712),a915),f927(x46713,a915)),x46712),f9(x46713,f927(f926(x46713,x46712),a915),a915)),f857(f857(f10(f927(x46713,f926(x46713,x46712)),f927(x46713,f927(f927(f926(x46713,x46712),a915),a915)),x46712),f857(f10(f926(x46713,x46712),f927(f927(f926(x46713,x46712),a915),a915),x46713),f328(f926(x46713,x46712)))),f857(f9(x46713,x46712,f926(x46713,x46712)),f251(x46713,x46712))))),x46715))))),f857(f857(f288(x46711,x46713,x46712),x46714),x46715))
% 15.02/14.79 [4735]~E(f26(x47351,x47352,x47353),f27(x47354,x47355,x47356))
% 15.02/14.79 [4287]E(f225(x42871,x42872,x42873,x42874,f221(x42871,x42872,x42875,x42876)),f857(f857(x42874,x42875),x42876))
% 15.02/14.79 [4288]E(f226(x42881,x42882,x42883,x42884,f221(x42881,x42882,x42885,x42886)),f857(f857(x42884,x42885),x42886))
% 15.02/14.79 [4413]E(f127(x44131,x44132,x44133,x44134,f126(x44132,x44135,x44136)),f857(f857(f857(x44134,x44135),x44136),f127(x44131,x44132,x44133,x44134,x44136)))
% 15.02/14.79 [4432]E(f74(x44321,x44322,f74(x44321,x44322,x44323,x44324,x44325),x44324,x44326),f74(x44321,x44322,x44323,x44324,x44326))
% 15.02/14.79 [4541]E(f857(f72(f926(x45411,x45412),x45412,f926(x45413,x45414),f255(x45411,x45412)),f257(x45413,x45411,x45414,x45412,x45415,x45416)),f857(f72(x45414,x45412,f926(x45413,x45414),x45416),f255(x45413,x45414)))
% 15.02/14.79 [4542]E(f857(f72(f926(x45421,x45422),x45421,f926(x45423,x45424),f250(x45421,x45422)),f257(x45423,x45421,x45424,x45422,x45425,x45426)),f857(f72(x45423,x45421,f926(x45423,x45424),x45425),f250(x45423,x45424)))
% 15.02/14.79 [4157]E(f857(f857(f72(x41571,x41572,x41573,x41574),x41575),x41576),f857(x41574,f857(x41575,x41576)))
% 15.02/14.79 [4297]E(f224(x42971,f926(x42972,f921(x42972)),x42973,f857(f256(x42972,f921(x42972),x42971),x42974),f857(f135(x42972),f126(x42972,x42975,x42976))),f857(f857(x42974,x42975),x42976))
% 15.02/14.79 [4347]E(f227(x43471,x43472,x43473,x43474,f221(x43471,x43472,x43475,x43476)),f857(f857(f79(a919),f857(f857(f79(a919),f857(x43473,x43475)),f857(x43474,x43476))),f857(a112,f2(a919))))
% 15.02/14.79 [3955]E(f857(f857(f256(x39551,x39552,x39553),x39554),f857(f857(f251(x39551,x39552),x39555),x39556)),f857(f857(x39554,x39555),x39556))
% 15.02/14.79 [4015]E(f857(f857(f857(f10(x40151,x40152,x40153),x40154),x40155),x40156),f857(x40154,f857(x40155,x40156)))
% 15.02/14.79 [4016]E(f857(f857(f857(f9(x40161,x40162,x40163),x40164),x40165),x40166),f857(f857(x40164,x40166),x40165))
% 15.02/14.79 [4034]E(f857(f857(f857(f20(x40341,x40342,x40343),x40344),x40345),x40346),f857(f857(x40344,x40346),f857(x40345,x40346)))
% 15.02/14.79 [4057]E(f857(f156(x40571,x40572,x40573,x40574),f857(f857(f151(x40572),x40575),x40576)),f857(f857(x40574,x40575),x40576))
% 15.02/14.79 [4095]E(f169(f926(x40951,x40952),f857(f857(f188(a919),x40953),x40954),f857(f857(f251(x40951,x40952),x40955),x40956)),f857(f857(f181(x40951,x40952),f169(x40951,x40953,x40955)),f169(x40952,x40954,x40956)))
% 15.02/14.79 [4161]E(f857(f857(f151(f926(x41611,x41612)),f857(f857(f251(x41611,x41612),x41613),x41614)),f857(f857(f181(x41611,x41612),x41615),x41616)),f857(f857(f181(x41611,x41612),f857(f857(f151(x41611),x41613),x41615)),f857(f857(f151(x41612),x41614),x41616)))
% 15.02/14.79 [4162]E(f857(f857(f154(x41621,x41622),x41623),f857(f857(f159(x41621,x41624),x41625),x41626)),f857(f857(f159(x41622,f857(f857(f154(x41621,x41622),x41623),x41624)),x41625),f857(x41623,x41626)))
% 15.02/14.79 [4186]E(f857(f857(f254(x41861,x41862,x41863,x41864),x41865),x41866),f857(x41864,f857(f857(f251(x41861,x41862),x41865),x41866)))
% 15.02/14.79 [4204]E(f857(f142(x42041,x42042,x42043,x42044),f857(f857(f151(x42042),x42045),x42046)),f857(f142(x42041,x42042,x42043,f857(f857(x42043,x42044),x42045)),x42046))
% 15.02/14.79 [4230]E(f259(x42301,x42302,x42303,x42304,f857(f857(f251(x42301,x42302),x42305),x42306)),f857(f857(x42304,x42305),x42306))
% 15.02/14.79 [4311]E(f857(f857(f39(x43111,f927(x43112,a915)),x43113),f857(f72(x43114,f927(x43112,a915),x43111,x43115),x43116)),f857(f857(f39(x43114,f927(x43112,a915)),f857(f309(x43111,x43114,x43116),x43113)),x43115))
% 15.02/14.79 [4361]E(f857(f857(f154(x43611,x43612),x43613),f857(f857(f154(x43614,x43611),x43615),x43616)),f857(f857(f154(x43614,x43612),f857(f72(x43611,x43612,x43614,x43613),x43615)),x43616))
% 15.02/14.79 [4367]E(f857(f310(x43671,x43672,f857(f72(x43673,x43672,x43671,x43674),x43675)),x43676),f857(f310(x43671,x43673,x43675),f857(f310(x43673,x43672,x43674),x43676)))
% 15.02/14.79 [4368]E(f857(f309(x43681,x43682,f857(f72(x43683,x43682,x43681,x43684),x43685)),x43686),f857(f309(x43683,x43682,x43684),f857(f309(x43681,x43683,x43685),x43686)))
% 15.02/14.79 [4396]E(f857(f142(x43961,x43962,x43963,f857(f142(x43961,x43962,x43963,x43964),x43965)),x43966),f857(f142(x43961,x43962,x43963,x43964),f857(f857(f134(x43962),x43965),x43966)))
% 15.02/14.79 [4531]E(f857(f257(x45311,x45311,x45312,x45313,f31(x45311),x45314),f857(f857(f251(x45311,x45312),x45315),x45316)),f857(f857(f251(x45311,x45313),x45315),f857(x45314,x45316)))
% 15.02/14.79 [4532]E(f857(f257(x45321,x45322,x45323,x45323,x45324,f31(x45323)),f857(f857(f251(x45321,x45323),x45325),x45326)),f857(f857(f251(x45322,x45323),f857(x45324,x45325)),x45326))
% 15.02/14.79 [4620]E(f857(f857(f154(f926(x46201,x46202),f926(x46201,x46203)),f857(f256(x46201,x46202,f926(x46201,x46203)),f857(f857(f9(x46201,f927(x46202,x46203),f927(x46202,f926(x46201,x46203))),f857(f857(f10(f927(x46203,f926(x46201,x46203)),f927(f927(x46202,x46203),f927(x46202,f926(x46201,x46203))),x46201),f10(x46203,f926(x46201,x46203),x46202)),f251(x46201,x46203))),x46204))),f857(f857(f181(x46201,x46202),x46205),x46206)),f857(f857(f181(x46201,x46203),x46205),f857(f857(f154(x46202,x46203),x46204),x46206)))
% 15.02/14.79 [4020]E(f94(x40201,x40202,x40203,f857(f857(f857(f90(x40201),x40204),x40205),x40206)),f857(f857(f857(x40203,x40204),x40205),x40206))
% 15.02/14.79 [4021]E(f95(x40211,x40212,x40213,f857(f857(f857(f90(x40211),x40214),x40215),x40216)),f857(f857(f857(x40213,x40214),x40215),x40216))
% 15.02/14.79 [4214]E(f857(f857(f72(x42141,x42142,x42143,f857(f18(x42142,x42141),x42144)),x42145),x42146),x42144)
% 15.02/14.79 [4246]E(f857(f309(x42461,x42462,x42463),f857(f309(x42464,x42461,x42465),x42466)),f857(f309(x42464,x42462,f857(f857(f10(x42461,x42462,x42464),x42463),x42465)),x42466))
% 15.02/14.79 [4252]E(f857(f857(f38(x42521,f927(x42522,a915)),f857(f309(x42523,x42521,x42524),x42525)),x42526),f857(f857(f38(x42523,f927(x42522,a915)),x42525),f857(f857(f10(x42521,f927(x42522,a915),x42523),x42526),x42524)))
% 15.02/14.79 [4253]E(f857(f857(f39(x42531,f927(x42532,a915)),f857(f309(x42533,x42531,x42534),x42535)),x42536),f857(f857(f39(x42533,f927(x42532,a915)),x42535),f857(f857(f10(x42531,f927(x42532,a915),x42533),x42536),x42534)))
% 15.02/14.79 [4254]E(f857(f857(f38(x42541,f927(x42542,a915)),x42543),f857(f857(f10(x42544,f927(x42542,a915),x42541),x42545),x42546)),f857(f857(f38(x42544,f927(x42542,a915)),f857(f309(x42541,x42544,x42546),x42543)),x42545))
% 15.02/14.79 [4255]E(f857(f857(f39(x42551,f927(x42552,a915)),x42553),f857(f857(f10(x42554,f927(x42552,a915),x42551),x42555),x42556)),f857(f857(f39(x42554,f927(x42552,a915)),f857(f309(x42551,x42554,x42556),x42553)),x42555))
% 15.02/14.79 [4313]E(f857(f857(f38(x43131,f927(x43132,a915)),x43133),f857(f857(f10(f927(x43134,a915),f927(x43132,a915),x43131),f310(x43132,x43134,x43135)),x43136)),f857(f310(x43132,x43134,x43135),f857(f857(f38(x43131,f927(x43134,a915)),x43133),x43136)))
% 15.02/14.79 [4314]E(f857(f857(f39(x43141,f927(x43142,a915)),x43143),f857(f857(f10(f927(x43144,a915),f927(x43142,a915),x43141),f310(x43142,x43144,x43145)),x43146)),f857(f310(x43142,x43144,x43145),f857(f857(f39(x43141,f927(x43144,a915)),x43143),x43146)))
% 15.02/14.79 [4315]E(f857(f857(f39(x43151,f927(x43152,a915)),x43153),f857(f857(f10(f927(x43154,a915),f927(x43152,a915),x43151),f284(x43154,x43152,x43155)),x43156)),f857(f284(x43154,x43152,x43155),f857(f857(f39(x43151,f927(x43154,a915)),x43153),x43156)))
% 15.02/14.79 [4316]E(f857(f857(f39(x43161,f927(x43162,a915)),x43163),f857(f857(f10(f927(x43164,a915),f927(x43162,a915),x43161),f309(x43164,x43162,x43165)),x43166)),f857(f309(x43164,x43162,x43165),f857(f857(f39(x43161,f927(x43164,a915)),x43163),x43166)))
% 15.02/14.79 [4401]E(f857(f142(x44011,x44012,f857(f9(x44012,x44011,x44011),x44013),x44014),f857(f168(x44012),f857(f857(f151(x44012),x44015),x44016))),f857(f857(x44013,x44015),f857(f142(x44011,x44012,f857(f9(x44012,x44011,x44011),x44013),x44014),f857(f168(x44012),x44016))))
% 15.02/14.79 [4459]E(f857(f857(f20(f926(x44591,x44592),x44592,x44593),f857(f857(f10(x44594,f927(x44592,x44593),f926(x44591,x44592)),x44595),f857(f857(f10(x44591,x44594,f926(x44591,x44592)),x44596),f250(x44591,x44592)))),f255(x44591,x44592)),f857(f256(x44591,x44592,x44593),f857(f857(f10(x44594,f927(x44592,x44593),x44591),x44595),x44596)))
% 15.02/14.79 [4466]E(f857(f142(x44661,x44662,f857(f9(x44662,x44661,x44661),x44663),f857(f142(x44661,x44662,f857(f9(x44662,x44661,x44661),x44663),x44664),f857(f168(x44662),x44665))),f857(f168(x44662),x44666)),f857(f142(x44661,x44662,f857(f9(x44662,x44661,x44661),x44663),x44664),f857(f168(x44662),f857(f857(f134(x44662),x44666),x44665))))
% 15.02/14.79 [4468]E(f857(f857(f154(f926(x44681,x44682),f926(x44683,x44682)),f857(f256(x44681,x44682,f926(x44683,x44682)),f857(f857(f10(x44683,f927(x44682,f926(x44683,x44682)),x44681),f251(x44683,x44682)),x44684))),f857(f857(f181(x44681,x44682),x44685),x44686)),f857(f857(f181(x44683,x44682),f857(f857(f154(x44681,x44683),x44684),x44685)),x44686))
% 15.02/14.79 [4513]P106(f857(f857(f234(f927(x45131,a915)),f857(f284(x45132,x45131,x45133),f857(f857(f38(x45134,f927(x45132,a915)),x45135),x45136))),f857(f857(f38(x45134,f927(x45131,a915)),x45135),f857(f857(f10(f927(x45132,a915),f927(x45131,a915),x45134),f284(x45132,x45131,x45133)),x45136))))
% 15.02/14.79 [4326]E(f857(f857(f181(x43261,x43262),f857(f857(f159(x43261,x43263),x43264),f857(f250(x43261,x43262),x43265))),f857(f857(f159(x43262,x43266),x43264),f857(f255(x43261,x43262),x43265))),f857(f857(f159(f926(x43261,x43262),f857(f857(f181(x43261,x43262),x43263),x43266)),x43264),x43265))
% 15.02/14.79 [4384]E(f857(f857(f110(f927(f926(x43841,x43842),a915)),f857(f857(f288(x43841,x43843,x43842),x43844),x43845)),f857(f857(f288(x43841,x43843,x43842),x43844),x43846)),f857(f857(f288(x43841,x43843,x43842),x43844),f857(f857(f110(f927(f926(x43843,x43842),a915)),x43845),x43846)))
% 15.02/14.79 [4478]E(f857(f857(f308(f926(x44781,x44782)),f857(f857(f251(x44781,x44782),x44783),x44784)),f857(f857(f110(f927(f926(x44781,x44782),a915)),f857(f857(f253(x44781,x44782),x44785),f857(f18(f927(x44782,a915),x44781),f857(f857(f308(x44782),x44784),x44786)))),f857(f857(f253(x44781,x44782),f857(f857(f308(x44781),x44783),x44785)),f857(f18(f927(x44782,a915),x44781),x44786)))),f857(f857(f253(x44781,x44782),f857(f857(f308(x44781),x44783),x44785)),f857(f18(f927(x44782,a915),x44781),f857(f857(f308(x44782),x44784),x44786))))
% 15.02/14.79 [4558]E(f857(f857(f101(f927(x45581,a915)),f857(f310(x45581,x45582,f857(f72(f926(x45582,x45583),x45582,x45581,f250(x45582,x45583)),x45584)),x45585)),f857(f310(x45581,x45583,f857(f72(f926(x45582,x45583),x45583,x45581,f255(x45582,x45583)),x45584)),x45586)),f857(f310(x45581,f926(x45582,x45583),x45584),f857(f857(f253(x45582,x45583),x45585),f857(f18(f927(x45583,a915),x45582),x45586))))
% 15.02/14.79 [4407]E(f857(f857(f110(f927(f926(x44071,x44072),a915)),f857(f857(f288(x44071,x44073,x44072),x44074),x44075)),f857(f857(f288(x44071,x44073,x44072),x44076),x44075)),f857(f857(f288(x44071,x44073,x44072),f857(f857(f110(f927(f926(x44071,x44073),a915)),x44074),x44076)),x44075))
% 15.02/14.79 [4539]E(f857(f857(f38(x45391,f927(x45392,a915)),x45393),f857(f857(f9(x45391,f927(x45394,f927(x45392,a915)),f927(x45392,a915)),f857(f857(f10(f927(x45394,a915),f927(f927(x45394,f927(x45392,a915)),f927(x45392,a915)),x45391),f38(x45394,f927(x45392,a915))),x45395)),x45396)),f857(f857(f38(x45394,f927(x45392,a915)),f857(f857(f39(x45391,f927(x45394,a915)),x45393),x45395)),x45396))
% 15.02/14.79 [4540]E(f857(f857(f39(x45401,f927(x45402,a915)),x45403),f857(f857(f9(x45401,f927(x45404,f927(x45402,a915)),f927(x45402,a915)),f857(f857(f10(f927(x45404,a915),f927(f927(x45404,f927(x45402,a915)),f927(x45402,a915)),x45401),f39(x45404,f927(x45402,a915))),x45405)),x45406)),f857(f857(f39(x45404,f927(x45402,a915)),f857(f857(f39(x45401,f927(x45404,a915)),x45403),x45405)),x45406))
% 15.02/14.79 [4592]E(f857(f256(x45921,x45922,f926(x45923,x45924)),f857(f857(f9(x45921,f927(x45922,x45924),f927(x45922,f926(x45923,x45924))),f857(f857(f10(f927(x45924,f926(x45923,x45924)),f927(f927(x45922,x45924),f927(x45922,f926(x45923,x45924))),x45921),f10(x45924,f926(x45923,x45924),x45922)),f857(f857(f10(x45923,f927(x45924,f926(x45923,x45924)),x45921),f251(x45923,x45924)),x45925))),x45926)),f257(x45921,x45923,x45922,x45924,x45925,x45926))
% 15.02/14.79 [4615]E(f857(f309(x46151,x46152,f857(f857(f20(x46151,x46152,x46152),f857(f857(f20(x46151,x46152,f927(x46152,x46152)),f857(f857(f10(a915,f927(x46152,f927(x46152,x46152)),x46151),f96(x46152)),x46153)),x46154)),x46155)),x46156),f857(f857(f110(f927(x46152,a915)),f857(f309(x46151,x46152,x46154),f857(f857(f101(f927(x46151,a915)),x46156),f857(f261(x46151),x46153)))),f857(f309(x46151,x46152,x46155),f857(f857(f101(f927(x46151,a915)),x46156),f857(f261(x46151),f857(f857(f10(a915,a915,x46151),a321),x46153))))))
% 15.02/14.79 [4627]E(f857(f309(x46271,f926(x46272,x46273),f857(f857(f20(x46271,x46273,f926(x46272,x46273)),f857(f857(f10(x46272,f927(x46273,f926(x46272,x46273)),x46271),f251(x46272,x46273)),x46274)),x46275)),x46276),f857(f857(f253(x46272,x46273),f857(f309(x46271,x46272,x46274),x46276)),f857(f857(f10(f927(x46271,a915),f927(x46273,a915),x46272),f309(x46271,x46273,x46275)),f857(f857(f9(x46272,f927(x46271,a915),f927(x46271,a915)),f857(f857(f10(f927(x46271,a915),f927(f927(x46271,a915),f927(x46271,a915)),x46272),f101(f927(x46271,a915))),f857(f857(f10(f927(x46272,a915),f927(x46271,a915),x46272),f310(x46271,x46272,x46274)),f857(f857(f9(x46272,f927(x46272,a915),f927(x46272,a915)),f308(x46272)),f189(f927(x46272,a915)))))),x46276))))
% 15.02/14.79 [4652]E(f245(x46521,x46522,x46523,x46524,x46525,x46526),f857(x46524,f857(f261(x46521),f857(f857(f10(f927(f927(x46523,x46521),a915),a915,x46521),f86(f927(x46523,x46521))),f857(f857(f10(f927(f927(x46523,x46521),a915),f927(f927(x46523,x46521),a915),x46521),f857(f20(f927(x46523,x46521),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x46523,x46521)),a325),f857(f857(f9(f927(x46523,x46521),f927(f927(x46523,x46521),a915),a915),f328(f927(x46523,x46521))),x46525)))),f857(f857(f9(x46521,f927(f927(x46523,x46521),x46521),f927(f927(x46523,x46521),a915)),f857(f857(f10(f927(x46521,a915),f927(f927(f927(x46523,x46521),x46521),f927(f927(x46523,x46521),a915)),x46521),f10(x46521,a915,f927(x46523,x46521))),a324)),f857(f857(f9(f927(x46523,x46521),x46523,x46521),f7(f927(x46523,x46521))),x46526)))))))
% 15.02/14.79 [4440]E(f857(f72(x44401,x44402,x44403,x44404),f74(x44403,x44401,x44405,x44406,x44407)),f74(x44403,x44402,f857(f72(x44401,x44402,x44403,x44404),x44405),x44406,f857(x44404,x44407)))
% 15.02/14.79 [4575]E(f857(f255(x45751,x45752),f857(f257(x45753,x45751,x45754,x45752,x45755,x45756),x45757)),f857(x45756,f857(f255(x45753,x45754),x45757)))
% 15.02/14.79 [4576]E(f857(f250(x45761,x45762),f857(f257(x45763,x45761,x45764,x45762,x45765,x45766),x45767)),f857(x45765,f857(f250(x45763,x45764),x45767)))
% 15.02/14.79 [4289]E(f857(f857(f181(x42891,x42892),f857(f857(f159(x42891,x42893),x42894),x42895)),f857(f857(f159(x42892,x42896),x42894),x42897)),f857(f857(f159(f926(x42891,x42892),f857(f857(f181(x42891,x42892),x42893),x42896)),x42894),f857(f857(f251(x42891,x42892),x42895),x42897)))
% 15.02/14.79 [4356]E(f857(f857(f857(f258(x43561,x43562,x43563,x43564),x43565),x43566),x43567),f857(f857(f256(x43562,x43563,x43564),x43566),f857(x43565,x43567)))
% 15.02/14.79 [4366]E(f857(f857(f857(f258(x43661,x43662,x43663,x43664),x43665),x43666),x43667),f857(f857(x43666,f857(f250(x43662,x43663),f857(x43665,x43667))),f857(f255(x43662,x43663),f857(x43665,x43667))))
% 15.02/14.79 [4418]E(f857(f72(x44181,x44182,x44183,x44184),f857(f72(x44185,x44181,x44183,x44186),x44187)),f857(f72(x44185,x44182,x44183,f857(f72(x44181,x44182,x44185,x44184),x44186)),x44187))
% 15.02/14.79 [4596]E(f857(f257(x45961,x45962,x45963,x45963,x45964,f31(x45963)),f857(f257(x45961,x45961,x45965,x45963,f31(x45961),x45966),x45967)),f857(f857(f251(x45962,x45963),f857(x45964,f857(f250(x45961,x45965),x45967))),f857(x45966,f857(f255(x45961,x45965),x45967))))
% 15.02/14.79 [4597]E(f857(f257(x45971,x45971,x45972,x45973,f31(x45971),x45974),f857(f257(x45975,x45971,x45972,x45972,x45976,f31(x45972)),x45977)),f857(f857(f251(x45971,x45973),f857(x45976,f857(f250(x45975,x45972),x45977))),f857(x45974,f857(f255(x45975,x45972),x45977))))
% 15.02/14.79 [4613]E(f857(f257(x46131,x46132,x46133,x46133,x46134,f31(x46133)),f857(f257(x46135,x46131,x46133,x46133,x46136,f31(x46133)),x46137)),f857(f257(x46135,x46132,x46133,x46133,f857(f72(x46131,x46132,x46135,x46134),x46136),f31(x46133)),x46137))
% 15.02/14.79 [4614]E(f857(f257(x46141,x46141,x46142,x46143,f31(x46141),x46144),f857(f257(x46141,x46141,x46145,x46142,f31(x46141),x46146),x46147)),f857(f257(x46141,x46141,x46145,x46143,f31(x46141),f857(f72(x46142,x46143,x46145,x46144),x46146)),x46147))
% 15.02/14.79 [4624]E(f857(f257(x46241,x46242,x46243,x46243,x46244,f31(x46243)),f857(f257(x46241,x46241,x46245,x46243,f31(x46241),x46246),x46247)),f857(f257(x46242,x46242,x46245,x46243,f31(x46242),x46246),f857(f257(x46241,x46242,x46245,x46245,x46244,f31(x46245)),x46247)))
% 15.02/14.79 [4323]E(f857(f857(f288(x43231,x43232,x43233),f857(f857(f288(x43231,x43234,x43232),x43235),x43236)),x43237),f857(f857(f288(x43231,x43234,x43233),x43235),f857(f857(f288(x43234,x43232,x43233),x43236),x43237)))
% 15.02/14.79 [4390]E(f857(f857(f256(x43901,x43902,x43903),f857(f72(x43904,f927(x43902,x43903),x43901,x43905),x43906)),x43907),f857(f857(x43905,f857(x43906,f857(f250(x43901,x43902),x43907))),f857(f255(x43901,x43902),x43907)))
% 15.02/14.79 [4471]E(f857(f142(x44711,x44712,f857(f9(x44712,x44711,x44711),x44713),x44714),f857(f168(x44712),f857(f857(f154(x44715,x44712),x44716),x44717))),f857(f142(x44711,x44715,f857(f9(x44715,x44711,x44711),f857(f72(x44712,f927(x44711,x44711),x44715,x44713),x44716)),x44714),f857(f168(x44715),x44717)))
% 15.02/14.79 [4419]E(f857(f857(f39(x44191,f927(f926(x44192,x44193),a915)),x44194),f857(f857(f10(f927(f926(x44195,x44193),a915),f927(f926(x44192,x44193),a915),x44191),f857(f288(x44192,x44195,x44193),x44196)),x44197)),f857(f857(f288(x44192,x44195,x44193),x44196),f857(f857(f39(x44191,f927(f926(x44195,x44193),a915)),x44194),x44197)))
% 15.02/14.79 [4563]E(f857(f857(f39(x45631,f927(f926(x45632,x45633),a915)),x45634),f857(f857(f9(x45631,f927(f926(x45635,x45633),a915),f927(f926(x45632,x45633),a915)),f857(f857(f10(f927(f926(x45632,x45635),a915),f927(f927(f926(x45635,x45633),a915),f927(f926(x45632,x45633),a915)),x45631),f288(x45632,x45635,x45633)),x45636)),x45637)),f857(f857(f288(x45632,x45635,x45633),f857(f857(f39(x45631,f927(f926(x45632,x45635),a915)),x45634),x45636)),x45637))
% 15.02/14.79 [4564]E(f857(f142(x45641,x45642,f857(f857(f9(x45641,f927(x45642,x45643),f927(x45642,x45641)),f857(f857(f10(f927(x45643,x45641),f927(f927(x45642,x45643),f927(x45642,x45641)),x45641),f10(x45643,x45641,x45642)),x45644)),x45645),x45646),x45647),f857(f142(x45641,x45643,x45644,x45646),f857(f857(f154(x45642,x45643),x45645),x45647)))
% 15.02/14.79 [4625]E(f857(f857(f38(x46251,f927(x46252,a915)),x46253),f857(f857(f10(f927(x46254,f927(x46252,a915)),f927(x46252,a915),x46251),f857(f38(x46254,f927(x46252,a915)),x46255)),f857(f857(f9(x46251,f927(x46254,f927(x46252,a915)),f927(x46254,f927(x46252,a915))),f857(f857(f10(f927(f927(x46252,a915),f927(x46252,a915)),f927(f927(x46254,f927(x46252,a915)),f927(x46254,f927(x46252,a915))),x46251),f10(f927(x46252,a915),f927(x46252,a915),x46254)),f857(f857(f10(f927(x46252,a915),f927(f927(x46252,a915),f927(x46252,a915)),x46251),f110(f927(x46252,a915))),x46256))),x46257))),f857(f857(f110(f927(x46252,a915)),f857(f857(f38(x46251,f927(x46252,a915)),x46253),x46256)),f857(f857(f38(x46254,f927(x46252,a915)),x46255),x46257)))
% 15.02/14.79 [4626]E(f857(f857(f39(x46261,f927(x46262,a915)),x46263),f857(f857(f10(f927(x46264,f927(x46262,a915)),f927(x46262,a915),x46261),f857(f39(x46264,f927(x46262,a915)),x46265)),f857(f857(f9(x46261,f927(x46264,f927(x46262,a915)),f927(x46264,f927(x46262,a915))),f857(f857(f10(f927(f927(x46262,a915),f927(x46262,a915)),f927(f927(x46264,f927(x46262,a915)),f927(x46264,f927(x46262,a915))),x46261),f10(f927(x46262,a915),f927(x46262,a915),x46264)),f857(f857(f10(f927(x46262,a915),f927(f927(x46262,a915),f927(x46262,a915)),x46261),f101(f927(x46262,a915))),x46266))),x46267))),f857(f857(f101(f927(x46262,a915)),f857(f857(f39(x46261,f927(x46262,a915)),x46263),x46266)),f857(f857(f39(x46264,f927(x46262,a915)),x46265),x46267)))
% 15.02/14.79 [4618]E(f198(x46181,x46182,f857(f857(f857(x46183,x46184),x46185),x46186),f857(f857(f9(x46181,f926(a99,a99),f927(a99,f921(x46182))),f857(f857(f9(x46181,a99,f927(f926(a99,a99),f927(a99,f921(x46182)))),f857(f857(f9(x46181,a99,f927(a99,f927(f926(a99,a99),f927(a99,f921(x46182))))),x46187),x46184)),x46185)),x46186)),f857(f857(f857(f210(x46181,x46182,x46183,x46187),x46184),x46185),x46186))
% 15.02/14.79 [4632]E(f199(x46321,x46322,f857(f857(f857(x46323,x46324),x46325),x46326),f857(f857(f9(x46321,f926(a99,a99),f927(a99,f921(x46322))),f857(f857(f9(x46321,a99,f927(f926(a99,a99),f927(a99,f921(x46322)))),f857(f857(f9(x46321,a99,f927(a99,f927(f926(a99,a99),f927(a99,f921(x46322))))),x46327),x46324)),x46325)),x46326)),f212(x46321,x46322,x46323,x46327,x46324,x46325,x46326))
% 15.02/14.79 [4623]E(f196(x46231,x46232,f857(f857(f857(x46233,x46234),x46235),x46236),f857(f857(f9(x46231,f926(a99,a99),f927(a99,f921(f923(x46232)))),f857(f857(f9(x46231,a99,f927(f926(a99,a99),f927(a99,f921(f923(x46232))))),f857(f857(f9(x46231,a99,f927(a99,f927(f926(a99,a99),f927(a99,f921(f923(x46232)))))),x46237),x46234)),x46235)),x46236)),f857(f857(f857(f206(x46231,x46232,x46233,x46237),x46234),x46235),x46236))
% 15.02/14.79 [4634]E(f197(x46341,x46342,f857(f857(f857(x46343,x46344),x46345),x46346),f857(f857(f9(x46341,f926(a99,a99),f927(a99,f921(f923(x46342)))),f857(f857(f9(x46341,a99,f927(f926(a99,a99),f927(a99,f921(f923(x46342))))),f857(f857(f9(x46341,a99,f927(a99,f927(f926(a99,a99),f927(a99,f921(f923(x46342)))))),x46347),x46344)),x46345)),x46346)),f208(x46341,x46342,x46343,x46347,x46344,x46345,x46346))
% 15.02/14.79 [4533]E(f857(f257(x45331,x45332,x45333,x45334,x45335,x45336),f857(f857(f251(x45331,x45333),x45337),x45338)),f857(f857(f251(x45332,x45334),f857(x45335,x45337)),f857(x45336,x45338)))
% 15.02/14.79 [4636]E(f857(f857(f154(f926(x46361,x46362),f926(x46363,x46364)),f857(f256(x46361,x46362,f926(x46363,x46364)),f857(f857(f9(x46361,f927(x46362,x46364),f927(x46362,f926(x46363,x46364))),f857(f857(f10(f927(x46364,f926(x46363,x46364)),f927(f927(x46362,x46364),f927(x46362,f926(x46363,x46364))),x46361),f10(x46364,f926(x46363,x46364),x46362)),f857(f857(f10(x46363,f927(x46364,f926(x46363,x46364)),x46361),f251(x46363,x46364)),x46365))),x46366))),f857(f857(f181(x46361,x46362),x46367),x46368)),f857(f857(f181(x46363,x46364),f857(f857(f154(x46361,x46363),x46365),x46367)),f857(f857(f154(x46362,x46364),x46366),x46368)))
% 15.02/14.79 [4639]E(f857(f857(f154(f926(x46391,x46392),x46393),f857(f256(x46391,x46392,x46393),f857(f857(f10(f927(x46392,f926(x46391,x46394)),f927(x46392,x46393),x46391),f857(f10(f926(x46391,x46394),x46393,x46392),x46395)),f857(f857(f9(x46391,f927(x46392,x46394),f927(x46392,f926(x46391,x46394))),f857(f857(f10(f927(x46394,f926(x46391,x46394)),f927(f927(x46392,x46394),f927(x46392,f926(x46391,x46394))),x46391),f10(x46394,f926(x46391,x46394),x46392)),f251(x46391,x46394))),x46396)))),f857(f857(f181(x46391,x46392),x46397),x46398)),f857(f857(f154(f926(x46391,x46394),x46393),x46395),f857(f857(f181(x46391,x46394),x46397),f857(f857(f154(x46392,x46394),x46396),x46398))))
% 15.02/14.79 [4567]E(f857(f857(f154(f926(x45671,x45672),x45673),f857(f256(x45671,x45672,x45673),f857(f857(f10(f927(x45672,f926(x45674,x45672)),f927(x45672,x45673),x45671),f857(f10(f926(x45674,x45672),x45673,x45672),x45675)),f857(f857(f10(x45674,f927(x45672,f926(x45674,x45672)),x45671),f251(x45674,x45672)),x45676)))),f857(f857(f181(x45671,x45672),x45677),x45678)),f857(f857(f154(f926(x45674,x45672),x45673),x45675),f857(f857(f181(x45674,x45672),f857(f857(f154(x45671,x45674),x45676),x45677)),x45678)))
% 15.02/14.79 [4524]E(f857(f857(f256(x45241,x45242,x45243),f857(f857(f10(f927(x45242,f926(x45244,x45245)),f927(x45242,x45243),x45241),f857(f10(f926(x45244,x45245),x45243,x45242),f857(f256(x45244,x45245,x45243),x45246))),x45247)),x45248),f857(f857(f256(x45244,x45245,x45243),x45246),f857(f857(f256(x45241,x45242,f926(x45244,x45245)),x45247),x45248)))
% 15.02/14.79 [4640]E(f857(f857(f39(f926(x46401,x46402),f927(f926(x46403,x46404),a915)),f857(f857(f253(x46401,x46402),x46405),f857(f18(f927(x46402,a915),x46401),x46406))),f857(f256(x46401,x46402,f927(f926(x46403,x46404),a915)),f857(f857(f9(x46401,f927(x46402,f927(x46403,f927(x46404,a915))),f927(x46402,f927(f926(x46403,x46404),a915))),f857(f857(f10(f927(f927(x46403,f927(x46404,a915)),f927(f926(x46403,x46404),a915)),f927(f927(x46402,f927(x46403,f927(x46404,a915))),f927(x46402,f927(f926(x46403,x46404),a915))),x46401),f10(f927(x46403,f927(x46404,a915)),f927(f926(x46403,x46404),a915),x46402)),f857(f857(f10(f927(x46403,a915),f927(f927(x46403,f927(x46404,a915)),f927(f926(x46403,x46404),a915)),x46401),f253(x46403,x46404)),x46407))),f857(f857(f10(f927(x46404,a915),f927(x46403,f927(x46404,a915)),x46402),f18(f927(x46404,a915),x46403)),x46408)))),f857(f857(f253(x46403,x46404),f857(f857(f39(x46401,f927(x46403,a915)),x46405),x46407)),f857(f18(f927(x46404,a915),x46403),f857(f857(f39(x46402,f927(x46404,a915)),x46406),x46408))))
% 15.02/14.79 [4581]E(f857(f857(f258(x45811,x45812,x45813,x45814),f857(f857(f258(x45811,x45815,x45816,f926(x45812,x45813)),x45817),x45818)),x45819),f857(f857(f258(x45811,x45815,x45816,x45814),x45817),f857(f857(f9(x45815,f927(x45812,f927(x45813,x45814)),f927(x45816,x45814)),f857(f857(f10(f927(x45816,f926(x45812,x45813)),f927(f927(x45812,f927(x45813,x45814)),f927(x45816,x45814)),x45815),f258(x45816,x45812,x45813,x45814)),x45818)),x45819)))
% 15.02/14.79 [4610]E(f857(f72(f926(x46101,x46102),f926(x46103,x46104),f926(x46105,x46106),f257(x46101,x46103,x46102,x46104,x46107,x46108)),f257(x46105,x46101,x46106,x46102,x46109,x461010)),f257(x46105,x46103,x46106,x46104,f857(f72(x46101,x46103,x46105,x46107),x46109),f857(f72(x46102,x46104,x46106,x46108),x461010)))
% 15.02/14.79 [4616]E(f857(f257(x46161,x46162,x46163,x46164,x46165,x46166),f857(f257(x46167,x46161,x46168,x46163,x46169,x461610),x461611)),f857(f257(x46167,x46162,x46168,x46164,f857(f72(x46161,x46162,x46167,x46165),x46169),f857(f72(x46163,x46164,x46168,x46166),x461610)),x461611))
% 15.02/14.79 [4764]~P5(x47641)+P5(f923(x47641))
% 15.02/14.79 [4765]~P64(x47651)+P64(f923(x47651))
% 15.02/14.79 [4766]~P104(x47661)+P104(f920(x47661))
% 15.02/14.79 [4769]~P145(x47691)+~E(f77(x47691),f2(x47691))
% 15.02/14.79 [4771]~E(x47711,f2(a99))+E(f857(a24,x47711),f2(a1))
% 15.02/14.79 [4772]~E(x47721,f2(a1))+E(f81(a1,x47721),f2(a1))
% 15.02/14.79 [4778]~P146(x47781)+P29(x47781,f2(x47781))
% 15.02/14.79 [4780]~P109(x47801)+P14(x47801,f113(x47801))
% 15.02/14.79 [4789]P106(x47891)+P106(f857(a321,x47891))
% 15.02/14.79 [4843]~P146(x48431)+~P29(x48431,f77(x48431))
% 15.02/14.79 [4884]~P106(x48841)+~P106(f857(a321,x48841))
% 15.02/14.79 [4905]E(f857(a104,x49051),f2(a919))+~P106(f857(a194,x49051))
% 15.02/14.79 [4971]~P70(x49711)+P17(x49711,x49711,f80(x49711))
% 15.02/14.79 [4972]~P101(x49721)+P15(x49721,x49721,f110(x49721))
% 15.02/14.79 [4973]~P97(x49731)+P15(x49731,x49731,f80(x49731))
% 15.02/14.79 [4974]~P102(x49741)+P15(x49741,x49741,f101(x49741))
% 15.02/14.79 [4975]~P109(x49751)+P15(x49751,x49751,f188(x49751))
% 15.02/14.79 [4976]~P109(x49761)+P15(x49761,x49761,f233(x49761))
% 15.02/14.79 [4775]~E(x47751,f2(a919))+E(f857(f100(a1),x47751),f2(a1))
% 15.02/14.79 [4782]~P94(x47821)+E(f857(f103(x47821),a82),f2(x47821))
% 15.02/14.79 [4785]~E(f580(x47851),f2(a919))+E(f857(f165(a919),x47851),f2(a919))
% 15.02/14.79 [4786]~P108(x47861)+E(f236(x47861,f234(x47861)),f188(x47861))
% 15.02/14.79 [4787]~P108(x47871)+E(f237(x47871,f234(x47871)),f233(x47871))
% 15.02/14.79 [4788]~P91(x47881)+E(f81(x47881,f2(x47881)),f2(x47881))
% 15.02/14.79 [4797]~P146(x47971)+E(f857(f100(x47971),f77(a919)),f77(x47971))
% 15.02/14.79 [4798]~P146(x47981)+E(f857(f100(x47981),f2(a919)),f2(x47981))
% 15.02/14.79 [4799]~P143(x47991)+E(f857(f102(x47991),f77(a1)),f77(x47991))
% 15.02/14.79 [4800]~P143(x48001)+E(f857(f102(x48001),f2(a1)),f2(x48001))
% 15.02/14.79 [4801]E(x48011,f2(a919))+~E(f857(f100(a1),x48011),f2(a1))
% 15.02/14.79 [4837]~P120(x48371)+E(f857(f75(x48371),f77(x48371)),f77(x48371))
% 15.02/14.79 [4838]~P87(x48381)+E(f857(f75(x48381),f2(x48381)),f2(x48381))
% 15.02/14.79 [4839]~P96(x48391)+E(f857(f78(x48391),f189(x48391)),f241(x48391))
% 15.02/14.79 [4840]~P76(x48401)+E(f857(f78(x48401),f2(x48401)),f2(x48401))
% 15.02/14.79 [4841]~P96(x48411)+E(f857(f78(x48411),f241(x48411)),f189(x48411))
% 15.02/14.79 [4842]~P83(x48421)+E(f857(f165(x48421),f113(x48421)),f2(x48421))
% 15.02/14.79 [4860]~P38(x48601)+P42(f857(f172(a1),x48601))
% 15.02/14.79 [4889]~P94(x48891)+E(f857(f78(x48891),f77(x48891)),f857(f103(x48891),a97))
% 15.02/14.79 [4904]~P94(x49041)+P29(x49041,f857(f103(x49041),a82))
% 15.02/14.79 [4930]P38(x49301)+~P42(f857(f172(a1),x49301))
% 15.02/14.79 [4977]E(f857(f100(a1),f857(a104,x49771)),x49771)+P106(f857(a194,x49771))
% 15.02/14.79 [5047]~P116(x50471)+E(f244(x50471,f77(x50471),f80(x50471)),f243(x50471))
% 15.02/14.79 [5080]~P94(x50801)+~P29(x50801,f857(f103(x50801),a97))
% 15.02/14.79 [5228]E(f857(f75(a1),x52281),x52281)+P106(f857(f857(f235(a1),x52281),f2(a1)))
% 15.02/14.79 [5246]~E(f857(a104,x52461),f2(a919))+P106(f857(f857(f234(a1),x52461),f2(a1)))
% 15.02/14.79 [5312]~P106(f857(a194,x53121))+P106(f857(f857(f235(a1),x53121),f2(a1)))
% 15.02/14.79 [5352]~P127(x53521)+P106(f857(f857(f234(x53521),f2(x53521)),f77(x53521)))
% 15.02/14.79 [5353]~P143(x53531)+P106(f857(f857(f328(x53531),f77(x53531)),f109(x53531)))
% 15.02/14.79 [5354]~P146(x53541)+P106(f857(f857(f328(x53541),f77(x53541)),f186(x53541)))
% 15.02/14.79 [5355]~P143(x53551)+P106(f857(f857(f328(x53551),f2(x53551)),f109(x53551)))
% 15.02/14.79 [5356]~P146(x53561)+P106(f857(f857(f328(x53561),f2(x53561)),f186(x53561)))
% 15.02/14.79 [5357]~P127(x53571)+P106(f857(f857(f235(x53571),f2(x53571)),f77(x53571)))
% 15.02/14.79 [5410]E(x54101,f2(a919))+~P106(f857(f857(f234(a919),x54101),f2(a919)))
% 15.02/14.79 [5452]E(f857(a104,x54521),f2(a919))+~P106(f857(f857(f234(a1),x54521),f2(a1)))
% 15.02/14.79 [5514]P106(f857(a194,x55141))+~P106(f857(f857(f235(a1),x55141),f2(a1)))
% 15.02/14.79 [5521]~P109(x55211)+P17(x55211,f920(x55211),f148(x55211,x55211,f7(x55211)))
% 15.02/14.79 [5539]P42(x55391)+~P106(f857(f857(f234(a1),f2(a1)),f406(x55391)))
% 15.02/14.79 [5544]E(f857(f75(a1),x55441),f857(f78(a1),x55441))+~P106(f857(f857(f235(a1),x55441),f2(a1)))
% 15.02/14.79 [5716]~P127(x57161)+~P106(f857(f857(f234(x57161),f77(x57161)),f2(x57161)))
% 15.02/14.79 [5717]~P127(x57171)+~P106(f857(f857(f235(x57171),f77(x57171)),f2(x57171)))
% 15.02/14.79 [5733]~E(x57331,f2(a919))+P106(f857(f857(f234(a1),f857(f100(a1),x57331)),f2(a1)))
% 15.02/14.79 [5734]~E(x57341,f2(a1))+P106(f857(f857(f235(a1),f857(f75(a1),x57341)),f77(a1)))
% 15.02/14.79 [5856]~P83(x58561)+E(f142(x58561,x58561,f79(x58561),f2(x58561)),f165(x58561))
% 15.02/14.79 [6030]~P103(x60301)+P26(a919,x60301,f100(x60301),f241(f927(a919,a915)))
% 15.02/14.79 [6236]E(x62361,f2(a919))+~P106(f857(f857(f234(a1),f857(f100(a1),x62361)),f2(a1)))
% 15.02/14.79 [6237]E(x62371,f2(a1))+~P106(f857(f857(f235(a1),f857(f75(a1),x62371)),f77(a1)))
% 15.02/14.79 [7046]~P106(f857(f857(f235(a1),x70461),f2(a1)))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x70461),x70461)),f2(a1)))
% 15.02/14.79 [7603]P106(f857(f857(f235(a1),x76031),f2(a1)))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),x76031),x76031)),f2(a1)))
% 15.02/14.79 [8150]E(x81501,f857(a5,f2(a919)))+P106(f857(f857(f235(a919),f857(f857(f3(a919),f857(a22,x81501)),f857(a112,f2(a919)))),f857(a22,x81501)))
% 15.02/14.79 [8913]~P106(f857(f857(f235(a1),x89131),f2(a1)))+P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x89131),x89131)),a97)),f2(a1)))
% 15.02/14.79 [9010]~P106(f857(f857(f235(a1),x90101),f2(a1)))+P106(f857(f857(f235(a1),f857(f857(f79(a1),f857(f857(f79(a1),f77(a1)),x90101)),x90101)),f2(a1)))
% 15.02/14.79 [9328]P106(f857(f857(f235(a1),x93281),f2(a1)))+~P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93281),x93281)),a97)),f2(a1)))
% 15.02/14.79 [9389]P106(f857(f857(f235(a1),x93891),f2(a1)))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),f857(f857(f79(a1),f77(a1)),x93891)),x93891)),f2(a1)))
% 15.02/14.79 [4878]~E(a82,x48781)+E(f857(f857(f79(a1),x48781),x48781),a82)
% 15.02/14.79 [4879]~E(x48791,a82)+E(f857(f857(f79(a1),x48791),x48791),a82)
% 15.02/14.79 [4890]E(x48901,f2(a1))+E(f857(f857(f35(a1),x48901),x48901),f77(a1))
% 15.02/14.79 [5024]E(x50241,a82)+~E(f857(f857(f79(a1),x50241),x50241),a82)
% 15.02/14.79 [5025]E(a82,x50251)+~E(f857(f857(f79(a1),x50251),x50251),a82)
% 15.02/14.79 [5037]~P6(x50371)+E(f36(x50371,f189(f927(x50371,a915))),f189(x50371))
% 15.02/14.79 [5038]~P6(x50381)+E(f36(x50381,f241(f927(x50381,a915))),f241(x50381))
% 15.02/14.79 [5039]~P6(x50391)+E(f37(x50391,f189(f927(x50391,a915))),f241(x50391))
% 15.02/14.79 [5040]~P6(x50401)+E(f37(x50401,f241(f927(x50401,a915))),f189(x50401))
% 15.02/14.79 [5041]~P109(x50411)+E(f139(x50411,f189(f927(x50411,a915))),f113(x50411))
% 15.02/14.79 [5183]E(x51831,f2(a919))+P106(f857(f857(f235(a919),f2(a919)),x51831))
% 15.02/14.79 [5203]~P7(x52031)+P106(f857(f857(f234(a1),f2(a1)),x52031))
% 15.02/14.79 [5237]~E(f857(f103(a919),x52371),f2(a919))+P106(f857(f857(f234(a1),x52371),a82))
% 15.02/14.79 [5242]P42(x52421)+P106(f857(f857(f328(a1),f406(x52421)),x52421))
% 15.02/14.79 [5243]E(x52431,f857(a5,f2(a919)))+P106(f857(f857(f234(a99),f77(a99)),x52431))
% 15.02/14.79 [5284]P106(f857(a194,x52841))+P106(f857(f857(f234(a1),f2(a1)),x52841))
% 15.02/14.79 [5334]E(f857(f100(a1),f857(a104,x53341)),f2(a1))+P106(f857(f857(f234(a1),f2(a1)),x53341))
% 15.02/14.79 [5391]E(f857(f100(a1),f857(f103(a919),x53911)),f857(f103(a1),x53911))+P106(f857(a194,f857(f103(a1),x53911)))
% 15.02/14.79 [5416]E(f857(f103(a919),x54161),f2(a919))+~P106(f857(a194,f857(f103(a1),x54161)))
% 15.02/14.79 [5417]E(f857(f103(a919),x54171),f2(a919))+~P106(f857(f857(f234(a1),x54171),a82))
% 15.02/14.79 [5449]P7(x54491)+~P106(f857(f857(f234(a1),f2(a1)),x54491))
% 15.02/14.79 [5524]E(f857(a112,f859(x55241)),x55241)+~P106(f857(f857(f235(a919),f2(a919)),x55241))
% 15.02/14.79 [5533]E(f857(a112,f857(f103(a919),x55331)),f77(a919))+~P106(f857(a194,f857(f103(a1),x55331)))
% 15.02/14.79 [5540]E(f857(f100(a1),f349(x55401)),x55401)+~P106(f857(f857(f235(a1),f2(a1)),x55401))
% 15.02/14.79 [5547]~E(x55471,f857(a5,f2(a919)))+~P106(f857(f857(f234(a99),f77(a99)),x55471))
% 15.02/14.79 [5554]E(f857(f100(a1),f857(f103(a919),x55541)),f2(a1))+~P106(f857(a194,f857(f103(a1),x55541)))
% 15.02/14.79 [5580]E(f857(f165(a919),x55801),f2(a919))+P106(f857(f857(f328(a919),f580(x55801)),f857(f172(a919),x55801)))
% 15.02/14.79 [5601]E(f857(f100(a1),f857(a104,x56011)),x56011)+~P106(f857(f857(f234(a1),f2(a1)),x56011))
% 15.02/14.79 [5609]~P106(f857(a194,x56091))+~P106(f857(f857(f234(a1),f2(a1)),x56091))
% 15.02/14.79 [5709]E(f857(f857(f79(a919),f77(a919)),f857(f103(a919),x57091)),f77(a919))+~P106(f857(f857(f235(a1),x57091),a82))
% 15.02/14.79 [5776]E(x57761,f2(a919))+~P106(f857(f857(f235(a919),x57761),f857(a112,f2(a919))))
% 15.02/14.79 [5815]E(f857(f857(f3(a919),f857(f103(a919),x58151)),f77(a919)),f2(a919))+~P106(f857(f857(f234(a1),x58151),a82))
% 15.02/14.79 [5816]E(f857(f857(f79(a919),f857(f103(a919),x58161)),f77(a919)),f77(a919))+~P106(f857(f857(f235(a1),x58161),a82))
% 15.02/14.79 [5828]~P42(x58281)+E(f857(f34(a919),f857(f309(a1,a919,a104),x58281)),f857(f34(a1),x58281))
% 15.02/14.79 [5857]~P109(x58571)+E(f236(x58571,f857(f9(x58571,x58571,a915),f234(x58571))),f233(x58571))
% 15.02/14.79 [5858]~P109(x58581)+E(f237(x58581,f857(f9(x58581,x58581,a915),f234(x58581))),f188(x58581))
% 15.02/14.79 [5868]E(f44(a919,f857(a112,f2(a919)),f857(f103(a919),x58681)),f857(a112,f2(a919)))+~P106(f857(a194,f857(f103(a1),x58681)))
% 15.02/14.79 [5877]~P106(f857(f857(f235(a1),f2(a1)),x58771))+P106(f857(f857(f234(a1),f77(a1)),x58771))
% 15.02/14.79 [5878]P106(f857(f857(f235(a1),f2(a1)),x58781))+~P106(f857(f857(f234(a1),f77(a1)),x58781))
% 15.02/14.79 [5889]E(f857(a112,f857(f857(f3(a919),x58891),f77(a919))),x58891)+~P106(f857(f857(f235(a919),f2(a919)),x58891))
% 15.02/14.79 [5945]P106(f857(f857(f235(a919),f2(a919)),f349(x59451)))+~P106(f857(f857(f235(a1),f2(a1)),x59451))
% 15.02/14.79 [6006]E(f44(a1,f857(f103(a1),a97),x60061),f857(f857(f3(a1),x60061),f77(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x60061))
% 15.02/14.79 [6043]~P106(f857(f857(f235(a1),a82),x60431))+P106(f857(f857(f235(a919),f2(a919)),f857(f103(a919),x60431)))
% 15.02/14.79 [6048]E(f857(a22,f809(x60481)),x60481)+~P106(f857(f857(f328(a919),x60481),f241(f927(a919,a915))))
% 15.02/14.79 [6101]P106(f857(f857(f235(a919),f2(a919)),f857(a104,x61011)))+~P106(f857(f857(f235(a1),f2(a1)),x61011))
% 15.02/14.79 [6151]~P106(f857(f857(f235(a919),f2(a919)),x61511))+P106(f857(f857(f235(a1),f2(a1)),f857(f100(a1),x61511)))
% 15.02/14.79 [6187]~P106(f857(f857(f235(a919),f2(a919)),f857(a104,x61871)))+P106(f857(f857(f235(a1),f2(a1)),x61871))
% 15.02/14.79 [6202]~P42(x62021)+E(f857(f309(a919,a1,f100(a1)),f857(f309(a1,a919,a104),x62021)),x62021)
% 15.02/14.79 [6215]P106(f857(f857(f235(a1),a82),x62151))+~P106(f857(f857(f235(a919),f2(a919)),f857(f103(a919),x62151)))
% 15.02/14.79 [6277]P106(f857(f857(f235(a919),f2(a919)),x62771))+~P106(f857(f857(f235(a1),f2(a1)),f857(f100(a1),x62771)))
% 15.02/14.79 [6394]E(f857(f309(a919,a1,f100(a1)),f857(f281(a919),f857(a104,x63941))),f857(f301(a1,f2(a1)),x63941))+~P106(f857(f857(f234(a1),f2(a1)),x63941))
% 15.02/14.79 [6410]~P127(x64101)+P106(f857(f857(f235(x64101),f2(x64101)),f857(f857(f79(x64101),f77(x64101)),f77(x64101))))
% 15.02/14.79 [6459]P106(f857(f857(f235(a919),f857(a112,f2(a919))),f857(a104,x64591)))+~P106(f857(f857(f235(a1),f77(a1)),x64591))
% 15.02/14.79 [6561]E(x65611,f2(a1))+P106(f857(f48(f2(a1),x65611),f857(f857(f251(a1,a1),f2(a1)),f2(a1))))
% 15.02/14.79 [6729]~P106(f857(f857(f235(a919),f857(a112,f2(a919))),f857(a104,x67291)))+P106(f857(f857(f235(a1),f77(a1)),x67291))
% 15.02/14.79 [7160]~P118(x71601)+P39(x71601,f857(f261(f926(x71601,x71601)),f857(f256(x71601,x71601,a915),f235(x71601))))
% 15.02/14.79 [5763]E(f857(f103(a919),f857(f857(f3(a1),x57631),a97)),f857(a112,f857(f103(a919),x57631)))+P106(f857(a194,f857(f103(a1),x57631)))
% 15.02/14.79 [5779]~P38(x57791)+E(f857(f857(f154(a919,a1),f100(a1)),f857(f857(f154(a1,a919),a104),x57791)),x57791)
% 15.02/14.79 [5895]E(f857(f78(a1),f857(f100(a1),f857(a112,f369(x58951)))),x58951)+~P106(f857(f857(f235(a1),x58951),f2(a1)))
% 15.02/14.79 [5905]E(f857(f857(f79(a919),f77(a919)),f857(f103(a919),x59051)),f857(f103(a919),f857(f857(f3(a1),x59051),a97)))+P106(f857(f857(f235(a1),x59051),a82))
% 15.02/14.79 [5947]E(f857(f857(f35(a1),f857(f103(a1),a97)),x59471),f857(f103(a1),a97))+~P106(f857(f857(f235(a1),f2(a1)),x59471))
% 15.02/14.79 [6039]E(f857(f857(f3(a919),f857(f103(a919),x60391)),f77(a919)),f857(f103(a919),f857(f857(f79(a1),x60391),a97)))+P106(f857(f857(f234(a1),x60391),a82))
% 15.02/14.79 [6040]E(f857(f857(f79(a919),f857(f103(a919),x60401)),f77(a919)),f857(f103(a919),f857(f857(f3(a1),x60401),a97)))+P106(f857(f857(f235(a1),x60401),a82))
% 15.02/14.79 [6086]E(f857(a104,f857(f857(f79(a1),f77(a1)),x60861)),f857(a112,f857(a104,x60861)))+~P106(f857(f857(f234(a1),f2(a1)),x60861))
% 15.02/14.79 [6122]E(f857(a112,f857(f857(f3(a919),x61221),f857(a112,f2(a919)))),x61221)+~P106(f857(f857(f235(a919),f2(a919)),x61221))
% 15.02/14.79 [6343]E(f44(a919,f857(a112,f2(a919)),f857(f103(a919),x63431)),f857(a104,f44(a1,f77(a1),f857(f103(a1),x63431))))+P106(f857(a194,f857(f103(a1),x63431)))
% 15.02/14.79 [6387]~P106(f857(f857(f234(a1),a82),x63871))+P106(f857(f857(f234(a1),a82),f857(f857(f79(a1),x63871),x63871)))
% 15.02/14.79 [6388]~P106(f857(f857(f235(a1),a97),x63881))+P106(f857(f857(f234(a1),a97),f857(f857(f79(a1),x63881),x63881)))
% 15.02/14.79 [6389]~P106(f857(f857(f235(a1),a82),x63891))+P106(f857(f857(f235(a1),a82),f857(f857(f79(a1),x63891),x63891)))
% 15.02/14.79 [6390]~P106(f857(f857(f235(a1),a97),x63901))+P106(f857(f857(f235(a1),a97),f857(f857(f79(a1),x63901),x63901)))
% 15.02/14.79 [6575]~P106(f857(f60(x65751),f241(f927(x65751,a915))))+P106(f857(f60(f923(x65751)),f241(f927(f923(x65751),a915))))
% 15.02/14.79 [6659]~P106(f857(f857(f234(a1),f2(a1)),x66591))+P106(f857(f857(f235(a1),f2(a1)),f857(f857(f79(a1),f77(a1)),x66591)))
% 15.02/14.79 [6666]E(f857(f250(a1,a1),f46(f77(a1),f857(f103(a1),x66661))),f857(f857(f35(a1),f77(a1)),f857(f103(a1),x66661)))+~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x66661)))
% 15.02/14.79 [6688]E(f857(f255(a1,a1),f46(f77(a1),f857(f103(a1),x66881))),f44(a1,f77(a1),f857(f103(a1),x66881)))+~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x66881)))
% 15.02/14.79 [6700]P106(f857(f60(x67001),f241(f927(x67001,a915))))+~P106(f857(f60(f923(x67001)),f241(f927(f923(x67001),a915))))
% 15.02/14.79 [6730]P106(f857(f857(f234(a1),a82),x67301))+~P106(f857(f857(f234(a1),a82),f857(f857(f79(a1),x67301),x67301)))
% 15.02/14.79 [6731]P106(f857(f857(f235(a1),a82),x67311))+~P106(f857(f857(f235(a1),a82),f857(f857(f79(a1),x67311),x67311)))
% 15.02/14.79 [6732]P106(f857(f857(f235(a1),a97),x67321))+~P106(f857(f857(f234(a1),a97),f857(f857(f79(a1),x67321),x67321)))
% 15.02/14.79 [6733]P106(f857(f857(f235(a1),a97),x67331))+~P106(f857(f857(f235(a1),a97),f857(f857(f79(a1),x67331),x67331)))
% 15.02/14.79 [7050]~P106(f857(f60(x70501),f241(f927(x70501,a915))))+P106(f857(f857(f235(a919),f2(a919)),f857(f34(x70501),f241(f927(x70501,a915)))))
% 15.02/14.79 [7642]P106(f857(f60(a919),x76421))+~P106(f857(f60(a1),f857(f309(a919,a1,f100(a1)),x76421)))
% 15.02/14.79 [5684]~E(a97,x56841)+E(f857(f857(f3(a1),f857(f857(f79(a1),x56841),x56841)),a97),a97)
% 15.02/14.79 [5685]~E(x56851,a97)+E(f857(f857(f3(a1),f857(f857(f79(a1),x56851),x56851)),a97),a97)
% 15.02/14.79 [6210]E(x62101,a97)+~E(f857(f857(f3(a1),f857(f857(f79(a1),x62101),x62101)),a97),a97)
% 15.02/14.79 [6211]E(a97,x62111)+~E(f857(f857(f3(a1),f857(f857(f79(a1),x62111),x62111)),a97),a97)
% 15.02/14.79 [6628]~E(f857(f103(a919),x66281),f2(a919))+P106(f857(a194,f857(f103(a1),f857(f857(f79(a1),x66281),a97))))
% 15.02/14.79 [6980]~P106(f857(a194,f857(f103(a1),x69801)))+P106(f857(a194,f857(f103(a1),f857(f857(f79(a1),x69801),x69801))))
% 15.02/14.79 [6981]~P106(f857(f857(f234(a1),x69811),a82))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x69811),x69811)),a82))
% 15.02/14.79 [6982]~P106(f857(f857(f234(a1),x69821),a97))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x69821),x69821)),a97))
% 15.02/14.79 [6983]~P106(f857(f857(f235(a1),x69831),a82))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x69831),x69831)),a82))
% 15.02/14.79 [6984]~P106(f857(f857(f234(a1),x69841),a97))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x69841),x69841)),a97))
% 15.02/14.79 [7306]E(f857(f103(a919),x73061),f2(a919))+~P106(f857(a194,f857(f103(a1),f857(f857(f79(a1),x73061),a97))))
% 15.02/14.79 [7557]~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x75571)))+P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),f857(f857(f79(a1),x75571),x75571))))
% 15.02/14.79 [7558]P106(f857(a194,f857(f103(a1),x75581)))+~P106(f857(a194,f857(f103(a1),f857(f857(f79(a1),x75581),x75581))))
% 15.02/14.79 [7559]P106(f857(f857(f234(a1),x75591),a82))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x75591),x75591)),a82))
% 15.02/14.79 [7560]P106(f857(f857(f234(a1),x75601),a97))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x75601),x75601)),a97))
% 15.02/14.79 [7561]P106(f857(f857(f234(a1),x75611),a97))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),x75611),x75611)),a97))
% 15.02/14.79 [7562]P106(f857(f857(f235(a1),x75621),a82))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),x75621),x75621)),a82))
% 15.02/14.79 [7921]E(f857(a106,f536(x79211)),x79211)+~P106(f857(f857(f328(f927(f926(a919,a919),a915)),x79211),a98))
% 15.02/14.79 [6548]~P94(x65481)+E(f857(f103(x65481),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f77(x65481))
% 15.02/14.79 [7030]~P106(f857(a194,f857(f103(a1),x70301)))+E(f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),x70301),x70301)),a97)),f2(a919))
% 15.02/14.79 [8095]~P106(f857(f857(f235(a1),f857(f103(a1),x80951)),f2(a1)))+E(f857(f250(a1,a1),f857(a50,f49(f857(f78(a1),f77(a1)),f857(f78(a1),f857(f103(a1),x80951))))),f857(f857(f35(a1),f77(a1)),f857(f103(a1),x80951)))
% 15.02/14.79 [8108]~P106(f857(f857(f235(a1),f857(f103(a1),x81081)),f2(a1)))+E(f857(f255(a1,a1),f857(a50,f49(f857(f78(a1),f77(a1)),f857(f78(a1),f857(f103(a1),x81081))))),f44(a1,f77(a1),f857(f103(a1),x81081)))
% 15.02/14.79 [8157]~P106(f857(f857(f234(a1),a82),x81571))+P106(f857(f857(f234(a1),a82),f857(f857(f3(a1),f857(f857(f79(a1),x81571),x81571)),a97)))
% 15.02/14.79 [8158]~P106(f857(f857(f234(a1),a97),x81581))+P106(f857(f857(f234(a1),a97),f857(f857(f3(a1),f857(f857(f79(a1),x81581),x81581)),a97)))
% 15.02/14.79 [8159]~P106(f857(f857(f234(a1),a82),x81591))+P106(f857(f857(f235(a1),a82),f857(f857(f3(a1),f857(f857(f79(a1),x81591),x81591)),a97)))
% 15.02/14.79 [8160]~P106(f857(f857(f235(a1),a97),x81601))+P106(f857(f857(f235(a1),a97),f857(f857(f3(a1),f857(f857(f79(a1),x81601),x81601)),a97)))
% 15.02/14.79 [8457]~P94(x84571)+~P29(x84571,f857(f103(x84571),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))
% 15.02/14.79 [8638]P106(f857(f857(f234(a1),a82),x86381))+~P106(f857(f857(f234(a1),a82),f857(f857(f3(a1),f857(f857(f79(a1),x86381),x86381)),a97)))
% 15.02/14.79 [8639]P106(f857(f857(f234(a1),a82),x86391))+~P106(f857(f857(f235(a1),a82),f857(f857(f3(a1),f857(f857(f79(a1),x86391),x86391)),a97)))
% 15.02/14.79 [8640]P106(f857(f857(f234(a1),a97),x86401))+~P106(f857(f857(f234(a1),a97),f857(f857(f3(a1),f857(f857(f79(a1),x86401),x86401)),a97)))
% 15.02/14.79 [8641]P106(f857(f857(f235(a1),a97),x86411))+~P106(f857(f857(f235(a1),a97),f857(f857(f3(a1),f857(f857(f79(a1),x86411),x86411)),a97)))
% 15.02/14.79 [8960]E(f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),x89601),x89601)),a97)),f857(f857(f85(a919,a919),f857(f103(a919),x89601)),f857(f857(f10(a919,a919,a919),a112),f857(f857(f20(a919,a919,a919),f79(a919)),f7(a919)))))+P106(f857(a194,f857(f103(a1),x89601)))
% 15.02/14.79 [9823]E(x98231,f189(f927(f926(a919,a919),a915)))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x98231),f189(f927(f926(a919,a919),a915)))),a68))
% 15.02/14.79 [8887]~P106(f857(a194,f857(f103(a1),x88871)))+P106(f857(a194,f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x88871),x88871)),a97))))
% 15.02/14.79 [8888]~P106(f857(f857(f235(a1),x88881),a82))+P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x88881),x88881)),a97)),a82))
% 15.02/14.79 [8889]~P106(f857(f857(f234(a1),x88891),a97))+P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x88891),x88891)),a97)),a97))
% 15.02/14.79 [8890]~P106(f857(f857(f235(a1),x88901),a82))+P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x88901),x88901)),a97)),a82))
% 15.02/14.79 [8891]~P106(f857(f857(f235(a1),x88911),a97))+P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x88911),x88911)),a97)),a97))
% 15.02/14.79 [9001]~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x90011)))+P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x90011),x90011)),a97))))
% 15.02/14.79 [9159]~P94(x91591)+E(f857(f857(f79(x91591),f77(x91591)),f77(x91591)),f857(f103(x91591),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))
% 15.02/14.79 [9312]P106(f857(a194,f857(f103(a1),x93121)))+~P106(f857(a194,f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93121),x93121)),a97))))
% 15.02/14.79 [9313]P106(f857(f857(f234(a1),x93131),a97))+~P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93131),x93131)),a97)),a97))
% 15.02/14.79 [9314]P106(f857(f857(f235(a1),x93141),a82))+~P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93141),x93141)),a97)),a82))
% 15.02/14.79 [9315]P106(f857(f857(f235(a1),x93151),a82))+~P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93151),x93151)),a97)),a82))
% 15.02/14.79 [9316]P106(f857(f857(f235(a1),x93161),a97))+~P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93161),x93161)),a97)),a97))
% 15.02/14.79 [9868]~P106(f857(f60(f926(a919,a919)),x98681))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),f189(f927(f926(a919,a919),a915))),x98681)),a69))
% 15.02/14.79 [9646]~P146(x96461)+E(f857(f857(f243(x96461),f77(x96461)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f77(x96461))
% 15.02/14.79 [9647]~P146(x96471)+E(f857(f857(f243(x96471),f2(x96471)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f2(x96471))
% 15.02/14.79 [10092]~P106(f857(f857(f235(a919),f77(a919)),x100921))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f35(a919),x100921),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.79 [10098]~P106(f857(f857(f235(a919),f2(a919)),x100981))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f35(a919),f857(f857(f79(a919),x100981),f77(a919))),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.79 [10138]~E(f44(a919,x101381,f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f77(a919))+P106(f857(f857(f235(a919),f2(a919)),f44(a919,x101381,f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.79 [10168]E(f44(a919,x101681,f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f77(a919))+~P106(f857(f857(f235(a919),f2(a919)),f44(a919,x101681,f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.79 [4806]~P8(x48061,x48062)+P45(x48061,x48062)
% 15.02/14.79 [4807]~P39(x48071,x48072)+P59(x48071,x48072)
% 15.02/14.79 [4808]~P46(x48081,x48082)+P59(x48081,x48082)
% 15.02/14.79 [4810]~P8(x48101,x48102)+P51(x48101,x48102)
% 15.02/14.79 [4812]~P16(x48121,x48122)+P51(x48121,x48122)
% 15.02/14.79 [4814]~P8(x48141,x48142)+P52(x48141,x48142)
% 15.02/14.79 [4816]~P16(x48161,x48162)+P52(x48161,x48162)
% 15.02/14.79 [4817]~P8(x48171,x48172)+P16(x48171,x48172)
% 15.02/14.79 [4767]~E(x47671,x47672)+E(f268(x47671,x47672),f77(a99))
% 15.02/14.79 [4770]E(f217(x47701,x47702),x47701)+~E(x47702,f2(a919))
% 15.02/14.79 [4777]~E(x47772,f113(x47771))+E(f152(x47771,x47772),f113(x47771))
% 15.02/14.79 [4796]~E(f152(x47962,x47961),f113(x47962))+E(x47961,f113(x47962))
% 15.02/14.79 [4821]~P1(x48212)+P1(f927(x48211,x48212))
% 15.02/14.79 [4822]~P107(x48222)+P107(f927(x48221,x48222))
% 15.02/14.79 [4823]~P108(x48232)+P108(f927(x48231,x48232))
% 15.02/14.79 [4824]~P110(x48242)+P110(f927(x48241,x48242))
% 15.02/14.79 [4825]~P2(x48252)+P2(f927(x48251,x48252))
% 15.02/14.79 [4826]~P98(x48262)+P3(f927(x48261,x48262))
% 15.02/14.79 [4827]~P2(x48272)+P101(f927(x48271,x48272))
% 15.02/14.79 [4828]~P4(x48282)+P4(f927(x48281,x48282))
% 15.02/14.79 [4829]~P2(x48292)+P102(f927(x48291,x48292))
% 15.02/14.79 [4830]~P99(x48302)+P99(f927(x48301,x48302))
% 15.02/14.79 [4831]~P6(x48312)+P6(f927(x48311,x48312))
% 15.02/14.79 [4832]~P96(x48322)+P96(f927(x48321,x48322))
% 15.02/14.79 [4833]~P90(x48332)+P90(f927(x48331,x48332))
% 15.02/14.79 [4834]~P117(x48342)+P117(f927(x48341,x48342))
% 15.02/14.79 [4835]~P98(x48352)+P100(f927(x48351,x48352))
% 15.02/14.79 [4836]~P98(x48362)+P98(f927(x48361,x48362))
% 15.02/14.79 [4849]E(x48491,x48492)+~E(f857(a112,x48491),f857(a112,x48492))
% 15.02/14.79 [4850]E(x48501,x48502)+~E(f857(a106,x48501),f857(a106,x48502))
% 15.02/14.79 [4851]E(x48511,x48512)+~E(f857(a5,x48511),f857(a5,x48512))
% 15.02/14.79 [4853]E(x48531,x48532)+~E(f857(a22,x48531),f857(a22,x48532))
% 15.02/14.79 [4906]P41(x49061,x49062)+~E(f706(x49062,x49061),f707(x49062,x49061))
% 15.02/14.79 [4936]~P59(x49361,x49362)+P41(x49361,f306(x49361,x49362))
% 15.02/14.79 [4937]~P53(x49371,x49372)+P53(x49371,f306(x49371,x49372))
% 15.02/14.79 [4950]~P62(x49501)+E(f44(x49501,x49502,x49502),f2(x49501))
% 15.02/14.79 [4984]~P39(x49841,x49842)+P39(f920(x49841),f146(x49841,x49842))
% 15.02/14.79 [4985]~P39(x49851,x49852)+P39(f920(x49851),f145(x49851,x49852))
% 15.02/14.79 [4986]~P40(x49861,x49862)+P40(f920(x49861),f147(x49861,x49862))
% 15.02/14.79 [4987]~P40(x49871,x49872)+P40(f920(x49871),f158(x49871,x49872))
% 15.02/14.79 [4988]~P53(x49881,x49882)+P53(f920(x49881),f158(x49881,x49882))
% 15.02/14.79 [5085]~P39(x50851,x50852)+P39(f927(x50851,a915),f319(x50851,x50852))
% 15.02/14.79 [5086]~P39(x50861,x50862)+P39(f927(x50861,a915),f317(x50861,x50862))
% 15.02/14.79 [5212]~P7(x52121)+P42(f302(a1,x52121,x52122))
% 15.02/14.79 [5315]~P39(x53151,x53152)+P61(x53151,f66(x53151,x53151,x53152))
% 15.02/14.79 [5822]~P80(x58221)+P26(x58221,x58221,f78(x58221),x58222)
% 15.02/14.79 [4791]~E(x47912,f113(x47911))+E(f857(f167(x47911),x47912),f113(x47911))
% 15.02/14.79 [4792]~E(x47922,f113(x47921))+E(f857(f168(x47921),x47922),f113(x47921))
% 15.02/14.79 [4855]E(x48551,f857(a104,x48552))+~E(f857(f100(a1),x48551),x48552)
% 15.02/14.79 [4858]E(x48581,f113(x48582))+~E(f857(f167(x48582),x48581),f113(x48582))
% 15.02/14.79 [4859]E(x48591,f113(x48592))+~E(f857(f168(x48592),x48591),f113(x48592))
% 15.02/14.79 [4875]~P94(x48751)+E(f857(f103(x48751),x48752),f857(f102(x48751),x48752))
% 15.02/14.79 [4883]~P5(x48831)+P106(f857(f60(x48831),x48832))
% 15.02/14.79 [4891]~E(f667(x48912,x48911),f113(x48911))+E(f179(x48911,x48912),f113(f920(x48911)))
% 15.02/14.79 [4900]~E(x49002,f113(x49001))+E(f857(f172(x49001),x49002),f189(f927(x49001,a915)))
% 15.02/14.79 [4901]~E(x49012,f113(x49011))+E(f189(f927(x49011,a915)),f857(f172(x49011),x49012))
% 15.02/14.79 [4903]E(x49031,x49032)+~E(f857(f100(a1),x49031),f857(f100(a1),x49032))
% 15.02/14.79 [4907]E(f215(x49071,x49072),f2(a919))+P106(f857(f60(x49071),x49072))
% 15.02/14.79 [4925]~P120(x49251)+E(f81(x49251,f81(x49251,x49252)),f81(x49251,x49252))
% 15.02/14.79 [4939]~P113(x49391)+E(f857(f857(f243(x49391),x49392),f77(a919)),x49392)
% 15.02/14.79 [4940]~P82(x49401)+E(f857(f857(f243(x49401),x49402),f77(a919)),x49402)
% 15.02/14.79 [4941]~P53(x49411,x49412)+E(f857(f285(x49411,x49411),x49412),x49412)
% 15.02/14.79 [4945]E(x49451,x49452)+E(f268(x49451,x49452),f857(f857(f79(a99),x49452),f77(a99)))
% 15.02/14.79 [4948]E(f857(f34(x49481),x49482),f2(a919))+P106(f857(f60(x49481),x49482))
% 15.02/14.79 [4951]~E(f152(x49511,x49512),x49512)+P106(f857(f137(x49511),x49512))
% 15.02/14.79 [4954]~P3(x49541)+E(f857(f857(f110(x49541),x49542),f189(x49541)),x49542)
% 15.02/14.79 [4955]~P76(x49551)+E(f857(f857(f3(x49551),x49552),f2(x49551)),x49552)
% 15.02/14.79 [4956]~P113(x49561)+E(f857(f857(f80(x49561),x49562),f77(x49561)),x49562)
% 15.02/14.79 [4957]~P77(x49571)+E(f857(f857(f80(x49571),x49572),f77(x49571)),x49572)
% 15.02/14.79 [4958]~P82(x49581)+E(f857(f857(f80(x49581),x49582),f77(x49581)),x49582)
% 15.02/14.79 [4959]~P100(x49591)+E(f857(f857(f101(x49591),x49592),f241(x49591)),x49592)
% 15.02/14.79 [4960]~P72(x49601)+E(f857(f857(f79(x49601),x49602),f2(x49601)),x49602)
% 15.02/14.79 [4961]~P113(x49611)+E(f857(f857(f79(x49611),x49612),f2(x49611)),x49612)
% 15.02/14.79 [4962]~P83(x49621)+E(f857(f857(f79(x49621),x49622),f2(x49621)),x49622)
% 15.02/14.79 [4963]~P124(x49631)+E(f857(f857(f290(x49631),x49632),f77(x49631)),x49632)
% 15.02/14.79 [4964]~P62(x49641)+E(f857(f857(f35(x49641),x49642),f77(x49641)),x49642)
% 15.02/14.79 [4965]~P113(x49651)+E(f857(f857(f243(x49651),x49652),f2(a919)),f77(x49651))
% 15.02/14.79 [4966]~P116(x49661)+E(f857(f857(f243(x49661),x49662),f2(a919)),f77(x49661))
% 15.02/14.79 [4967]~E(x49672,f189(f927(x49671,a915)))+E(f857(f34(x49671),x49672),f2(a919))
% 15.02/14.79 [4978]~P62(x49781)+E(f44(x49781,x49782,f2(x49781)),x49782)
% 15.02/14.79 [4989]~P100(x49891)+E(f857(f857(f110(x49891),x49892),f241(x49891)),f241(x49891))
% 15.02/14.79 [4990]~P113(x49901)+E(f857(f857(f80(x49901),x49902),f2(x49901)),f2(x49901))
% 15.02/14.79 [4991]~P134(x49911)+E(f857(f857(f80(x49911),x49912),f2(x49911)),f2(x49911))
% 15.02/14.79 [4992]~P3(x49921)+E(f857(f857(f101(x49921),x49922),f189(x49921)),f189(x49921))
% 15.02/14.79 [4993]~P125(x49931)+E(f857(f857(f290(x49931),x49932),f2(x49931)),f2(x49931))
% 15.02/14.79 [4994]~P62(x49941)+E(f857(f857(f35(x49941),x49942),f2(x49941)),f2(x49941))
% 15.02/14.79 [4996]~P62(x49961)+E(f44(x49961,x49962,f77(x49961)),f2(x49961))
% 15.02/14.79 [4997]~P62(x49971)+E(f44(x49971,f2(x49971),x49972),f2(x49971))
% 15.02/14.79 [5026]E(x50261,f2(a919))+E(f54(x50262,x50261,f113(x50262)),f113(f920(x50262)))
% 15.02/14.79 [5049]P53(x50491,x50492)+~E(f857(f285(x50491,x50491),x50492),x50492)
% 15.02/14.79 [5050]P39(x50501,x50502)+~E(f581(x50502,x50501),f189(f927(x50501,a915)))
% 15.02/14.79 [5051]E(x50511,f113(x50512))+~E(f857(f172(x50512),x50511),f189(f927(x50512,a915)))
% 15.02/14.79 [5052]E(x50521,f113(x50522))+~E(f189(f927(x50522,a915)),f857(f172(x50522),x50521))
% 15.02/14.79 [5055]~E(x50551,x50552)+P106(f857(f857(a324,x50551),x50552))
% 15.02/14.79 [5065]P106(x50651)+P106(f857(f857(a329,x50651),x50652))
% 15.02/14.79 [5066]E(x50661,f113(x50662))+E(f857(f857(f164(x50662),x50661),f2(a919)),f857(f141(x50662),x50661))
% 15.02/14.79 [5069]E(f152(x50691,x50692),x50692)+~P106(f857(f137(x50691),x50692))
% 15.02/14.79 [5076]~P106(x50762)+P106(f857(f857(a329,x50761),x50762))
% 15.02/14.79 [5077]~P106(x50772)+P106(f857(f857(a326,x50771),x50772))
% 15.02/14.79 [5078]~P106(x50781)+P106(f857(f857(a326,x50781),x50782))
% 15.02/14.79 [5088]~E(f668(x50882,x50881),f672(x50882,x50881))+P106(f857(f137(x50881),x50882))
% 15.02/14.79 [5095]E(f857(f261(x50951),x50952),f189(f927(x50951,a915)))+P106(f857(x50952,f535(x50952)))
% 15.02/14.79 [5096]E(f189(f927(x50961,a915)),f857(f261(x50961),x50962))+P106(f857(x50962,f553(x50962)))
% 15.02/14.79 [5165]~P120(x51651)+E(f857(f857(f80(x51651),x51652),f81(x51651,x51652)),f857(f75(x51651),x51652))
% 15.02/14.79 [5176]~E(x51761,f2(a1))+E(f45(x51761,x51762),f857(f857(f251(a1,a1),f2(a1)),f2(a1)))
% 15.02/14.79 [5208]~P59(x52081,x52082)+P59(x52081,f857(f285(x52081,x52081),x52082))
% 15.02/14.79 [5209]~P40(x52091,x52092)+P40(x52091,f857(f285(x52091,x52091),x52092))
% 15.02/14.79 [5210]~P41(x52101,x52102)+P41(x52101,f857(f285(x52101,x52101),x52102))
% 15.02/14.79 [5211]~P53(x52111,x52112)+P53(x52111,f857(f285(x52111,x52111),x52112))
% 15.02/14.79 [5233]E(x52331,x52332)+~P106(f857(f857(a324,x52331),x52332))
% 15.02/14.79 [5244]P106(x52441)+~P106(f857(f857(a325,x52442),x52441))
% 15.02/14.79 [5245]P106(x52451)+~P106(f857(f857(a325,x52451),x52452))
% 15.02/14.79 [5250]~P117(x52501)+P106(f857(f857(f234(x52501),x52502),f241(x52501)))
% 15.02/14.79 [5251]~P113(x52511)+P106(f857(f857(f286(x52511),x52512),f2(x52511)))
% 15.02/14.79 [5255]E(x52551,x52552)+~E(f857(x52551,f407(x52552,x52551)),f857(x52552,f407(x52552,x52551)))
% 15.02/14.79 [5286]E(x52861,f2(a919))+E(f217(x52861,f44(a919,x52862,x52861)),f217(x52862,x52861))
% 15.02/14.79 [5291]~P109(x52911)+P14(x52911,f857(f857(f151(x52911),x52912),f113(x52911)))
% 15.02/14.79 [5293]E(x52931,f2(a1))+P106(f857(f48(x52932,x52931),f45(x52932,x52931)))
% 15.02/14.79 [5310]~P16(x53102,x53101)+P106(f857(f857(x53101,f801(x53101)),f801(x53101)))
% 15.02/14.79 [5313]~E(x53131,x53132)+P106(f857(f857(f235(a919),x53131),f857(a112,x53132)))
% 15.02/14.79 [5323]~E(x53231,f2(a919))+P106(f857(f857(f235(a919),x53231),f857(a112,x53232)))
% 15.02/14.79 [5333]P106(f857(x53331,x53332))+P106(f857(f857(f234(a1),f2(a1)),f333(x53331)))
% 15.02/14.79 [5396]E(f857(f857(f308(x53962),f408(x53962,x53961)),f432(x53962,x53961)),x53961)+E(x53961,f189(f927(x53962,a915)))
% 15.02/14.79 [5397]P59(x53971,x53972)+~P59(x53971,f857(f285(x53971,x53971),x53972))
% 15.02/14.79 [5398]P40(x53981,x53982)+~P40(x53981,f857(f285(x53981,x53981),x53982))
% 15.02/14.79 [5399]P41(x53991,x53992)+~P41(x53991,f857(f285(x53991,x53991),x53992))
% 15.02/14.79 [5400]P53(x54001,x54002)+~P53(x54001,f857(f285(x54001,x54001),x54002))
% 15.02/14.79 [5403]~E(f44(a919,x54032,x54031),f2(a919))+E(f857(f857(f80(a919),x54031),f334(x54031,x54032)),x54032)
% 15.02/14.79 [5404]~E(f44(a1,x54042,x54041),f2(a1))+E(f857(f857(f80(a1),x54041),f335(x54041,x54042)),x54042)
% 15.02/14.79 [5430]~P106(f857(x54301,x54302))+P106(f857(f857(f234(a1),f2(a1)),f332(x54301)))
% 15.02/14.79 [5441]E(f857(f857(f3(a919),f857(a104,x54411)),f857(a104,x54412)),f857(a104,x54411))+~P106(f857(a194,x54412))
% 15.02/14.79 [5470]E(f271(x54701,x54702),f77(a99))+~P106(f857(f857(f234(a99),x54701),f77(a99)))
% 15.02/14.79 [5566]E(f857(f857(f164(x55661),x55662),f668(x55662,x55661)),f857(f857(f164(x55661),x55662),f672(x55662,x55661)))+P106(f857(f137(x55661),x55662))
% 15.02/14.79 [5610]~P106(f857(x56101,f89(x56102,x56101)))+P106(f857(x56101,f596(x56102,x56101)))
% 15.02/14.79 [5674]P61(x56741,x56742)+~P106(f857(f314(x56741,x56742),f554(x56742,x56741)))
% 15.02/14.79 [5819]~P16(x58192,x58191)+P106(f857(f857(x58191,f802(x58191,x58192)),f802(x58191,x58192)))
% 15.02/14.79 [5820]~P16(x58202,x58201)+P106(f857(f857(x58201,f805(x58201,x58202)),f805(x58201,x58202)))
% 15.02/14.79 [5829]~E(f857(a112,f44(a919,x58291,x58292)),x58292)+E(f44(a919,f857(a112,x58291),x58292),f2(a919))
% 15.02/14.79 [5884]P39(x58841,x58842)+P106(f857(f857(f328(x58841),f616(x58842,x58841)),f617(x58842,x58841)))
% 15.02/14.79 [5891]~P94(x58911)+P106(f857(f857(f328(x58911),f857(f103(x58911),x58912)),f109(x58911)))
% 15.02/14.79 [5892]~P143(x58921)+P106(f857(f857(f328(x58921),f857(f100(x58921),x58922)),f109(x58921)))
% 15.02/14.79 [5893]~P146(x58931)+P106(f857(f857(f328(x58931),f857(f100(x58931),x58932)),f186(x58931)))
% 15.02/14.79 [5894]~P143(x58941)+P106(f857(f857(f328(x58941),f857(f102(x58941),x58942)),f109(x58941)))
% 15.02/14.79 [6028]~P40(x60281,x60282)+E(f857(f857(f288(x60281,x60281,x60281),x60282),f306(x60281,x60282)),x60282)
% 15.02/14.79 [6042]E(f857(a112,f44(a919,x60421,x60422)),x60422)+E(f44(a919,f857(a112,x60421),x60422),f857(a112,f44(a919,x60421,x60422)))
% 15.02/14.79 [6472]P39(x64721,x64722)+~P106(f857(f857(f328(x64721),f555(x64722,x64721)),f315(x64721,x64722)))
% 15.02/14.79 [6510]~P127(x65101)+~P106(f857(f857(f235(x65101),f857(f100(x65101),x65102)),f2(x65101)))
% 15.02/14.79 [6511]~P87(x65111)+~P106(f857(f857(f235(x65111),f857(f75(x65111),x65112)),f2(x65111)))
% 15.02/14.79 [6544]E(x65441,f189(f927(x65442,a915)))+~P106(f857(f857(f328(x65442),f408(x65442,x65441)),f432(x65442,x65441)))
% 15.02/14.79 [6602]P106(f857(f857(f235(a1),x66021),f44(a1,x66022,x66021)))+~P106(f857(f857(f235(a1),x66021),f2(a1)))
% 15.02/14.79 [6702]E(f857(f857(f308(a919),f857(a112,x67021)),f302(a919,x67022,x67021)),f302(a919,x67022,f857(a112,x67021)))+~P106(f857(f857(f234(a919),x67022),f857(a112,x67021)))
% 15.02/14.79 [6793]~P109(x67931)+P14(x67931,f150(x67931,x67931,f7(x67931),x67932))
% 15.02/14.79 [6922]E(f857(f167(x69221),x69222),x69222)+~P106(f857(f857(f234(a919),f857(f190(f920(x69221)),x69222)),f77(a919)))
% 15.02/14.79 [6944]~P87(x69441)+P106(f857(f857(f234(x69441),f857(f78(x69441),f857(f75(x69441),x69442))),f2(x69441)))
% 15.02/14.79 [6976]~P39(x69761,x69762)+P39(x69761,f857(f857(f288(x69761,x69761,x69761),x69762),f306(x69761,x69762)))
% 15.02/14.79 [6977]~P53(x69771,x69772)+P53(x69771,f857(f857(f288(x69771,x69771,x69771),x69772),f306(x69771,x69772)))
% 15.02/14.79 [7199]~P106(f857(f857(f235(a1),x71992),f2(a1)))+P106(f857(f857(f234(a1),f44(a1,x71991,x71992)),f2(a1)))
% 15.02/14.79 [7599]~P146(x75991)+E(f191(x75991,f857(f857(f9(x75991,x75991,x75991),f79(x75991)),f77(x75991)),x75992,f2(x75991)),f857(f100(x75991),x75992))
% 15.02/14.79 [7628]~P128(x76281)+~P106(f857(f857(f235(x76281),f857(f857(f80(x76281),x76282),x76282)),f2(x76281)))
% 15.02/14.79 [10259]~P120(x102591)+~P106(f857(f857(f235(x102591),f857(f857(f243(x102591),x102592),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f2(x102591)))
% 15.02/14.79 [4856]~E(x48562,f113(x48561))+E(f857(f190(f920(x48561)),x48562),f2(a919))
% 15.02/14.79 [4892]~E(x48921,f2(a919))+E(f857(f857(f79(a919),x48921),x48922),x48922)
% 15.02/14.79 [4893]~E(x48932,f2(a919))+E(f857(f857(f80(a919),x48931),x48932),f2(a919))
% 15.02/14.79 [4895]~E(x48951,f2(a919))+E(f857(f857(f80(a919),x48951),x48952),f2(a919))
% 15.02/14.79 [4896]~E(x48962,f2(a1))+E(f857(f857(f35(a1),x48961),x48962),f2(a1))
% 15.02/14.79 [4897]~E(x48972,f2(a919))+E(f857(f857(f243(a919),x48971),x48972),f77(a919))
% 15.02/14.79 [4908]E(x49081,f113(x49082))+~E(f857(f190(f920(x49082)),x49081),f2(a919))
% 15.02/14.79 [4909]~P2(x49091)+E(f857(f857(f110(x49091),x49092),x49092),x49092)
% 15.02/14.79 [4911]~P101(x49111)+E(f857(f857(f110(x49111),x49112),x49112),x49112)
% 15.02/14.79 [4913]~P97(x49131)+E(f857(f857(f80(x49131),x49132),x49132),x49132)
% 15.02/14.79 [4914]~P2(x49141)+E(f857(f857(f101(x49141),x49142),x49142),x49142)
% 15.02/14.79 [4916]~P102(x49161)+E(f857(f857(f101(x49161),x49162),x49162),x49162)
% 15.02/14.79 [4918]~P109(x49181)+E(f857(f857(f188(x49181),x49182),x49182),x49182)
% 15.02/14.79 [4920]~P109(x49201)+E(f857(f857(f233(x49201),x49202),x49202),x49202)
% 15.02/14.79 [4938]~P76(x49381)+E(f857(f857(f3(x49381),x49382),x49382),f2(x49381))
% 15.02/14.79 [4952]~P76(x49521)+E(f857(f78(x49521),f857(f78(x49521),x49522)),x49522)
% 15.02/14.79 [4953]~P96(x49531)+E(f857(f78(x49531),f857(f78(x49531),x49532)),x49532)
% 15.02/14.79 [4970]~E(x49702,f2(a919))+E(f857(f857(f243(a919),x49701),x49702),f857(a112,f2(a919)))
% 15.02/14.79 [5005]~P3(x50051)+E(f857(f857(f110(x50051),f189(x50051)),x50052),x50052)
% 15.02/14.79 [5006]~P113(x50061)+E(f857(f857(f80(x50061),f77(x50061)),x50062),x50062)
% 15.02/14.79 [5007]~P77(x50071)+E(f857(f857(f80(x50071),f77(x50071)),x50072),x50072)
% 15.02/14.79 [5008]~P82(x50081)+E(f857(f857(f80(x50081),f77(x50081)),x50082),x50082)
% 15.02/14.79 [5009]~P100(x50091)+E(f857(f857(f101(x50091),f241(x50091)),x50092),x50092)
% 15.02/14.79 [5010]~P72(x50101)+E(f857(f857(f79(x50101),f2(x50101)),x50102),x50102)
% 15.02/14.79 [5011]~P113(x50111)+E(f857(f857(f79(x50111),f2(x50111)),x50112),x50112)
% 15.02/14.79 [5012]~P83(x50121)+E(f857(f857(f79(x50121),f2(x50121)),x50122),x50122)
% 15.02/14.79 [5030]~P100(x50301)+E(f857(f857(f110(x50301),f241(x50301)),x50302),f241(x50301))
% 15.02/14.79 [5031]~P113(x50311)+E(f857(f857(f80(x50311),f2(x50311)),x50312),f2(x50311))
% 15.02/14.79 [5032]~P134(x50321)+E(f857(f857(f80(x50321),f2(x50321)),x50322),f2(x50321))
% 15.02/14.79 [5033]~P3(x50331)+E(f857(f857(f101(x50331),f189(x50331)),x50332),f189(x50331))
% 15.02/14.79 [5034]~P124(x50341)+E(f857(f857(f290(x50341),f2(x50341)),x50342),f2(x50341))
% 15.02/14.79 [5035]~P62(x50351)+E(f857(f857(f35(x50351),f2(x50351)),x50352),f2(x50351))
% 15.02/14.79 [5036]~P82(x50361)+E(f857(f857(f243(x50361),f77(x50361)),x50362),f77(x50361))
% 15.02/14.79 [5044]E(x50441,f113(x50442))+E(f144(x50442,f857(f168(x50442),x50441)),f857(f141(x50442),x50441))
% 15.02/14.79 [5045]E(x50451,f113(x50452))+E(f857(f141(x50452),f857(f168(x50452),x50451)),f144(x50452,x50451))
% 15.02/14.79 [5046]E(x50461,f2(a919))+~E(f857(f857(f79(a919),x50462),x50461),x50462)
% 15.02/14.79 [5053]~P94(x50531)+E(f857(f102(x50531),f857(f103(a1),x50532)),f857(f103(x50531),x50532))
% 15.02/14.79 [5054]~P143(x50541)+E(f857(f102(x50541),f857(f100(a1),x50542)),f857(f100(x50541),x50542))
% 15.02/14.79 [5061]E(x50611,f77(a919))+~E(f857(f857(f80(a919),x50612),x50611),f77(a919))
% 15.02/14.79 [5062]E(x50621,f77(a919))+~E(f857(f857(f80(a919),x50621),x50622),f77(a919))
% 15.02/14.79 [5063]E(x50631,f2(a919))+~E(f857(f857(f79(a919),x50632),x50631),f2(a919))
% 15.02/14.79 [5064]E(x50641,f2(a919))+~E(f857(f857(f79(a919),x50641),x50642),f2(a919))
% 15.02/14.79 [5081]~P120(x50811)+E(f857(f75(x50811),f857(f100(x50811),x50812)),f857(f100(x50811),x50812))
% 15.02/14.79 [5082]~P87(x50821)+E(f857(f75(x50821),f857(f75(x50821),x50822)),f857(f75(x50821),x50822))
% 15.02/14.79 [5083]~P87(x50831)+E(f857(f75(x50831),f857(f78(x50831),x50832)),f857(f75(x50831),x50832))
% 15.02/14.79 [5084]~P72(x50841)+E(f857(f165(x50841),f857(f168(x50841),x50842)),f857(f165(x50841),x50842))
% 15.02/14.79 [5089]~E(x50891,f857(a112,f2(a919)))+E(f857(f857(f243(a919),x50891),x50892),f857(a112,f2(a919)))
% 15.02/14.79 [5098]~P76(x50981)+E(f857(f857(f3(x50981),f2(x50981)),x50982),f857(f78(x50981),x50982))
% 15.02/14.79 [5099]~E(x50992,f2(a919))+E(f139(a919,f857(f301(a919,x50991),x50992)),f113(a919))
% 15.02/14.79 [5108]~P94(x51081)+E(f857(f857(f79(x51081),x51082),f857(f103(x51081),a82)),x51082)
% 15.02/14.79 [5109]E(x51091,f2(a1))+E(f46(f857(f75(a1),x51092),f857(f75(a1),x51091)),f52(x51092,x51091))
% 15.02/14.79 [5125]~E(x51251,x51252)+P106(f857(f857(f234(a919),x51251),x51252))
% 15.02/14.79 [5132]~E(x51321,f2(a99))+E(f857(f857(f79(a919),f857(a22,x51321)),x51322),x51322)
% 15.02/14.79 [5146]~P7(x51461)+P7(f857(f857(f243(a1),x51461),x51462))
% 15.02/14.79 [5147]~P96(x51471)+E(f857(f857(f110(x51471),x51472),f857(f78(x51471),x51472)),f241(x51471))
% 15.02/14.79 [5148]~P96(x51481)+E(f857(f857(f101(x51481),x51482),f857(f78(x51481),x51482)),f189(x51481))
% 15.02/14.79 [5149]~P76(x51491)+E(f857(f857(f79(x51491),x51492),f857(f78(x51491),x51492)),f2(x51491))
% 15.02/14.79 [5173]E(x51731,f2(a919))+~E(f857(f78(a1),f857(f100(a1),x51732)),f857(f100(a1),x51731))
% 15.02/14.79 [5174]E(x51741,f2(a919))+~E(f857(f78(a1),f857(f100(a1),x51741)),f857(f100(a1),x51742))
% 15.02/14.79 [5184]E(f195(x51841,x51842),f2(a1))+P106(f857(f857(f234(a1),x51842),x51841))
% 15.02/14.79 [5185]E(f178(x51851,x51852),f113(a1))+P106(f857(f857(f234(a1),x51851),x51852))
% 15.02/14.79 [5186]E(f240(x51861,x51862),f2(a99))+P106(f857(f857(f235(a99),x51861),x51862))
% 15.02/14.79 [5199]E(x51991,f857(a112,f2(a919)))+~E(f857(f857(f80(a919),x51992),x51991),f857(a112,f2(a919)))
% 15.02/14.79 [5200]E(x52001,f857(a112,f2(a919)))+~E(f857(f857(f80(a919),x52001),x52002),f857(a112,f2(a919)))
% 15.02/14.79 [5201]~P107(x52011)+P106(f857(f857(f234(x52011),x52012),x52012))
% 15.02/14.79 [5202]~P113(x52021)+P106(f857(f857(f286(x52021),x52022),x52022))
% 15.02/14.79 [5205]~P94(x52051)+E(f857(f857(f80(x52051),x52052),f857(f103(x52051),a97)),f857(f78(x52051),x52052))
% 15.02/14.79 [5225]~P94(x52251)+E(f857(f78(x52251),f857(f103(x52251),x52252)),f857(f103(x52251),f857(f78(a1),x52252)))
% 15.02/14.79 [5226]~P143(x52261)+E(f857(f78(x52261),f857(f102(x52261),x52262)),f857(f102(x52261),f857(f78(a1),x52262)))
% 15.02/14.79 [5256]~E(x52561,f857(a112,x52562))+P106(f857(f857(f235(a919),f2(a919)),x52561))
% 15.02/14.79 [5274]~P109(x52741)+E(f857(f78(f927(x52741,a915)),f857(f281(x52741),x52742)),f857(f282(x52741),x52742))
% 15.02/14.79 [5275]~P109(x52751)+E(f857(f78(f927(x52751,a915)),f857(f300(x52751),x52752)),f857(f303(x52751),x52752))
% 15.02/14.79 [5276]~P109(x52761)+E(f857(f78(f927(x52761,a915)),f857(f282(x52761),x52762)),f857(f281(x52761),x52762))
% 15.02/14.79 [5277]~P109(x52771)+E(f857(f78(f927(x52771,a915)),f857(f303(x52771),x52772)),f857(f300(x52771),x52772))
% 15.02/14.79 [5285]~E(f857(f100(a1),x52852),x52851)+P106(f857(f857(f234(a1),f2(a1)),x52851))
% 15.02/14.79 [5292]~E(x52922,f2(a1))+E(f52(x52921,x52922),f857(f857(f251(a1,a1),f2(a1)),f857(f75(a1),x52921)))
% 15.02/14.79 [5294]~P1(x52941)+P106(f857(f857(f234(x52941),f189(x52941)),x52942))
% 15.02/14.79 [5328]E(x53281,x53282)+~E(f857(f857(f79(a1),x53281),x53281),f857(f857(f79(a1),x53282),x53282))
% 15.02/14.79 [5332]~P106(f857(x53321,x53322))+P106(f857(x53321,f857(a104,f332(x53321))))
% 15.02/14.79 [5358]~P120(x53581)+E(f857(f857(f80(x53581),f81(x53581,x53582)),f857(f75(x53581),x53582)),x53582)
% 15.02/14.79 [5365]~E(x53652,f2(a919))+E(f84(f926(a919,a919),f47(x53651,x53652)),f857(f857(f251(a919,a919),f2(a919)),x53651))
% 15.02/14.79 [5370]~E(x53701,x53702)+~P106(f857(f857(f235(a919),x53701),x53702))
% 15.02/14.79 [5371]~E(x53711,x53712)+~P106(f857(f857(f235(a1),x53711),x53712))
% 15.02/14.79 [5374]~P146(x53741)+E(f857(f857(f79(x53741),f77(x53741)),f857(f100(x53741),x53742)),f857(f100(x53741),f857(a112,x53742)))
% 15.02/14.79 [5378]~E(x53781,f2(a919))+~P106(f857(f857(f235(a919),x53782),x53781))
% 15.02/14.79 [5392]E(f152(x53921,x53922),x53922)+~E(f857(f190(f920(x53921)),f152(x53921,x53922)),f857(f190(f920(x53921)),x53922))
% 15.02/14.79 [5393]E(f857(f34(x53931),f857(f172(x53931),x53932)),f857(f190(f920(x53931)),x53932))+~P106(f857(f137(x53931),x53932))
% 15.02/14.79 [5408]~P106(f857(x54081,f336(x54081)))+P106(f857(x54081,f857(f100(a1),x54082)))
% 15.02/14.79 [5418]E(f240(x54181,x54182),x54182)+~P106(f857(f857(f235(a99),x54181),x54182))
% 15.02/14.79 [5420]E(f271(x54201,x54202),f77(a99))+~P106(f857(f857(f235(a99),x54202),x54201))
% 15.02/14.79 [5421]E(f178(x54211,x54212),f113(a1))+~P106(f857(f857(f235(a1),x54212),x54211))
% 15.02/14.79 [5422]E(f128(x54221,x54222),f115(a1))+~P106(f857(f857(f235(a1),x54221),x54222))
% 15.02/14.79 [5424]~P110(x54241)+E(f302(x54241,x54242,x54242),f857(f857(f308(x54241),x54242),f189(f927(x54241,a915))))
% 15.02/14.79 [5444]~E(f857(f857(f3(a919),x54441),x54442),f2(a919))+P106(f857(f857(f234(a919),x54441),x54442))
% 15.02/14.79 [5467]~E(x54672,f2(a919))+E(f54(x54671,x54672,f113(x54671)),f857(f857(f151(f920(x54671)),f113(x54671)),f113(f920(x54671))))
% 15.02/14.79 [5471]~P107(x54711)+~P106(f857(f857(f235(x54711),x54712),x54712))
% 15.02/14.79 [5473]~E(f44(a1,x54731,x54732),f2(a1))+E(f44(a1,x54731,f857(f78(a1),x54732)),f2(a1))
% 15.02/14.79 [5475]~E(f44(a1,x54751,x54752),f2(a1))+E(f44(a1,f857(f78(a1),x54751),x54752),f2(a1))
% 15.02/14.79 [5483]E(f857(f301(a919,x54831),f857(a112,x54832)),f189(f927(a919,a915)))+P106(f857(f857(f234(a919),x54831),x54832))
% 15.02/14.79 [5506]E(f139(a919,f857(f301(a919,x55061),x55062)),f113(a919))+P106(f857(f857(f235(a919),x55061),x55062))
% 15.02/14.79 [5511]~E(f857(f34(x55111),f857(f172(x55111),x55112)),f857(f190(f920(x55111)),x55112))+P106(f857(f137(x55111),x55112))
% 15.02/14.79 [5515]~P106(f857(f137(x55151),x55152))+P106(f857(f137(x55151),f857(f167(x55151),x55152)))
% 15.02/14.79 [5516]~P106(f857(f137(x55161),x55162))+P106(f857(f137(x55161),f857(f171(x55161),x55162)))
% 15.02/14.79 [5517]~P106(f857(f137(x55171),x55172))+P106(f857(f137(x55171),f857(f168(x55171),x55172)))
% 15.02/14.79 [5525]P106(f857(x55251,x55252))+~P106(f857(x55251,f857(a104,f333(x55251))))
% 15.02/14.79 [5526]P106(f857(f857(f234(a919),x55262),x55261))+P106(f857(f857(f234(a919),x55261),x55262))
% 15.02/14.79 [5527]P106(f857(f857(f234(a1),x55272),x55271))+P106(f857(f857(f234(a1),x55271),x55272))
% 15.02/14.79 [5531]~P87(x55311)+P106(f857(f857(f234(x55311),x55312),f857(f75(x55311),x55312)))
% 15.02/14.79 [5534]P106(f857(x55341,f337(x55341)))+~P106(f857(x55341,f857(f100(a1),x55342)))
% 15.02/14.79 [5558]E(f857(f857(f3(a919),x55581),x55582),f2(a919))+~P106(f857(f857(f234(a919),x55581),x55582))
% 15.02/14.79 [5559]E(f857(f857(f35(a919),x55591),x55592),f2(a919))+~P106(f857(f857(f235(a919),x55591),x55592))
% 15.02/14.79 [5578]E(f44(a919,x55781,x55782),x55781)+~P106(f857(f857(f235(a919),x55781),x55782))
% 15.02/14.79 [5586]E(f44(a1,x55861,f857(f78(a1),x55862)),f291(x55861,x55862))+P106(f857(f857(f234(a1),f2(a1)),x55862))
% 15.02/14.79 [5599]E(f857(f857(f3(a1),x55991),x55992),f195(x55991,x55992))+~P106(f857(f857(f234(a1),x55992),x55991))
% 15.02/14.79 [5619]P106(f857(f857(f234(a1),f2(a1)),f336(x56191)))+P106(f857(x56191,f857(f100(a1),x56192)))
% 15.02/14.79 [5632]~P127(x56321)+P106(f857(f857(f234(x56321),f2(x56321)),f857(f100(x56321),x56322)))
% 15.02/14.79 [5633]~P87(x56331)+P106(f857(f857(f234(x56331),f2(x56331)),f857(f75(x56331),x56332)))
% 15.02/14.79 [5660]E(f857(f857(f79(a919),x56601),f673(x56602,x56601)),x56602)+~P106(f857(f857(f234(a919),x56601),x56602))
% 15.02/14.79 [5675]E(f302(a1,x56751,x56752),f189(f927(a1,a915)))+~P106(f857(f857(f235(a1),x56752),x56751))
% 15.02/14.79 [5677]~P120(x56771)+E(f857(f857(f80(x56771),f857(f75(x56771),x56772)),f857(f75(x56771),x56772)),f857(f857(f80(x56771),x56772),x56772))
% 15.02/14.79 [5683]E(f139(a919,f857(f301(a919,x56831),f857(a112,x56832))),f113(a919))+P106(f857(f857(f234(a919),x56831),x56832))
% 15.02/14.79 [5687]E(f857(f857(f35(a1),x56871),x56872),f292(x56871,x56872))+~P106(f857(f857(f234(a1),f2(a1)),x56872))
% 15.02/14.79 [5707]P106(f857(f137(x57071),x57072))+~P106(f857(f137(x57071),f857(f167(x57071),x57072)))
% 15.02/14.79 [5708]P106(f857(f137(x57081),x57082))+~P106(f857(f137(x57081),f857(f168(x57081),x57082)))
% 15.02/14.79 [5735]P106(f857(f60(a919),x57351))+P106(f857(f857(f328(a919),f409(x57351,x57352)),x57351))
% 15.02/14.79 [5736]P106(f857(f60(a919),x57361))+P106(f857(f857(f328(a919),f412(x57361,x57362)),x57361))
% 15.02/14.79 [5739]P106(f857(f857(f235(a919),x57392),f857(a112,x57391)))+P106(f857(f857(f235(a919),x57391),x57392))
% 15.02/14.79 [5740]E(f44(a1,x57401,x57402),f291(x57401,x57402))+~P106(f857(f857(f234(a1),f2(a1)),x57402))
% 15.02/14.79 [5744]E(f139(a919,f857(f301(a919,x57441),x57442)),f113(a919))+~P106(f857(f857(f234(a919),x57442),x57441))
% 15.02/14.79 [5745]~P80(x57451)+E(f857(f309(x57451,x57451,f78(x57451)),f857(f281(x57451),x57452)),f857(f303(x57451),f857(f78(x57451),x57452)))
% 15.02/14.79 [5746]~P80(x57461)+E(f857(f309(x57461,x57461,f78(x57461)),f857(f300(x57461),x57462)),f857(f282(x57461),f857(f78(x57461),x57462)))
% 15.02/14.79 [5747]~P80(x57471)+E(f857(f309(x57471,x57471,f78(x57471)),f857(f282(x57471),x57472)),f857(f300(x57471),f857(f78(x57471),x57472)))
% 15.02/14.79 [5748]~P80(x57481)+E(f857(f309(x57481,x57481,f78(x57481)),f857(f303(x57481),x57482)),f857(f281(x57481),f857(f78(x57481),x57482)))
% 15.02/14.79 [5759]E(x57591,f189(f927(x57592,a915)))+P106(f857(f857(f328(x57592),f410(x57591,x57592)),x57591))
% 15.02/14.79 [5760]E(x57601,f189(f927(x57602,a915)))+P106(f857(f857(f328(x57602),f414(x57601,x57602)),x57601))
% 15.02/14.79 [5771]~P106(f857(f857(f235(a919),x57711),x57712))+P106(f857(f857(f234(a919),x57711),x57712))
% 15.02/14.79 [5772]~P106(f857(f857(f235(a1),x57721),x57722))+P106(f857(f857(f234(a1),x57721),x57722))
% 15.02/14.79 [5788]E(f46(x57881,x57882),f857(f857(f251(a1,a1),f2(a1)),x57881))+~P106(f857(f857(f235(a1),x57881),x57882))
% 15.02/14.79 [5790]E(f216(f857(f78(a1),x57901),f857(f78(a1),x57902)),f216(x57901,x57902))+~P106(f857(f857(f235(a1),x57902),f2(a1)))
% 15.02/14.79 [5801]E(x58011,x58012)+~E(f857(a5,f857(a112,f857(a22,x58011))),f857(a5,f857(a112,f857(a22,x58012))))
% 15.02/14.79 [5806]E(f46(x58061,x58062),f857(f857(f251(a1,a1),f2(a1)),x58061))+~P106(f857(f857(f234(a1),x58062),f2(a1)))
% 15.02/14.79 [5835]E(f44(a919,f857(f103(a919),x58351),f857(f103(a919),x58352)),f2(a919))+~P106(f857(a194,f857(f103(a1),x58351)))
% 15.02/14.79 [5849]P106(f857(f857(f234(a1),f2(a1)),f337(x58491)))+~P106(f857(x58491,f857(f100(a1),x58492)))
% 15.02/14.79 [5882]P42(f302(a1,x58821,x58822))+~P106(f857(f857(f234(a1),f2(a1)),x58821))
% 15.02/14.79 [5887]~P106(f857(f60(x58871),x58872))+P106(f857(f60(f927(x58871,a915)),f857(f307(x58871),x58872)))
% 15.02/14.79 [5900]E(f857(f857(f79(a1),x59001),f857(f100(a1),f350(x59002,x59001))),x59002)+~P106(f857(f857(f234(a1),x59001),x59002))
% 15.02/14.79 [5908]P106(f857(f857(f234(a919),x59081),x59082))+P106(f857(f857(f234(a919),f857(a112,x59082)),x59081))
% 15.02/14.79 [5952]E(f857(f857(f35(a919),f857(f103(a919),x59521)),f857(f103(a919),x59522)),f2(a919))+~P106(f857(a194,f857(f103(a1),x59521)))
% 15.02/14.79 [5953]E(f857(f857(f80(a919),f857(f103(a919),x59531)),f857(f103(a919),x59532)),f2(a919))+~P106(f857(f857(f235(a1),x59531),a82))
% 15.02/14.79 [5955]P106(f857(f857(f234(a919),x59551),f857(a112,x59552)))+~P106(f857(f857(f234(a919),x59551),x59552))
% 15.02/14.79 [5957]P106(f857(f857(f235(a919),x59571),f857(a112,x59572)))+~P106(f857(f857(f234(a919),x59571),x59572))
% 15.02/14.79 [5959]P106(f857(f857(f235(a919),x59591),f857(a112,x59592)))+~P106(f857(f857(f235(a919),x59591),x59592))
% 15.02/14.79 [5962]~E(x59621,x59622)+P106(f857(f857(f235(a1),x59621),f857(f857(f79(a1),x59622),f77(a1))))
% 15.02/14.79 [5965]E(f44(a1,x59651,x59652),f2(a1))+E(f857(f857(f3(a1),x59652),f44(a1,x59651,x59652)),f44(a1,f857(f78(a1),x59651),x59652))
% 15.02/14.79 [5974]E(x59741,f113(x59742))+P106(f857(f857(f328(x59742),f144(x59742,x59741)),f857(f172(x59742),x59741)))
% 15.02/14.79 [5986]E(f84(f926(a919,a919),f47(x59861,x59862)),f857(f857(f251(a919,a919),f2(a919)),x59861))+~P106(f857(f857(f235(a919),x59861),x59862))
% 15.02/14.79 [6021]E(f857(f857(f3(a919),f857(f103(a919),x60211)),f857(f103(a919),x60212)),f857(f103(a919),x60211))+~P106(f857(f857(f235(a1),x60212),a82))
% 15.02/14.79 [6022]E(f857(f857(f79(a919),f857(f103(a919),x60221)),f857(f103(a919),x60222)),f857(f103(a919),x60222))+~P106(f857(f857(f235(a1),x60221),a82))
% 15.02/14.79 [6029]E(f857(a112,f857(f857(f79(a919),x60291),f861(x60292,x60291))),x60292)+~P106(f857(f857(f235(a919),x60291),x60292))
% 15.02/14.79 [6053]P106(f857(x60531,x60532))+~P106(f857(x60531,f857(a88,f582(x60532,x60531))))
% 15.02/14.79 [6054]P106(f857(x60541,x60542))+~P106(f857(x60541,f857(a5,f817(x60542,x60541))))
% 15.02/14.79 [6063]~P106(f857(f857(f235(a919),x60631),f857(a112,x60632)))+P106(f857(f857(f234(a919),x60631),x60632))
% 15.02/14.79 [6113]E(f857(f857(f308(a919),x61131),f857(f301(a919,x61132),x61131)),f857(f301(a919,x61132),f857(a112,x61131)))+~P106(f857(f857(f234(a919),x61132),x61131))
% 15.02/14.79 [6115]E(x61151,f113(x61152))+E(f857(f857(f134(x61152),f114(x61152,x61151)),f857(f857(f151(x61152),f144(x61152,x61151)),f113(x61152))),x61151)
% 15.02/14.79 [6132]P106(f857(f60(x61321),x61322))+~P106(f857(f857(f235(a919),f2(a919)),f857(f34(x61321),x61322)))
% 15.02/14.79 [6136]~E(x61361,f189(f927(x61362,a915)))+~P106(f857(f857(f235(a919),f2(a919)),f857(f34(x61362),x61361)))
% 15.02/14.79 [6148]~P106(f857(f857(f235(a919),x61481),x61482))+P106(f857(f857(f234(a919),f857(a112,x61481)),x61482))
% 15.02/14.79 [6152]~P109(x61521)+E(f150(x61521,x61521,f7(x61521),f152(x61521,x61522)),f139(x61521,f857(f172(x61521),x61522)))
% 15.02/14.79 [6155]E(x61551,f113(x61552))+P106(f857(f857(f328(x61552),f857(f141(x61552),x61551)),f857(f172(x61552),x61551)))
% 15.02/14.79 [6161]~P127(x61611)+P106(f857(f857(f235(x61611),x61612),f857(f857(f79(x61611),x61612),f77(x61611))))
% 15.02/14.79 [6163]~P87(x61631)+P106(f857(f857(f234(x61631),f857(f78(x61631),x61632)),f857(f75(x61631),x61632)))
% 15.02/14.79 [6177]~E(x61771,x61772)+E(f289(a919,f286(a919),x61771,x61772),f857(f857(f308(a919),x61771),f189(f927(a919,a915))))
% 15.02/14.79 [6195]P106(f857(f60(a919),x61951))+~P106(f857(f857(f234(a919),f412(x61951,x61952)),x61952))
% 15.02/14.79 [6196]P106(f857(f60(a919),x61961))+~P106(f857(f857(f235(a919),f409(x61961,x61962)),x61962))
% 15.02/14.79 [6199]~P106(f857(f60(f926(x61991,x61991)),x61992))+P106(f857(f60(x61991),f857(f280(x61991),x61992)))
% 15.02/14.79 [6255]E(f289(a919,f286(a919),x62551,x62552),f189(f927(a919,a915)))+P106(f857(f857(f286(a919),x62551),x62552))
% 15.02/14.79 [6261]~P106(f857(f857(f235(a919),x62612),f857(a112,x62611)))+~P106(f857(f857(f235(a919),x62611),x62612))
% 15.02/14.79 [6262]~P110(x62621)+E(f857(f857(f101(f927(x62621,a915)),f857(f300(x62621),x62622)),f857(f282(x62621),x62622)),f857(f857(f308(x62621),x62622),f189(f927(x62621,a915))))
% 15.02/14.79 [6274]P106(f857(f60(x62741),x62742))+~P106(f857(f60(f927(x62741,a915)),f857(f307(x62741),x62742)))
% 15.02/14.79 [6297]P106(f857(f857(f234(a919),f857(a112,x62971)),f857(a112,x62972)))+~P106(f857(f857(f234(a919),x62971),x62972))
% 15.02/14.79 [6298]P106(f857(f857(f234(a919),f857(a22,x62981)),f857(a22,x62982)))+~P106(f857(f857(f234(a99),x62981),x62982))
% 15.02/14.79 [6299]P106(f857(f857(f234(a99),f857(a5,x62991)),f857(a5,x62992)))+~P106(f857(f857(f234(a919),x62991),x62992))
% 15.02/14.79 [6301]P106(f857(f857(f235(a919),f857(a112,x63011)),f857(a112,x63012)))+~P106(f857(f857(f235(a919),x63011),x63012))
% 15.02/14.79 [6302]P106(f857(f857(f235(a919),f857(a22,x63021)),f857(a22,x63022)))+~P106(f857(f857(f235(a99),x63021),x63022))
% 15.02/14.79 [6303]P106(f857(f857(f235(a99),f857(a5,x63031)),f857(a5,x63032)))+~P106(f857(f857(f235(a919),x63031),x63032))
% 15.02/14.79 [6308]E(x63081,x63082)+~E(f857(f309(a919,a1,f100(a1)),x63081),f857(f309(a919,a1,f100(a1)),x63082))
% 15.02/14.79 [6324]P106(f857(f857(f234(a919),x63241),x63242))+~P106(f857(f857(f234(a919),f857(a112,x63241)),x63242))
% 15.02/14.79 [6327]P106(f857(f857(f235(a919),x63271),x63272))+~P106(f857(f857(f234(a919),f857(a112,x63271)),x63272))
% 15.02/14.79 [6328]P106(f857(f857(f235(a919),x63281),x63282))+~P106(f857(f857(f235(a919),f857(a112,x63281)),x63282))
% 15.02/14.79 [6346]E(f44(a1,x63461,x63462),f2(a1))+E(f857(f857(f3(a1),f44(a1,x63461,x63462)),x63462),f44(a1,x63461,f857(f78(a1),x63462)))
% 15.02/14.79 [6413]E(f857(f34(f927(x64131,a915)),f857(f307(x64131),x64132)),f857(f857(f243(a919),f857(a112,f857(a112,f2(a919)))),f857(f34(x64131),x64132)))+~P106(f857(f60(x64131),x64132))
% 15.02/14.79 [6416]E(x64161,f113(x64162))+E(f857(f857(f164(x64162),x64161),f857(f857(f3(a919),f857(f190(f920(x64162)),x64161)),f77(a919))),f144(x64162,x64161))
% 15.02/14.79 [6438]E(x64381,f113(x64382))+E(f857(f857(f134(x64382),f857(f171(x64382),x64381)),f857(f857(f151(x64382),f857(f141(x64382),x64381)),f113(x64382))),f857(f167(x64382),x64381))
% 15.02/14.79 [6469]~P106(f857(f60(x64691),f36(f927(x64691,a915),x64692)))+P106(f857(f60(f927(x64691,a915)),x64692))
% 15.02/14.79 [6491]P106(f857(f857(f234(a919),f857(f103(a919),x64911)),f857(f103(a919),x64912)))+~P106(f857(f857(f234(a1),x64911),a82))
% 15.02/14.79 [6514]~P106(f857(f857(f235(a1),x65141),x65142))+P106(f857(f857(f234(a1),x65141),f857(f857(f3(a1),x65142),f77(a1))))
% 15.02/14.79 [6515]~P106(f857(f857(f234(a1),x65151),x65152))+P106(f857(f857(f235(a1),x65151),f857(f857(f79(a1),x65152),f77(a1))))
% 15.02/14.79 [6516]~P106(f857(f857(f235(a1),x65161),x65162))+P106(f857(f857(f235(a1),x65161),f857(f857(f79(a1),x65162),f77(a1))))
% 15.02/14.79 [6518]~P106(f857(f857(f234(a1),x65181),x65182))+P106(f857(f857(f234(a919),f857(f103(a919),x65181)),f857(f103(a919),x65182)))
% 15.02/14.79 [6519]~P106(f857(f857(f234(a1),x65191),x65192))+P106(f857(f857(f234(a1),f857(f103(a1),x65191)),f857(f103(a1),x65192)))
% 15.02/14.79 [6521]~P106(f857(f857(f234(a919),x65211),x65212))+P106(f857(f857(f234(a1),f857(f100(a1),x65211)),f857(f100(a1),x65212)))
% 15.02/14.79 [6522]~P106(f857(f857(f235(a1),x65221),x65222))+P106(f857(f857(f235(a1),f857(f103(a1),x65221)),f857(f103(a1),x65222)))
% 15.02/14.79 [6524]~P106(f857(f857(f235(a919),x65241),x65242))+P106(f857(f857(f235(a1),f857(f100(a1),x65241)),f857(f100(a1),x65242)))
% 15.02/14.79 [6545]~P106(f857(f857(f234(a919),x65451),x65452))+~P106(f857(f857(f234(a919),f857(a112,x65452)),x65451))
% 15.02/14.79 [6588]~P106(f857(f857(f234(a919),f857(a112,x65881)),f857(a112,x65882)))+P106(f857(f857(f234(a919),x65881),x65882))
% 15.02/14.79 [6589]~P106(f857(f857(f234(a99),f857(a5,x65891)),f857(a5,x65892)))+P106(f857(f857(f234(a919),x65891),x65892))
% 15.02/14.79 [6590]~P106(f857(f857(f234(a919),f857(a22,x65901)),f857(a22,x65902)))+P106(f857(f857(f234(a99),x65901),x65902))
% 15.02/14.79 [6592]~P106(f857(f857(f235(a919),f857(a112,x65921)),f857(a112,x65922)))+P106(f857(f857(f235(a919),x65921),x65922))
% 15.02/14.79 [6593]~P106(f857(f857(f235(a99),f857(a5,x65931)),f857(a5,x65932)))+P106(f857(f857(f235(a919),x65931),x65932))
% 15.02/14.79 [6594]~P106(f857(f857(f235(a919),f857(a104,x65941)),f857(a104,x65942)))+P106(f857(f857(f235(a1),x65941),x65942))
% 15.02/14.79 [6595]~P106(f857(f857(f235(a919),f857(a22,x65951)),f857(a22,x65952)))+P106(f857(f857(f235(a99),x65951),x65952))
% 15.02/14.79 [6634]~P106(f857(f857(f235(a919),f857(a104,x66342)),f857(a104,x66341)))+P106(f857(f857(f235(a1),f2(a1)),x66341))
% 15.02/14.79 [6665]P106(f857(f857(f234(a1),f2(a1)),f44(a1,x66651,x66652)))+~P106(f857(f857(f235(a1),f2(a1)),x66652))
% 15.02/14.79 [6827]P39(x68271,x68272)+~E(f857(f857(f288(x68271,x68271,x68271),x68272),x68272),f189(f927(f926(x68271,x68271),a915)))
% 15.02/14.79 [6841]~P39(x68411,x68412)+P39(x68411,f857(f857(f288(x68411,x68411,x68411),x68412),x68412))
% 15.02/14.79 [6852]P106(f857(f857(f234(a1),x68521),x68522))+~P106(f857(f857(f235(a1),x68521),f857(f857(f79(a1),x68522),f77(a1))))
% 15.02/14.79 [6853]P106(f857(f857(f235(a1),x68531),x68532))+~P106(f857(f857(f234(a1),x68531),f857(f857(f3(a1),x68532),f77(a1))))
% 15.02/14.79 [6856]P106(f857(f857(f234(a919),x68561),x68562))+~P106(f857(f857(f234(a1),f857(f100(a1),x68561)),f857(f100(a1),x68562)))
% 15.02/14.79 [6857]P106(f857(f857(f234(a1),x68571),x68572))+~P106(f857(f857(f234(a1),f857(f103(a1),x68571)),f857(f103(a1),x68572)))
% 15.02/14.79 [6859]P106(f857(f857(f235(a919),x68591),x68592))+~P106(f857(f857(f235(a1),f857(f100(a1),x68591)),f857(f100(a1),x68592)))
% 15.02/14.79 [6860]P106(f857(f857(f235(a1),x68601),x68602))+~P106(f857(f857(f235(a919),f857(f103(a919),x68601)),f857(f103(a919),x68602)))
% 15.02/14.79 [6861]P106(f857(f857(f235(a1),x68611),x68612))+~P106(f857(f857(f235(a1),f857(f103(a1),x68611)),f857(f103(a1),x68612)))
% 15.02/14.79 [6933]~E(f289(a919,f286(a919),x69331,x69332),f189(f927(a919,a915)))+~P106(f857(f857(f286(a919),x69331),x69332))
% 15.02/14.79 [6958]~E(f699(x69582,x69581),f113(x69581))+E(f857(f142(f920(x69581),f920(x69581),f134(x69581),f113(x69581)),x69582),f113(x69581))
% 15.02/14.79 [6959]~E(f700(x69592,x69591),f113(x69591))+E(f857(f142(f920(x69591),f920(x69591),f134(x69591),f113(x69591)),x69592),f113(x69591))
% 15.02/14.79 [6963]~P6(x69631)+E(f857(f142(x69631,x69631,f110(x69631),f189(x69631)),x69632),f36(x69631,f857(f172(x69631),x69632)))
% 15.02/14.79 [6964]~P6(x69641)+E(f857(f142(x69641,x69641,f101(x69641),f241(x69641)),x69642),f37(x69641,f857(f172(x69641),x69642)))
% 15.02/14.79 [6978]E(x69781,f2(a99))+E(f857(f857(f79(a919),f857(a22,f857(f857(f3(a99),x69781),f77(a99)))),f857(a112,x69782)),f857(f857(f79(a919),f857(a22,x69781)),x69782))
% 15.02/14.79 [7027]P106(f857(f857(f235(a1),f857(f857(f3(a1),x70271),x70272)),f2(a1)))+~P106(f857(f857(f235(a1),x70271),x70272))
% 15.02/14.79 [7052]~P109(x70521)+E(f857(f857(f110(f927(x70521,a915)),f857(f857(f308(x70521),x70522),f189(f927(x70521,a915)))),f857(f303(x70521),x70522)),f857(f282(x70521),x70522))
% 15.02/14.79 [7129]~P61(x71291,x71292)+P39(x71291,f857(f261(f926(x71291,x71291)),f857(f256(x71291,x71291,a915),x71292)))
% 15.02/14.79 [7130]~P61(x71301,x71302)+P59(x71301,f857(f261(f926(x71301,x71301)),f857(f256(x71301,x71301,a915),x71302)))
% 15.02/14.79 [7131]~P51(x71311,x71312)+P40(x71311,f857(f261(f926(x71311,x71311)),f857(f256(x71311,x71311,a915),x71312)))
% 15.02/14.79 [7132]~P52(x71321,x71322)+P53(x71321,f857(f261(f926(x71321,x71321)),f857(f256(x71321,x71321,a915),x71322)))
% 15.02/14.79 [7133]E(x71331,f189(f927(x71332,a915)))+~P106(f857(f857(f234(f927(x71332,a915)),x71331),f189(f927(x71332,a915))))
% 15.02/14.79 [7214]~P106(f857(f857(f235(a919),f2(a919)),x72142))+P106(f857(f857(f234(a919),f44(a919,x72141,x72142)),x72142))
% 15.02/14.79 [7215]~P106(f857(f857(f234(a1),f2(a1)),x72151))+P106(f857(f857(f234(a1),f44(a1,x72151,x72152)),x72151))
% 15.02/14.79 [7216]~P106(f857(f857(f235(a919),f2(a919)),x72162))+P106(f857(f857(f235(a919),f44(a919,x72161,x72162)),x72162))
% 15.02/14.79 [7218]~P106(f857(f857(f235(a1),f2(a1)),x72182))+P106(f857(f857(f235(a1),f44(a1,x72181,x72182)),x72182))
% 15.02/14.79 [7296]~P110(x72961)+E(f857(f857(f3(f927(x72961,a915)),f857(f857(f308(x72961),x72962),f189(f927(x72961,a915)))),f857(f281(x72961),x72962)),f857(f857(f308(x72961),x72962),f189(f927(x72961,a915))))
% 15.02/14.79 [7371]~P45(x73711,x73712)+P54(x73711,f241(f927(x73711,a915)),f857(f261(f926(x73711,x73711)),f857(f256(x73711,x73711,a915),x73712)))
% 15.02/14.79 [7372]P106(f857(x73721,x73722))+P106(f857(f857(f328(f927(f926(a919,a919),a915)),f582(x73722,x73721)),a98))
% 15.02/14.79 [7417]E(f857(f857(f134(a919),f139(a919,f857(f301(a919,x74171),x74172))),f857(f857(f151(a919),x74172),f113(a919))),f139(a919,f857(f301(a919,x74171),f857(a112,x74172))))+~P106(f857(f857(f234(a919),x74171),x74172))
% 15.02/14.79 [7566]E(x75661,f2(a919))+~E(f857(f142(a919,a919,f79(a919),x75661),x75662),f2(a919))
% 15.02/14.79 [7591]~P106(f857(f857(f235(a1),f857(f857(f3(a1),x75911),x75912)),f2(a1)))+P106(f857(f857(f235(a1),x75911),x75912))
% 15.02/14.79 [7619]P39(x76191,x76192)+~P39(x76191,f857(f857(f288(x76191,x76191,x76191),x76192),x76192))
% 15.02/14.79 [7645]~P106(f857(f857(f234(a919),f857(a112,x76451)),x76452))+P106(f185(a915,a238,f857(f234(a919),x76451),x76452))
% 15.02/14.79 [7798]P26(a919,a919,f857(f857(f9(a919,a919,a919),f3(a919)),x77981),x77982)+P106(f857(f857(f328(a919),f583(x77981,x77982)),x77982))
% 15.02/14.79 [7856]E(f857(f857(f857(f64(a919,x78561,f79(a919)),f857(f18(a919,x78561),f77(a919))),f2(a919)),x78562),f857(f34(x78561),x78562))+~P106(f857(f60(x78561),x78562))
% 15.02/14.79 [7898]P26(a919,a919,f857(f857(f9(a919,a919,a919),f3(a919)),x78981),x78982)+~P106(f857(f857(f234(a919),x78981),f583(x78981,x78982)))
% 15.02/14.79 [7953]P39(x79531,x79532)+P106(f857(f857(f234(f927(x79531,a915)),f581(x79532,x79531)),f857(f284(x79531,x79531,x79532),f581(x79532,x79531))))
% 15.02/14.79 [7958]P61(x79581,x79582)+~P39(x79581,f857(f261(f926(x79581,x79581)),f857(f256(x79581,x79581,a915),x79582)))
% 15.02/14.79 [7959]P51(x79591,x79592)+~P40(x79591,f857(f261(f926(x79591,x79591)),f857(f256(x79591,x79591,a915),x79592)))
% 15.02/14.79 [7960]P52(x79601,x79602)+~P53(x79601,f857(f261(f926(x79601,x79601)),f857(f256(x79601,x79601,a915),x79602)))
% 15.02/14.79 [8026]P106(f857(f857(f234(a919),f857(a112,x80261)),x80262))+~P106(f185(a915,a238,f857(f234(a919),x80261),x80262))
% 15.02/14.79 [8083]P106(f857(f857(f328(f926(a919,a919)),f857(f857(f251(a919,a919),x80831),x80832)),f306(a919,a316)))+~P106(f857(f857(f234(a919),x80831),x80832))
% 15.02/14.79 [8180]P45(x81801,x81802)+~P54(x81801,f241(f927(x81801,a915)),f857(f261(f926(x81801,x81801)),f857(f256(x81801,x81801,a915),x81802)))
% 15.02/14.79 [8235]~P106(f857(f137(x82351),x82352))+P106(f857(f137(f927(x82351,a915)),f857(f857(f154(f920(x82351),f927(x82351,a915)),f172(x82351)),f53(x82351,x82352))))
% 15.02/14.79 [8435]~P39(x84351,f857(f285(x84351,x84351),x84352))+P39(x84351,f857(f285(x84351,x84351),f857(f857(f288(x84351,x84351,x84351),x84352),f306(x84351,x84352))))
% 15.02/14.79 [8533]P27(x85331,a919,f821(x85332,x85331),x85332,f857(f301(a919,f2(a919)),f857(f34(x85331),x85332)))+~P106(f857(f60(x85331),x85332))
% 15.02/14.79 [8534]P27(a919,x85341,f822(x85342,x85341),f857(f301(a919,f2(a919)),f857(f34(x85341),x85342)),x85342)+~P106(f857(f60(x85341),x85342))
% 15.02/14.79 [8551]P27(a919,x85511,f823(x85512,x85511),f302(a919,f77(a919),f857(f34(x85511),x85512)),x85512)+~P106(f857(f60(x85511),x85512))
% 15.02/14.79 [8560]P106(f857(f60(f926(x85601,x85601)),f857(f857(f288(x85601,x85601,x85601),x85602),f306(x85601,x85602))))+~P106(f857(f60(f926(x85601,x85601)),x85602))
% 15.02/14.79 [8587]E(x85871,f2(a1))+P106(f857(f48(x85872,x85871),f857(f857(f251(a1,a1),f857(f857(f35(a1),x85872),x85871)),f44(a1,x85872,x85871))))
% 15.02/14.79 [8600]~P106(f857(f857(f328(f926(a919,a919)),f857(f857(f251(a919,a919),x86001),x86002)),f306(a919,a316)))+P106(f857(f857(f234(a919),x86001),x86002))
% 15.02/14.79 [8616]~P83(x86161)+E(f857(f142(x86161,x86161,f857(f9(x86161,x86161,x86161),f79(x86161)),f2(x86161)),f857(f168(x86161),x86162)),f857(f142(x86161,x86161,f79(x86161),f2(x86161)),x86162))
% 15.02/14.79 [8787]~P109(x87871)+E(f857(f142(f920(x87871),x87871,f857(f9(x87871,f920(x87871),f920(x87871)),f148(x87871,x87871,f7(x87871))),f113(x87871)),x87872),f150(x87871,x87871,f7(x87871),x87872))
% 15.02/14.79 [8898]~P59(x88981,f857(f261(f926(x88981,x88981)),f857(f256(x88981,x88981,a915),x88982)))+P59(x88981,f857(f261(f926(x88981,x88981)),f857(f256(x88981,x88981,a915),f242(x88981,x88981,x88982))))
% 15.02/14.79 [8912]P106(f857(f857(f328(f926(a919,a919)),f857(f857(f251(a919,a919),x89121),x89122)),f857(f857(f288(a919,a919,a919),a316),f306(a919,a316))))+~P106(f857(f857(f235(a919),x89121),x89122))
% 15.02/14.79 [8958]~P106(f857(f60(f926(x89581,x89581)),f857(f857(f288(x89581,x89581,x89581),x89582),f306(x89581,x89582))))+P106(f857(f60(f926(x89581,x89581)),x89582))
% 15.02/14.79 [9016]~P59(x90161,f857(f261(f926(x90161,x90161)),f857(f256(x90161,x90161,a915),f242(x90161,x90161,x90162))))+P59(x90161,f857(f261(f926(x90161,x90161)),f857(f256(x90161,x90161,a915),x90162)))
% 15.02/14.79 [9213]P59(x92131,x92132)+P106(f857(f857(f328(f926(x92131,x92131)),f857(f857(f251(x92131,x92131),f610(x92132,x92131)),f610(x92132,x92131))),f857(f857(f288(x92131,x92131,x92131),x92132),f306(x92131,x92132))))
% 15.02/14.79 [9214]P59(x92141,x92142)+P106(f857(f857(f328(f926(x92141,x92141)),f857(f857(f251(x92141,x92141),f621(x92142,x92141)),f621(x92142,x92141))),f857(f857(f288(x92141,x92141,x92141),x92142),f306(x92141,x92142))))
% 15.02/14.79 [9331]~P106(f857(f857(f328(f926(a919,a919)),f857(f857(f251(a919,a919),x93311),x93312)),f857(f857(f288(a919,a919,a919),a316),f306(a919,a316))))+P106(f857(f857(f235(a919),x93311),x93312))
% 15.02/14.79 [5270]~P94(x52701)+E(f857(f857(f79(x52701),f857(f103(x52701),a82)),x52702),x52702)
% 15.02/14.79 [5299]~P96(x52991)+E(f857(f857(f110(x52991),f857(f78(x52991),x52992)),x52992),f241(x52991))
% 15.02/14.79 [5300]~P96(x53001)+E(f857(f857(f101(x53001),f857(f78(x53001),x53002)),x53002),f189(x53001))
% 15.02/14.79 [5301]~P69(x53011)+E(f857(f857(f79(x53011),f857(f78(x53011),x53012)),x53012),f2(x53011))
% 15.02/14.79 [5302]~P76(x53021)+E(f857(f857(f79(x53021),f857(f78(x53021),x53022)),x53022),f2(x53021))
% 15.02/14.79 [5336]~P94(x53361)+E(f857(f857(f80(x53361),f857(f103(x53361),a97)),x53362),f857(f78(x53361),x53362))
% 15.02/14.79 [5498]~P115(x54981)+E(f857(f857(f80(x54981),f857(f78(x54981),f77(x54981))),x54982),f857(f78(x54981),x54982))
% 15.02/14.79 [5543]E(f857(f75(a1),x55431),f77(a1))+~E(f857(f75(a1),f857(f857(f80(a1),x55431),x55432)),f77(a1))
% 15.02/14.79 [5635]~P94(x56351)+E(f857(f857(f79(x56351),f77(x56351)),f857(f103(x56351),x56352)),f857(f103(x56351),f857(f857(f3(a1),x56352),a97)))
% 15.02/14.79 [5688]~P2(x56881)+E(f12(x56881,f857(f857(f308(x56881),x56882),f189(f927(x56881,a915)))),x56882)
% 15.02/14.79 [5689]~P2(x56891)+E(f13(x56891,f857(f857(f308(x56891),x56892),f189(f927(x56891,a915)))),x56892)
% 15.02/14.79 [5690]~P109(x56901)+E(f16(x56901,f857(f857(f308(x56901),x56902),f189(f927(x56901,a915)))),x56902)
% 15.02/14.79 [5691]~P6(x56911)+E(f36(x56911,f857(f857(f308(x56911),x56912),f189(f927(x56911,a915)))),x56912)
% 15.02/14.79 [5692]~P6(x56921)+E(f37(x56921,f857(f857(f308(x56921),x56922),f189(f927(x56921,a915)))),x56922)
% 15.02/14.79 [5693]~P109(x56931)+E(f17(x56931,f857(f857(f308(x56931),x56932),f189(f927(x56931,a915)))),x56932)
% 15.02/14.79 [5715]E(f857(f857(f79(a919),x57151),f857(f857(f3(a919),x57152),x57151)),x57152)+P106(f857(f857(f235(a919),x57152),x57151))
% 15.02/14.79 [5754]E(x57541,f113(x57542))+P106(f857(f857(f235(a919),f2(a919)),f857(f190(f920(x57542)),x57541)))
% 15.02/14.79 [5879]~P109(x58791)+E(f14(x58791,f188(x58791),f857(f857(f308(x58791),x58792),f189(f927(x58791,a915)))),x58792)
% 15.02/14.79 [5880]~P109(x58801)+E(f15(x58801,f233(x58801),f857(f857(f308(x58801),x58802),f189(f927(x58801,a915)))),x58802)
% 15.02/14.79 [5941]E(f857(f857(f3(a919),x59411),f857(f857(f3(a919),x59411),x59412)),x59412)+~P106(f857(f857(f234(a919),x59412),x59411))
% 15.02/14.79 [5942]E(f857(f857(f79(a919),x59421),f857(f857(f3(a919),x59422),x59421)),x59422)+~P106(f857(f857(f234(a919),x59421),x59422))
% 15.02/14.79 [5964]E(f44(a919,f857(f857(f3(a919),x59641),x59642),x59642),f44(a919,x59641,x59642))+P106(f857(f857(f235(a919),x59641),x59642))
% 15.02/14.79 [5975]E(f857(f78(a1),f857(f857(f35(a1),x59751),f857(f78(a1),x59752))),f292(x59751,x59752))+P106(f857(f857(f234(a1),f2(a1)),x59752))
% 15.02/14.79 [5977]~E(x59772,f2(a919))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f243(a919),x59771),x59772)))
% 15.02/14.79 [6031]~P94(x60311)+E(f857(f857(f79(x60311),f857(f78(x60311),f77(x60311))),f857(f103(x60311),x60312)),f857(f103(x60311),f857(f857(f79(a1),x60312),a97)))
% 15.02/14.79 [6033]E(f857(f857(f243(a919),f857(f103(a919),x60331)),x60332),f857(f857(f243(a919),f2(a919)),x60332))+~P106(f857(a194,f857(f103(a1),x60331)))
% 15.02/14.79 [6140]E(f857(f141(a919),f139(a919,f857(f301(a919,x61401),x61402))),x61401)+~P106(f857(f857(f235(a919),x61401),x61402))
% 15.02/14.79 [6156]E(f857(f857(f80(a919),f857(f103(a919),x61561)),f857(f103(a919),x61562)),f857(f103(a919),f857(f857(f80(a1),x61561),x61562)))+P106(f857(f857(f235(a1),x61561),a82))
% 15.02/14.79 [6162]~P128(x61621)+P106(f857(f857(f234(x61621),f2(x61621)),f857(f857(f80(x61621),x61622),x61622)))
% 15.02/14.79 [6174]E(f857(f857(f3(a919),f857(a112,x61741)),x61742),f857(a112,f857(f857(f3(a919),x61741),x61742)))+~P106(f857(f857(f234(a919),x61742),x61741))
% 15.02/14.79 [6178]E(f44(a919,f857(f857(f3(a919),x61781),x61782),x61782),f44(a919,x61781,x61782))+~P106(f857(f857(f234(a919),x61782),x61781))
% 15.02/14.79 [6232]E(f857(f857(f243(a919),f857(a104,x62321)),x62322),f857(a104,f857(f857(f243(a1),x62321),x62322)))+~P106(f857(f857(f234(a1),f2(a1)),x62321))
% 15.02/14.79 [6250]P106(f857(f137(x62501),x62502))+P106(f857(f857(f235(a919),f668(x62502,x62501)),f857(f190(f920(x62501)),x62502)))
% 15.02/14.79 [6251]P106(f857(f137(x62511),x62512))+P106(f857(f857(f235(a919),f672(x62512,x62511)),f857(f190(f920(x62511)),x62512)))
% 15.02/14.79 [6268]~E(x62681,f113(x62682))+~P106(f857(f857(f235(a919),f2(a919)),f857(f190(f920(x62682)),x62681)))
% 15.02/14.79 [6279]E(f144(a919,f139(a919,f857(f301(a919,x62791),x62792))),f857(f857(f3(a919),x62792),f77(a919)))+~P106(f857(f857(f235(a919),x62791),x62792))
% 15.02/14.79 [6282]E(f857(f857(f79(a1),x62821),f857(f100(a1),f857(a112,f352(x62822,x62821)))),x62822)+~P106(f857(f857(f235(a1),x62821),x62822))
% 15.02/14.79 [6289]E(x62891,f2(a919))+E(f857(f857(f80(a919),x62892),f857(f857(f243(a919),x62892),f857(f857(f3(a919),x62891),f77(a919)))),f857(f857(f243(a919),x62892),x62891))
% 15.02/14.79 [6318]E(f857(f857(f80(a919),f857(a104,x63181)),f857(a104,x63182)),f857(a104,f857(f857(f80(a1),x63181),x63182)))+~P106(f857(f857(f234(a1),f2(a1)),x63181))
% 15.02/14.79 [6319]E(f857(f857(f35(a919),f857(a104,x63191)),f857(a104,x63192)),f857(a104,f857(f857(f35(a1),x63191),x63192)))+~P106(f857(f857(f234(a1),f2(a1)),x63191))
% 15.02/14.79 [6334]~P113(x63341)+E(f857(f857(f79(x63341),x63342),x63342),f857(f857(f80(x63341),f857(f857(f79(x63341),f77(x63341)),f77(x63341))),x63342))
% 15.02/14.79 [6355]E(f857(f857(f3(a1),f857(f100(a1),x63551)),f857(f100(a1),x63552)),f857(f100(a1),f857(f857(f3(a919),x63551),x63552)))+~P106(f857(f857(f234(a919),x63552),x63551))
% 15.02/14.79 [6357]E(f857(f857(f251(a1,a1),f857(f103(a1),a97)),f857(f857(f79(a1),x63571),x63572)),f49(x63571,x63572))+~P106(f857(f857(f234(a1),x63572),f2(a1)))
% 15.02/14.79 [6391]E(f179(x63911,x63912),f113(f920(x63911)))+P106(f857(f857(f328(f920(x63911)),f667(x63912,x63911)),f857(f172(f920(x63911)),x63912)))
% 15.02/14.79 [6400]E(f116(a1,f857(f129(a1),x64001),f128(x64002,f857(f857(f79(a1),x64001),f77(a1)))),f128(x64002,x64001))+P106(f857(f857(f235(a1),x64002),x64001))
% 15.02/14.79 [6475]E(f857(f857(f151(a1),x64751),f178(f857(f857(f79(a1),x64751),f77(a1)),x64752)),f178(x64751,x64752))+~P106(f857(f857(f234(a1),x64751),x64752))
% 15.02/14.79 [6517]~P106(f857(f857(f235(a919),x65172),x65171))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f3(a919),x65171),x65172)))
% 15.02/14.79 [6550]~P106(f857(f857(f235(a919),x65501),f857(a104,x65502)))+P106(f857(f857(f235(a1),f857(f100(a1),x65501)),x65502))
% 15.02/14.79 [6579]~P109(x65791)+E(f857(f857(f110(f927(x65791,a915)),f857(f281(x65791),x65792)),f857(f857(f308(x65791),x65792),f189(f927(x65791,a915)))),f857(f300(x65791),x65792))
% 15.02/14.79 [6580]~P106(f857(f857(f234(a1),f2(a1)),x65801))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f243(a1),x65801),x65802)))
% 15.02/14.79 [6583]~P106(f857(f857(f235(a919),f2(a919)),x65831))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f243(a919),x65831),x65832)))
% 15.02/14.79 [6610]~E(f857(x66101,f2(a919)),f2(a919))+E(f857(f857(f8(a919,a919),x66101),f302(a919,f857(a112,f2(a919)),x66102)),f857(f857(f8(a919,a919),x66101),f302(a919,f2(a919),x66102)))
% 15.02/14.79 [6673]~P94(x66731)+E(f857(f857(f80(x66731),f857(f857(f79(x66731),f77(x66731)),f77(x66731))),f857(f103(x66731),x66732)),f857(f103(x66731),f857(f857(f79(a1),x66732),x66732)))
% 15.02/14.79 [6690]E(f857(f857(f308(a1),x66901),f302(a1,f857(f857(f79(a1),x66901),f77(a1)),x66902)),f302(a1,x66901,x66902))+P106(f857(f857(f235(a1),x66902),x66901))
% 15.02/14.79 [6691]P106(f857(f857(f235(a919),x66911),f857(a104,x66912)))+~P106(f857(f857(f235(a1),f857(f100(a1),x66911)),x66912))
% 15.02/14.79 [6795]E(f857(a104,f857(f857(f35(a1),f857(f103(a1),x67951)),f857(f103(a1),x67952))),f857(f857(f35(a919),f857(f103(a919),x67951)),f857(f103(a919),x67952)))+P106(f857(a194,f857(f103(a1),x67951)))
% 15.02/14.79 [6854]P106(f857(f857(f235(a919),x68541),x68542))+~P106(f857(f857(f235(a919),f2(a919)),f857(f857(f3(a919),x68542),x68541)))
% 15.02/14.79 [6897]P106(f857(f857(f235(a919),f2(a919)),x68971))+~P106(f857(f857(f235(a919),f2(a919)),f857(f857(f80(a919),x68972),x68971)))
% 15.02/14.79 [6898]P106(f857(f857(f235(a919),f2(a919)),x68981))+~P106(f857(f857(f235(a919),f2(a919)),f857(f857(f80(a919),x68981),x68982)))
% 15.02/14.79 [6916]~P106(f857(f857(f234(a1),x69161),f2(a1)))+E(f857(f857(f80(a919),f857(a104,f857(f78(a1),x69161))),f857(a104,f857(f78(a1),x69162))),f857(a104,f857(f857(f80(a1),x69161),x69162)))
% 15.02/14.79 [6975]~E(x69752,f189(f927(x69751,a915)))+P106(f857(f857(f234(f927(x69751,a915)),x69752),f857(f78(f927(x69751,a915)),x69752)))
% 15.02/14.79 [7037]~P94(x70371)+E(f857(f857(f79(x70371),f857(f857(f79(x70371),f2(x70371)),f857(f103(x70371),x70372))),f857(f103(x70371),x70372)),f857(f103(x70371),f857(f857(f79(a1),x70372),x70372)))
% 15.02/14.79 [7093]~P106(f857(f857(f235(a1),x70931),x70932))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x70931),f77(a1))),x70932))
% 15.02/14.79 [7161]E(x71611,f2(a919))+~P106(f857(f857(f234(a1),f857(f100(a1),x71612)),f857(f78(a1),f857(f100(a1),x71611))))
% 15.02/14.79 [7162]E(x71621,f2(a919))+~P106(f857(f857(f234(a1),f857(f100(a1),x71621)),f857(f78(a1),f857(f100(a1),x71622))))
% 15.02/14.79 [7264]E(f857(f857(f251(a1,a1),f857(f103(a1),a97)),f857(f857(f79(a1),x72641),x72642)),f49(x72641,x72642))+~P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),x72641),x72642)))
% 15.02/14.79 [7308]~P28(x73081,x73082)+P39(x73081,f857(f250(f927(f926(x73081,x73081),a915),f927(f926(x73081,x73081),a915)),x73082))
% 15.02/14.79 [7327]~P106(f857(f857(f234(a919),f857(a112,f2(a919))),x73271))+P106(f857(f857(f234(a919),f857(a112,f2(a919))),f857(f857(f243(a919),x73271),x73272)))
% 15.02/14.79 [7507]~P106(f857(f857(f234(a1),x75071),x75072))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x75071),x75071)),f857(f857(f79(a1),x75072),x75072)))
% 15.02/14.79 [7512]~P106(f857(f857(f235(a1),x75121),x75122))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x75121),x75121)),f857(f857(f79(a1),x75122),x75122)))
% 15.02/14.79 [7567]~P106(f857(f857(f235(a919),f2(a919)),x75671))+P106(f857(f857(f235(a919),f857(f857(f3(a919),x75671),f857(a112,x75672))),x75671))
% 15.02/14.79 [7601]P106(f857(f857(f234(a919),f857(a112,f2(a919))),x76011))+~P106(f857(f857(f234(a919),f857(a112,f2(a919))),f857(f857(f80(a919),x76012),x76011)))
% 15.02/14.79 [7602]P106(f857(f857(f234(a919),f857(a112,f2(a919))),x76021))+~P106(f857(f857(f234(a919),f857(a112,f2(a919))),f857(f857(f80(a919),x76021),x76022)))
% 15.02/14.79 [7606]P106(f857(f857(f234(a919),f857(f857(f164(a919),x76061),x76062)),f857(f165(a919),x76061)))+~P106(f857(f857(f235(a919),x76062),f857(f190(f920(a919)),x76061)))
% 15.02/14.79 [7644]P106(f857(f857(f235(a1),x76441),x76442))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x76441),f77(a1))),x76442))
% 15.02/14.79 [7686]P106(f857(f60(x76861),f241(f927(x76861,a915))))+~P106(f857(f60(f927(x76862,x76861)),f241(f927(f927(x76862,x76861),a915))))
% 15.02/14.79 [7687]P106(f857(f60(x76871),f241(f927(x76871,a915))))+~P106(f857(f60(f925(x76872,x76871)),f241(f927(f925(x76872,x76871),a915))))
% 15.02/14.79 [7688]P106(f857(f60(x76881),f241(f927(x76881,a915))))+~P106(f857(f60(f925(x76881,x76882)),f241(f927(f925(x76881,x76882),a915))))
% 15.02/14.79 [7726]E(x77261,f189(f927(x77262,a915)))+~P106(f857(f857(f234(f927(x77262,a915)),x77261),f857(f78(f927(x77262,a915)),x77261)))
% 15.02/14.79 [7866]E(f857(f142(f920(x78661),f920(x78661),f134(x78661),f113(x78661)),x78662),f113(x78661))+P106(f857(f857(f328(f920(x78661)),f699(x78662,x78661)),f857(f172(f920(x78661)),x78662)))
% 15.02/14.79 [7867]E(f857(f142(f920(x78671),f920(x78671),f134(x78671),f113(x78671)),x78672),f113(x78671))+P106(f857(f857(f328(f920(x78671)),f700(x78672,x78671)),f857(f172(f920(x78671)),x78672)))
% 15.02/14.79 [8101]P106(f857(f857(f234(a1),x81011),x81012))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x81011),x81011)),f857(f857(f79(a1),x81012),x81012)))
% 15.02/14.79 [8106]P106(f857(f857(f235(a1),x81061),x81062))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),x81061),x81061)),f857(f857(f79(a1),x81062),x81062)))
% 15.02/14.79 [8200]~P113(x82001)+E(f857(f857(f80(x82001),f857(f857(f79(x82001),f77(x82001)),f77(x82001))),f857(f857(f8(a919,x82001),f100(x82001)),f302(a919,f77(a919),x82002))),f857(f857(f80(x82001),f857(f100(x82001),x82002)),f857(f857(f79(x82001),f857(f100(x82001),x82002)),f77(x82001))))
% 15.02/14.79 [8249]P106(f857(f857(f328(a919),x82491),x82492))+~P106(f857(f857(f328(a1),f857(f100(a1),x82491)),f857(f309(a919,a1,f100(a1)),x82492)))
% 15.02/14.79 [8407]~P106(f857(f60(x84071),x84072))+E(f857(f309(a919,x84071,f557(x84072,x84071)),f857(f261(a919),f857(f857(f9(a919,a919,a915),f235(a919)),f558(x84072,x84071)))),x84072)
% 15.02/14.79 [8684]P55(x86841,x86842)+P106(f857(f857(f328(f926(x86841,x86841)),f857(f857(f251(x86841,x86841),f395(x86842,x86841)),f395(x86842,x86841))),x86842))
% 15.02/14.79 [8685]P40(x86851,x86852)+P106(f857(f857(f328(f926(x86851,x86851)),f857(f857(f251(x86851,x86851),f788(x86852,x86851)),f792(x86852,x86851))),x86852))
% 15.02/14.79 [8686]P40(x86861,x86862)+P106(f857(f857(f328(f926(x86861,x86861)),f857(f857(f251(x86861,x86861),f792(x86862,x86861)),f793(x86862,x86861))),x86862))
% 15.02/14.79 [8687]P41(x86871,x86872)+P106(f857(f857(f328(f926(x86871,x86871)),f857(f857(f251(x86871,x86871),f707(x86872,x86871)),f706(x86872,x86871))),x86872))
% 15.02/14.79 [8688]P41(x86881,x86882)+P106(f857(f857(f328(f926(x86881,x86881)),f857(f857(f251(x86881,x86881),f706(x86882,x86881)),f707(x86882,x86881))),x86882))
% 15.02/14.79 [8689]P53(x86891,x86892)+P106(f857(f857(f328(f926(x86891,x86891)),f857(f857(f251(x86891,x86891),f803(x86892,x86891)),f804(x86892,x86891))),x86892))
% 15.02/14.79 [8830]~P94(x88301)+E(f857(f857(f3(x88301),f77(x88301)),f857(f103(x88301),x88302)),f857(f103(x88301),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f78(a1),x88302))))
% 15.02/14.79 [8955]~P106(f857(f857(f235(f927(a919,a915)),x89551),x89552))+P106(f857(f857(f235(f927(a1,a915)),f857(f309(a919,a1,f100(a1)),x89551)),f857(f309(a919,a1,f100(a1)),x89552)))
% 15.02/14.79 [8989]~P106(f857(f857(f235(a1),x89891),x89892))+P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x89891),x89891)),a97)),f857(f857(f79(a1),x89892),x89892)))
% 15.02/14.79 [8991]~P106(f857(f857(f235(a1),x89911),x89912))+P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x89911),x89911)),a97)),f857(f857(f79(a1),x89912),x89912)))
% 15.02/14.79 [9064]~P106(f857(f857(f328(a919),x90641),f857(f172(a919),x90642)))+P106(f857(f857(f234(a919),x90641),f857(f142(a919,a919,f79(a919),f2(a919)),x90642)))
% 15.02/14.79 [9153]P48(x91531,x91532)+~P106(f857(f857(f328(f926(x91531,x91531)),f857(f857(f251(x91531,x91531),f386(x91532,x91531)),f386(x91532,x91531))),x91532))
% 15.02/14.79 [9154]P40(x91541,x91542)+~P106(f857(f857(f328(f926(x91541,x91541)),f857(f857(f251(x91541,x91541),f788(x91542,x91541)),f793(x91542,x91541))),x91542))
% 15.02/14.79 [9155]P53(x91551,x91552)+~P106(f857(f857(f328(f926(x91551,x91551)),f857(f857(f251(x91551,x91551),f804(x91552,x91551)),f803(x91552,x91551))),x91552))
% 15.02/14.79 [9294]~P106(f857(f857(f234(f927(a1,a915)),f857(f309(a919,a1,f100(a1)),x92941)),f857(f309(a919,a1,f100(a1)),x92942)))+P106(f857(f857(f234(f927(a919,a915)),x92941),x92942))
% 15.02/14.79 [9295]~P106(f857(f857(f235(f927(a1,a915)),f857(f309(a919,a1,f100(a1)),x92951)),f857(f309(a919,a1,f100(a1)),x92952)))+P106(f857(f857(f235(f927(a919,a915)),x92951),x92952))
% 15.02/14.79 [9379]P106(f857(f857(f235(a1),x93791),x93792))+~P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93791),x93791)),a97)),f857(f857(f79(a1),x93792),x93792)))
% 15.02/14.79 [9381]P106(f857(f857(f235(a1),x93811),x93812))+~P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x93811),x93811)),a97)),f857(f857(f79(a1),x93812),x93812)))
% 15.02/14.79 [10279]~P104(x102791)+E(f116(f920(x102791),f857(f129(f920(x102791)),f113(x102791)),f857(f857(f857(f96(f921(f920(x102791))),f857(f857(f235(a1),f2(a1)),x102792)),f857(f118(f926(x102791,f920(x102791)),f920(x102791),f131(x102791,f920(x102791),f132(x102791,f857(f857(f3(a1),x102792),f77(a1))),f132(f920(x102791),f857(f857(f3(a1),x102792),f77(a1))))),f857(f256(x102791,f920(x102791),f921(f920(x102791))),f857(f857(f10(f927(f920(x102791),f920(x102791)),f927(f920(x102791),f921(f920(x102791))),x102791),f857(f10(f920(x102791),f921(f920(x102791)),f920(x102791)),f129(f920(x102791)))),f151(x102791))))),f115(f920(x102791)))),f132(f920(x102791),x102792))
% 15.02/14.79 [10301]~P106(f857(f60(x103011),x103012))+E(f857(f190(f920(x103011)),f89(f920(x103011),f857(f857(f20(f920(x103011),a915,a915),f857(f857(f10(a915,f927(a915,a915),f920(x103011)),a325),f857(f857(f9(f920(x103011),f927(x103011,a915),a915),f857(f857(f10(f927(x103011,a915),f927(f927(x103011,a915),a915),f920(x103011)),a324),f172(x103011))),x103012))),f137(x103011)))),f215(x103011,x103012))
% 15.02/14.79 [6278]E(f857(f857(f79(a919),f857(f857(f3(a919),x62781),x62782)),x62782),x62781)+~P106(f857(f857(f234(a919),x62782),x62781))
% 15.02/14.79 [6351]E(f857(f857(f35(a919),f857(f857(f80(a919),x63511),x63512)),x63512),x63511)+~P106(f857(f857(f235(a919),f2(a919)),x63512))
% 15.02/14.79 [6352]E(f857(f857(f35(a919),f857(f857(f80(a919),x63521),x63522)),x63521),x63522)+~P106(f857(f857(f235(a919),f2(a919)),x63521))
% 15.02/14.79 [6356]~P72(x63561)+E(f857(f857(f8(a919,x63561),f857(f164(x63561),x63562)),f857(f301(a919,f2(a919)),f857(f190(f920(x63561)),x63562))),f857(f165(x63561),x63562))
% 15.02/14.79 [6467]E(f44(a919,f857(a112,f857(f857(f80(a919),x64671),x64672)),x64671),f77(a919))+~P106(f857(f857(f235(a919),f77(a919)),x64671))
% 15.02/14.79 [6473]E(f857(a112,f857(f857(f79(a919),f857(f103(a919),x64731)),x64732)),f857(f857(f79(a919),f77(a919)),x64732))+~P106(f857(a194,f857(f103(a1),x64731)))
% 15.02/14.79 [6502]E(f857(a104,f857(f857(f243(a1),f857(f103(a1),x65021)),x65022)),f857(f857(f243(a919),f857(f103(a919),x65021)),x65022))+P106(f857(a194,f857(f103(a1),x65021)))
% 15.02/14.79 [6745]E(f857(f857(f3(a919),x67451),f857(f103(a919),f857(f857(f79(a1),x67452),a97))),f857(f857(f3(a919),f857(a112,x67451)),f857(f103(a919),x67452)))+~P106(f857(f857(f235(a1),a82),x67452))
% 15.02/14.79 [6826]E(x68261,f2(a919))+E(f857(a112,f857(f857(f79(a919),f857(f857(f3(a919),x68261),f77(a919))),x68262)),f857(f857(f79(a919),x68261),x68262))
% 15.02/14.79 [6867]E(x68671,f2(a1))+P106(f857(f857(f235(a1),f2(a1)),f857(f857(f243(a1),f857(f75(a1),x68671)),x68672)))
% 15.02/14.79 [6882]~E(x68822,f2(a919))+P106(f857(f857(f235(a1),f2(a1)),f857(f857(f243(a1),f857(f75(a1),x68821)),x68822)))
% 15.02/14.79 [6919]E(x69191,f2(a919))+E(f857(f857(f79(a919),x69192),f857(f857(f80(a919),f857(f857(f3(a919),x69191),f77(a919))),x69192)),f857(f857(f80(a919),x69191),x69192))
% 15.02/14.79 [6968]~P106(f857(f857(f234(a1),x69681),x69682))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x69681),a97)),x69682))
% 15.02/14.79 [7097]E(f857(f857(f151(a919),x70971),f139(a919,f857(f301(a919,f857(a112,x70971)),x70972))),f139(a919,f857(f301(a919,x70971),x70972)))+~P106(f857(f857(f235(a919),x70971),x70972))
% 15.02/14.79 [7299]E(x72991,x72992)+~E(f857(f857(f3(a1),f857(f857(f79(a1),x72991),x72991)),a97),f857(f857(f3(a1),f857(f857(f79(a1),x72992),x72992)),a97))
% 15.02/14.79 [7302]E(x73021,f113(x73022))+E(f265(x73022,f857(f857(f154(x73022,f926(a99,x73022)),f857(f251(a99,x73022),f77(a99))),x73021)),f274(x73022,x73021))
% 15.02/14.79 [7538]P106(f857(f857(f234(a1),x75381),x75382))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),x75381),a97)),x75382))
% 15.02/14.79 [8006]~P106(f857(f857(f235(a919),x80061),x80062))+P106(f857(f857(f328(f926(a919,a919)),f857(f857(f251(a919,a919),x80061),x80062)),a239))
% 15.02/14.79 [8226]~P106(f857(f857(f235(a99),f2(a99)),x82261))+P106(f857(f857(f235(a99),f857(f250(a99,f926(a99,a99)),f857(f266(x82261),x82262))),x82261))
% 15.02/14.79 [8488]~P40(x84881,x84882)+P40(x84881,f857(f857(f110(f927(f926(x84881,x84881),a915)),x84882),f306(x84881,f189(f927(f926(x84881,x84881),a915)))))
% 15.02/14.79 [8489]~P41(x84891,x84892)+P41(x84891,f857(f857(f110(f927(f926(x84891,x84891),a915)),x84892),f306(x84891,f189(f927(f926(x84891,x84891),a915)))))
% 15.02/14.79 [8537]~P87(x85371)+P106(f857(f857(f234(x85371),f857(f75(x85371),f857(f165(x85371),x85372))),f857(f165(x85371),f857(f857(f154(x85371,x85371),f75(x85371)),x85372))))
% 15.02/14.79 [8562]P106(f857(f857(f235(a919),x85621),x85622))+~P106(f857(f857(f328(f926(a919,a919)),f857(f857(f251(a919,a919),x85621),x85622)),a239))
% 15.02/14.79 [8708]E(f857(f857(f251(x87081,x87081),f619(x87082,x87081)),f619(x87082,x87081)),x87082)+~P106(f857(f857(f328(f926(x87081,x87081)),x87082),f306(x87081,f189(f927(f926(x87081,x87081),a915)))))
% 15.02/14.79 [8752]E(f857(f301(a919,x87521),f857(f857(f79(a919),x87521),f857(f34(a919),x87522))),x87522)+~P106(f857(f857(f234(f927(a919,a915)),x87522),f857(f301(a919,x87521),f857(f857(f79(a919),x87521),f857(f34(a919),x87522)))))
% 15.02/14.79 [8982]P41(x89821,x89822)+~P41(x89821,f857(f857(f110(f927(f926(x89821,x89821),a915)),x89822),f306(x89821,f189(f927(f926(x89821,x89821),a915)))))
% 15.02/14.79 [9108]E(f857(f857(f35(a1),f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x91081),x91081)),a97))),f857(f103(a1),f857(f857(f79(a1),x91082),x91082))),f857(f857(f35(a1),f857(f103(a1),x91081)),f857(f103(a1),x91082)))+~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x91082)))
% 15.02/14.79 [9198]~P40(x91981,x91982)+P106(f857(f857(f234(f927(f926(x91981,x91981),a915)),f857(f857(f288(x91981,x91981,x91981),x91982),x91982)),x91982))
% 15.02/14.79 [9224]E(f177(f920(x92241),f857(f857(f10(a915,a915,f920(x92241)),a321),f857(f857(f9(f920(x92241),f920(x92241),a915),a324),f113(x92241))),x92242),f179(x92241,f179(x92241,x92242)))+~P14(a919,f857(f168(a919),f857(f857(f154(f920(x92241),a919),f190(f920(x92241))),x92242)))
% 15.02/14.79 [9227]E(f857(f857(f35(a1),f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x92271),x92271)),a97))),f857(f103(a1),f857(f857(f79(a1),x92272),x92272))),f857(f857(f35(a1),f857(f857(f79(a1),f857(f103(a1),x92271)),f77(a1))),f857(f103(a1),x92272)))+P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x92272)))
% 15.02/14.79 [10073]P106(f857(a194,x100732))+E(f857(f857(f85(a1,a919),f857(f857(f3(a1),x100731),x100732)),f857(f857(f20(a1,a919,a919),f857(f857(f9(a1,a919,f927(a919,a919)),f857(f857(f10(a915,f927(a919,f927(a919,a919)),a1),f96(a919)),a194)),f2(a919))),a104)),f857(f857(f3(a919),f857(a104,x100731)),f857(a104,x100732)))
% 15.02/14.79 [10081]E(f857(f857(f85(a1,a919),f857(f103(a1),f857(f857(f79(a1),x100811),f857(f78(a1),x100812)))),f857(f857(f20(a1,a919,a919),f857(f857(f9(a1,a919,f927(a919,a919)),f857(f857(f10(a915,f927(a919,f927(a919,a919)),a1),f96(a919)),a194)),f2(a919))),a104)),f857(f857(f3(a919),f857(f103(a919),x100811)),f857(f103(a919),x100812)))+P106(f857(f857(f235(a1),x100812),a82))
% 15.02/14.79 [10082]~P28(x100821,x100822)+P106(f857(f857(f234(f927(f926(x100821,x100821),a915)),f857(f857(f288(x100821,x100821,x100821),f857(f250(f927(f926(x100821,x100821),a915),f927(f926(x100821,x100821),a915)),x100822)),f857(f255(f927(f926(x100821,x100821),a915),f927(f926(x100821,x100821),a915)),x100822))),f857(f250(f927(f926(x100821,x100821),a915),f927(f926(x100821,x100821),a915)),x100822)))
% 15.02/14.79 [10139]~E(f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,f927(a919,a915),a915),f328(a919)),x101391))),f857(f857(f9(a919,a919,a915),f235(a919)),f857(a112,x101392))))),f2(a919))+~P106(f857(f857(f328(a919),f2(a919)),x101391))
% 15.02/14.79 [10150]E(f298(a919,f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x101501,x101502),f189(f927(a919,a915)))+~P106(f857(f857(f286(a919),x101502),x101501))
% 15.02/14.79 [10155]E(f299(a919,f286(a919),f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x101551,x101552),f189(f927(a919,a915)))+P106(f857(f857(f286(a919),x101551),x101552))
% 15.02/14.79 [10156]E(f296(a919,f286(a919),f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x101561,x101562),f189(f927(a919,a915)))+P106(f857(f857(f286(a919),x101561),x101562))
% 15.02/14.79 [10160]E(f299(a919,f286(a919),f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x101601,x101602),f189(f927(a919,a915)))+~P106(f857(f857(f286(a919),x101602),x101601))
% 15.02/14.79 [10162]E(f296(a919,f286(a919),f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x101621,x101622),f189(f927(a919,a915)))+~P106(f857(f857(f286(a919),x101622),x101621))
% 15.02/14.79 [10205]E(f44(a1,f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x102051),x102051)),a97)),f857(f103(a1),f857(f857(f79(a1),x102052),x102052))),f857(f857(f79(a1),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f44(a1,f857(f103(a1),x102051),f857(f103(a1),x102052)))),f77(a1)))+~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x102052)))
% 15.02/14.79 [10214]E(f44(a1,f857(f103(a1),f857(f857(f3(a1),f857(f857(f79(a1),x102141),x102141)),a97)),f857(f103(a1),f857(f857(f79(a1),x102142),x102142))),f857(f857(f3(a1),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f44(a1,f857(f857(f79(a1),f857(f103(a1),x102141)),f77(a1)),f857(f103(a1),x102142)))),f77(a1)))+P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x102142)))
% 15.02/14.79 [10268]~P6(x102681)+E(f36(x102681,f857(f261(x102681),f857(f857(f10(f927(x102681,a915),a915,x102681),f87(x102681)),f857(f857(f10(f927(x102681,a915),f927(x102681,a915),x102681),f857(f20(x102681,a915,a915),f857(f857(f10(a915,f927(a915,a915),x102681),a329),f857(f857(f9(x102681,f927(x102681,a915),a915),f328(x102681)),x102682)))),f234(x102681))))),f37(x102681,x102682))
% 15.02/14.79 [10294]~P39(x102941,x102942)+P61(x102941,f857(f857(f9(x102941,f927(f926(x102941,x102941),a915),f927(x102941,a915)),f857(f857(f10(f927(x102941,f927(f927(f926(x102941,x102941),a915),a915)),f927(f927(f926(x102941,x102941),a915),f927(x102941,a915)),x102941),f9(x102941,f927(f926(x102941,x102941),a915),a915)),f857(f857(f10(f927(x102941,f926(x102941,x102941)),f927(x102941,f927(f927(f926(x102941,x102941),a915),a915)),x102941),f857(f10(f926(x102941,x102941),f927(f927(f926(x102941,x102941),a915),a915),x102941),f328(f926(x102941,x102941)))),f251(x102941,x102941)))),x102942))
% 15.02/14.79 [10295]~P9(x102951,f241(f927(x102951,a915)),x102952)+P8(x102951,f857(f857(f9(x102951,f927(f926(x102951,x102951),a915),f927(x102951,a915)),f857(f857(f10(f927(x102951,f927(f927(f926(x102951,x102951),a915),a915)),f927(f927(f926(x102951,x102951),a915),f927(x102951,a915)),x102951),f9(x102951,f927(f926(x102951,x102951),a915),a915)),f857(f857(f10(f927(x102951,f926(x102951,x102951)),f927(x102951,f927(f927(f926(x102951,x102951),a915),a915)),x102951),f857(f10(f926(x102951,x102951),f927(f927(f926(x102951,x102951),a915),a915),x102951),f328(f926(x102951,x102951)))),f251(x102951,x102951)))),x102952))
% 15.02/14.79 [10339]P39(x103391,x103392)+~P61(x103391,f857(f857(f9(x103391,f927(f926(x103391,x103391),a915),f927(x103391,a915)),f857(f857(f10(f927(x103391,f927(f927(f926(x103391,x103391),a915),a915)),f927(f927(f926(x103391,x103391),a915),f927(x103391,a915)),x103391),f9(x103391,f927(f926(x103391,x103391),a915),a915)),f857(f857(f10(f927(x103391,f926(x103391,x103391)),f927(x103391,f927(f927(f926(x103391,x103391),a915),a915)),x103391),f857(f10(f926(x103391,x103391),f927(f927(f926(x103391,x103391),a915),a915),x103391),f328(f926(x103391,x103391)))),f251(x103391,x103391)))),x103392))
% 15.02/14.79 [10340]P9(x103401,f241(f927(x103401,a915)),x103402)+~P8(x103401,f857(f857(f9(x103401,f927(f926(x103401,x103401),a915),f927(x103401,a915)),f857(f857(f10(f927(x103401,f927(f927(f926(x103401,x103401),a915),a915)),f927(f927(f926(x103401,x103401),a915),f927(x103401,a915)),x103401),f9(x103401,f927(f926(x103401,x103401),a915),a915)),f857(f857(f10(f927(x103401,f926(x103401,x103401)),f927(x103401,f927(f927(f926(x103401,x103401),a915),a915)),x103401),f857(f10(f926(x103401,x103401),f927(f927(f926(x103401,x103401),a915),a915),x103401),f328(f926(x103401,x103401)))),f251(x103401,x103401)))),x103402))
% 15.02/14.79 [7487]E(f857(f857(f79(a919),f857(f103(a919),f857(f857(f3(a1),x74871),a97))),x74872),f857(a112,f857(f857(f79(a919),f857(f103(a919),x74871)),x74872)))+P106(f857(a194,f857(f103(a1),x74871)))
% 15.02/14.79 [7924]~P94(x79241)+E(f857(f857(f79(x79241),f857(f857(f79(x79241),f77(x79241)),f857(f103(x79241),x79242))),f857(f103(x79241),x79242)),f857(f103(x79241),f857(f857(f3(a1),f857(f857(f79(a1),x79242),x79242)),a97)))
% 15.02/14.79 [8564]~P106(f857(f857(f234(a1),x85641),x85642))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x85641),x85641)),f857(f857(f3(a1),f857(f857(f79(a1),x85642),x85642)),a97)))
% 15.02/14.79 [8566]~P106(f857(f857(f234(a1),x85661),x85662))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x85661),x85661)),f857(f857(f3(a1),f857(f857(f79(a1),x85662),x85662)),a97)))
% 15.02/14.79 [8993]P106(f857(f857(f234(a1),x89931),x89932))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x89931),x89931)),f857(f857(f3(a1),f857(f857(f79(a1),x89932),x89932)),a97)))
% 15.02/14.79 [8995]P106(f857(f857(f234(a1),x89951),x89952))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),x89951),x89951)),f857(f857(f3(a1),f857(f857(f79(a1),x89952),x89952)),a97)))
% 15.02/14.79 [9283]~P106(f857(f857(f234(a1),x92831),x92832))+P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x92831),x92831)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),x92832),x92832)),a97)))
% 15.02/14.79 [9285]~P106(f857(f857(f235(a1),x92851),x92852))+P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x92851),x92851)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),x92852),x92852)),a97)))
% 15.02/14.79 [9554]P106(f857(f857(f234(a1),x95541),x95542))+~P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),x95541),x95541)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),x95542),x95542)),a97)))
% 15.02/14.79 [9556]P106(f857(f857(f235(a1),x95561),x95562))+~P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),x95561),x95561)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),x95562),x95562)),a97)))
% 15.02/14.79 [9589]~P106(f857(f60(x95891),x95892))+P106(f857(f60(f927(x95891,a915)),f857(f261(f927(x95891,a915)),f857(f857(f9(f927(x95891,a915),f927(x95891,a915),a915),f234(f927(x95891,a915))),x95892))))
% 15.02/14.79 [9641]~E(f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),x96411),f189(f927(f926(a919,a919),a915)))),f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),x96412),f189(f927(f926(a919,a919),a915)))))+P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),x96411),x96412)),a108))
% 15.02/14.79 [9734]E(f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),x97341),f189(f927(f926(a919,a919),a915)))),f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),x97342),f189(f927(f926(a919,a919),a915)))))+~P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),x97341),x97342)),a108))
% 15.02/14.79 [9770]P106(f857(f857(f234(a1),f2(a1)),f642(x97701,x97702)))+E(f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x97701)),f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x97702)))
% 15.02/14.79 [10278]~P6(x102781)+E(f37(x102781,f857(f261(x102781),f857(f857(f10(f927(x102781,a915),a915,x102781),f87(x102781)),f857(f857(f10(f927(x102781,a915),f927(x102781,a915),x102781),f857(f20(x102781,a915,a915),f857(f857(f10(a915,f927(a915,a915),x102781),a329),f857(f857(f9(x102781,f927(x102781,a915),a915),f328(x102781)),x102782)))),f857(f9(x102781,x102781,a915),f234(x102781)))))),f36(x102781,x102782))
% 15.02/14.79 [10300]P106(f857(f857(f328(a919),f2(a919)),x103001))+E(f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),a919),f328(a919)),a112)),x103001))),f857(f857(f9(a919,a919,a915),f235(a919)),x103002)))),f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,f927(a919,a915),a915),f328(a919)),x103001))),f857(f857(f9(a919,a919,a915),f235(a919)),f857(a112,x103002))))))
% 15.02/14.79 [7792]~P94(x77921)+E(f857(f857(f80(x77921),x77922),f857(f103(x77921),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),x77922)
% 15.02/14.79 [8053]~P94(x80531)+E(f857(f857(f79(x80531),f857(f103(x80531),x80532)),f77(x80531)),f857(f103(x80531),f857(f857(f79(a1),x80532),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))
% 15.02/14.79 [8198]P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x81982)))+E(f857(f857(f243(a1),x81981),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),x81982),x81982)),a97))),f77(a1))
% 15.02/14.79 [9616]~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x96162)))+E(f857(f857(f243(a1),x96161),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),x96162),x96162)),a97))),f857(f857(f85(a1,a1),f857(f857(f243(a1),x96161),f857(f103(a919),x96162))),f857(f857(f20(a1,a1,a1),f857(f857(f10(a1,f927(a1,a1),a1),f80(a1)),f857(f80(a1),x96161))),f7(a1))))
% 15.02/14.79 [9991]~P106(f857(f857(f234(a919),f652(x99912,x99911)),f857(x99911,f652(x99912,x99911))))+P106(f857(f60(a919),f857(f261(a919),f857(f857(f9(a919,a919,a915),f857(f857(f10(a919,f927(a919,a915),a919),f234(a919)),x99911)),x99912))))
% 15.02/14.79 [10129]~P106(f857(f857(f234(a919),f857(f103(a919),x101291)),f857(a112,x101292)))+P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x101291),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),f234(a919)),a104)),x101292))))
% 15.02/14.79 [10130]~P106(f857(f857(f235(a919),f857(f103(a919),x101301)),f857(a112,x101302)))+P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x101301),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),f235(a919)),a104)),x101302))))
% 15.02/14.79 [10189]P106(f857(f857(f234(a919),f857(f103(a919),x101891)),f857(a112,x101892)))+~P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x101891),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),f234(a919)),a104)),x101892))))
% 15.02/14.79 [10190]P106(f857(f857(f235(a919),f857(f103(a919),x101901)),f857(a112,x101902)))+~P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x101901),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),f235(a919)),a104)),x101902))))
% 15.02/14.79 [10220]~P106(f857(f857(f234(a919),f857(a112,x102202)),f857(f103(a919),x102201)))+P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x102201),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f10(a919,a915,a1),f857(f234(a919),x102202)),a104)))))
% 15.02/14.79 [10221]~P106(f857(f857(f235(a919),f857(a112,x102212)),f857(f103(a919),x102211)))+P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x102211),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f10(a919,a915,a1),f857(f235(a919),x102212)),a104)))))
% 15.02/14.79 [10266]P106(f857(f857(f234(a919),f857(a112,x102661)),f857(f103(a919),x102662)))+~P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x102662),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f10(a919,a915,a1),f857(f234(a919),x102661)),a104)))))
% 15.02/14.79 [10267]P106(f857(f857(f235(a919),f857(a112,x102671)),f857(f103(a919),x102672)))+~P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x102672),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f10(a919,a915,a1),f857(f235(a919),x102671)),a104)))))
% 15.02/14.79 [10349]~P106(f857(f857(f328(a919),f2(a919)),x103491))+E(f857(a112,f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,f927(a919,a915),a915),f857(f857(f10(a919,f927(f927(a919,a915),a915),a919),f328(a919)),a112)),x103491))),f857(f857(f9(a919,a919,a915),f235(a919)),x103492))))),f857(f34(a919),f857(f261(a919),f857(f857(f20(a919,a915,a915),f857(f857(f10(a915,f927(a915,a915),a919),a325),f857(f857(f9(a919,f927(a919,a915),a915),f328(a919)),x103491))),f857(f857(f9(a919,a919,a915),f235(a919)),f857(a112,x103492))))))
% 15.02/14.79 [8735]~P94(x87351)+E(f857(f857(f80(x87351),f857(f103(x87351),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),x87352),x87352)
% 15.02/14.79 [8796]~P94(x87961)+E(f857(f857(f79(x87961),f77(x87961)),f857(f103(x87961),x87962)),f857(f103(x87961),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),x87962)))
% 15.02/14.79 [8858]~P94(x88581)+E(f857(f857(f3(x88581),f857(f103(x88581),x88582)),f77(x88581)),f857(f103(x88581),f857(f857(f79(a1),x88582),f857(f78(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [9012]~P106(f857(f857(f235(a919),f857(f103(a919),a82)),x90122))+E(f857(f857(f3(a919),x90121),f857(f857(f3(a919),x90122),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f3(a919),f857(a112,x90121)),x90122))
% 15.02/14.79 [9659]~P113(x96591)+E(f857(f857(f80(x96591),x96592),x96592),f857(f857(f243(x96591),x96592),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [9660]~P82(x96601)+E(f857(f857(f243(x96601),x96602),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f80(x96601),x96602),x96602))
% 15.02/14.79 [9662]~P94(x96621)+E(f857(f857(f80(x96621),x96622),f857(f103(x96621),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f79(x96621),x96622),x96622))
% 15.02/14.79 [9909]~P120(x99091)+E(f857(f857(f243(x99091),f857(f75(x99091),x99092)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f243(x99091),x99092),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [9910]~P143(x99101)+E(f857(f857(f243(x99101),f857(f78(x99101),x99102)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f243(x99101),x99102),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [9906]~P94(x99061)+E(f857(f857(f80(x99061),f857(f103(x99061),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x99062),f857(f857(f79(x99061),x99062),x99062))
% 15.02/14.79 [10024]~P120(x100241)+E(f857(f75(x100241),f857(f857(f243(x100241),x100242),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x100241),x100242),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.79 [10089]~P120(x100891)+P106(f857(f857(f234(x100891),f2(x100891)),f857(f857(f243(x100891),x100892),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.79 [10257]~E(f857(a112,x102572),f857(f103(a919),x102571))+P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x102571),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),a324),a104)),x102572)))))
% 15.02/14.79 [10258]~E(f857(f103(a919),x102581),f857(a112,x102582))+P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x102581),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),a324),a104)),x102582)))))
% 15.02/14.79 [10303]E(f857(a112,x103031),f857(f103(a919),x103032))+~P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x103032),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),a324),a104)),x103031)))))
% 15.02/14.79 [10304]E(f857(f103(a919),x103041),f857(a112,x103042))+~P106(f857(f857(f85(a1,a915),f857(f103(a1),f857(f857(f79(a1),x103041),a97))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a329),f857(f857(f10(a915,a915,a1),a321),a194))),f857(f857(f9(a1,a919,a915),f857(f857(f10(a919,f927(a919,a915),a1),a324),a104)),x103042)))))
% 15.02/14.79 [10350]~P16(x103501,x103502)+P106(f857(f857(f328(f927(x103501,a915)),f812(x103502,x103501)),f857(f857(f10(f927(x103501,a915),a915,f927(x103501,a915)),f86(x103501)),f857(f857(f10(f927(x103501,a915),f927(x103501,a915),f927(x103501,a915)),f857(f20(x103501,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103501),a325),f857(f857(f20(x103501,x103501,a915),x103502),f7(x103501))))),f857(f857(f9(f927(x103501,a915),f927(x103501,f927(x103501,a915)),f927(x103501,a915)),f857(f857(f10(f927(f927(x103501,a915),a915),f927(f927(x103501,f927(x103501,a915)),f927(x103501,a915)),f927(x103501,a915)),f10(f927(x103501,a915),a915,x103501)),a324)),x103502)))))
% 15.02/14.79 [10087]~P94(x100871)+E(f857(f857(f243(x100871),f857(f103(x100871),a97)),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x100872)),f77(x100871))
% 15.02/14.79 [10088]~P143(x100881)+E(f857(f857(f243(x100881),f857(f78(x100881),f77(x100881))),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x100882)),f77(x100881))
% 15.02/14.79 [10091]~P82(x100911)+E(f857(f857(f243(x100911),x100912),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),a97))),f857(f857(f80(x100911),f857(f857(f80(x100911),x100912),x100912)),x100912))
% 15.02/14.79 [10283]~P106(f857(f857(f234(a1),f2(a1)),x102832))+E(f44(a1,f857(f857(f79(a1),f77(a1)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x102831)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x102832)),f857(f857(f79(a1),f77(a1)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f44(a1,x102831,x102832))))
% 15.02/14.79 [10306]~P106(f857(f857(f234(a1),f2(a1)),x103062))+E(f857(f857(f35(a1),f857(f857(f79(a1),f77(a1)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103061))),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103062)),f857(f857(f35(a1),x103061),x103062))
% 15.02/14.79 [10308]~P106(f857(f857(f234(a1),x103082),f2(a1)))+E(f857(f857(f35(a1),f857(f857(f79(a1),f77(a1)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103081))),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103082)),f857(f857(f35(a1),f857(f857(f79(a1),x103081),f77(a1))),x103082))
% 15.02/14.79 [10309]~P106(f857(f857(f234(a1),x103092),f2(a1)))+E(f44(a1,f857(f857(f79(a1),f77(a1)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103091)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103092)),f857(f857(f3(a1),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f44(a1,f857(f857(f79(a1),x103091),f77(a1)),x103092))),f77(a1)))
% 15.02/14.79 [10180]~P94(x101801)+E(f857(f857(f243(x101801),f857(f103(x101801),a97)),f857(a112,f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101802))),f857(f103(x101801),a97))
% 15.02/14.79 [10182]~P143(x101821)+E(f857(f857(f243(x101821),f857(f78(x101821),f77(x101821))),f857(a112,f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101822))),f857(f78(x101821),f77(x101821)))
% 15.02/14.79 [5135]P40(x51351,x51352)+~P9(x51351,x51353,x51352)
% 15.02/14.79 [5137]P53(x51371,x51372)+~P9(x51371,x51373,x51372)
% 15.02/14.79 [5307]~P25(x53071,x53072,x53073)+P30(x53071,x53072,x53073)
% 15.02/14.79 [5309]~P9(x53091,x53092,x53093)+P54(x53091,x53092,x53093)
% 15.02/14.79 [8264]~E(x82642,x82643)+P36(x82641,x82641,a324,x82642,x82643)
% 15.02/14.79 [8809]E(x88091,x88092)+~P36(x88093,x88093,a324,x88091,x88092)
% 15.02/14.79 [4943]E(f169(x49431,x49432,x49433),f113(x49431))+~E(x49432,f2(a919))
% 15.02/14.79 [5111]~E(f169(x51112,x51111,x51113),f113(x51112))+E(x51111,f2(a919))
% 15.02/14.79 [5314]~P39(x53141,x53143)+P39(x53141,f320(x53141,x53142,x53143))
% 15.02/14.79 [5423]~P31(x54231,x54232,x54233)+P33(a1,x54231,f178(x54232,x54233))
% 15.02/14.79 [5496]P31(x54961,x54962,x54963)+~P33(a1,x54961,f178(x54962,x54963))
% 15.02/14.79 [5567]~P9(x55671,x55672,x55673)+P9(f920(x55671),f161(x55671,x55672),f158(x55671,x55673))
% 15.02/14.79 [5568]~P54(x55681,x55682,x55683)+P54(f920(x55681),f161(x55681,x55682),f158(x55681,x55683))
% 15.02/14.79 [5680]P56(x56801,x56802,x56803)+~E(f598(x56803,x56802,x56801),f599(x56803,x56802,x56801))
% 15.02/14.79 [5681]P57(x56811,x56812,x56813)+~E(f614(x56813,x56812,x56811),f615(x56813,x56812,x56811))
% 15.02/14.79 [8270]~E(x82702,x82703)+P27(x82701,x82701,f31(x82701),x82702,x82703)
% 15.02/14.79 [8817]E(x88171,x88172)+~P27(x88173,x88173,f31(x88173),x88171,x88172)
% 15.02/14.79 [4898]~E(f857(f168(x48982),x48981),x48983)+E(x48981,f857(f168(x48982),x48983))
% 15.02/14.79 [4899]~E(x48992,f857(f168(x48991),x48993))+E(f857(f168(x48991),x48992),x48993)
% 15.02/14.79 [4949]E(x49491,x49492)+~E(f857(f168(x49493),x49491),f857(f168(x49493),x49492))
% 15.02/14.79 [5161]~P8(x51613,x51611)+P106(f857(f857(x51611,x51612),x51612))
% 15.02/14.79 [5162]~P45(x51623,x51621)+P106(f857(f857(x51621,x51622),x51622))
% 15.02/14.79 [5164]~P61(x51641,x51642)+P106(f857(f314(x51641,x51642),x51643))
% 15.02/14.79 [5229]~P39(x52291,x52292)+P39(f920(x52291),f857(f143(x52291,x52292),x52293))
% 15.02/14.79 [5234]~P106(f857(x52342,x52343))+~E(f857(f261(x52341),x52342),f189(f927(x52341,a915)))
% 15.02/14.79 [5235]~P106(f857(x52352,x52353))+~E(f189(f927(x52351,a915)),f857(f261(x52351),x52352))
% 15.02/14.79 [5247]E(x52471,f2(a919))+E(f144(x52472,f169(x52472,x52471,x52473)),x52473)
% 15.02/14.79 [5266]~P106(f857(x52661,x52663))+P106(f857(x52661,f89(x52662,x52661)))
% 15.02/14.79 [5267]~P106(f857(x52671,x52673))+P106(f857(x52671,f738(x52671,x52672)))
% 15.02/14.79 [5279]E(x52791,f2(a919))+E(f857(f141(x52792),f169(x52792,x52791,x52793)),x52793)
% 15.02/14.79 [5385]~E(x53852,x53853)+P106(f857(f857(f328(x53851),x53852),f857(a324,x53853)))
% 15.02/14.79 [5401]~E(x54012,f2(a919))+E(f857(f172(x54011),f169(x54011,x54012,x54013)),f189(f927(x54011,a915)))
% 15.02/14.79 [5445]E(f857(f168(x54451),x54452),f857(f857(f151(x54451),x54453),f113(x54451)))+~E(x54452,f857(f857(f151(x54451),x54453),f113(x54451)))
% 15.02/14.79 [5446]~E(x54463,f857(f857(f151(x54461),x54462),f113(x54461)))+E(f857(f857(f151(x54461),x54462),f113(x54461)),f857(f168(x54461),x54463))
% 15.02/14.79 [5492]~P35(x54921,x54922,x54923)+P35(x54921,x54922,f857(f168(x54921),x54923))
% 15.02/14.79 [5493]~P33(x54931,x54932,x54933)+P33(x54931,x54932,f857(f168(x54931),x54933))
% 15.02/14.79 [5497]E(f857(f34(x54971),f858(x54972,x54973,x54971)),x54972)+~E(f857(f34(x54971),x54973),f857(a112,x54972))
% 15.02/14.79 [5504]~P39(x55041,x55043)+P106(f857(f857(f328(x55041),x55042),f315(x55041,x55043)))
% 15.02/14.79 [5508]~E(f857(f168(x55082),x55081),f857(f857(f151(x55082),x55083),f113(x55082)))+E(x55081,f857(f857(f151(x55082),x55083),f113(x55082)))
% 15.02/14.79 [5509]~E(f857(f857(f151(x55092),x55093),f113(x55092)),f857(f168(x55092),x55091))+E(x55091,f857(f857(f151(x55092),x55093),f113(x55092)))
% 15.02/14.79 [5532]E(f84(f926(a919,a919),f47(x55321,x55322)),x55323)+~P106(f857(f47(x55321,x55322),x55323))
% 15.02/14.79 [5571]P35(x55711,x55712,x55713)+~P35(x55711,x55712,f857(f168(x55711),x55713))
% 15.02/14.79 [5572]P33(x55721,x55722,x55723)+~P33(x55721,x55722,f857(f168(x55721),x55723))
% 15.02/14.79 [5611]P106(f857(f857(x56111,x56112),x56112))+~P106(f857(f269(x56113,x56111),x56112))
% 15.02/14.79 [5612]~P106(f857(f857(x56122,x56123),x56123))+P106(f857(f269(x56121,x56122),x56123))
% 15.02/14.79 [5634]~E(x56342,f113(x56341))+P106(f857(f857(f328(f920(x56341)),x56342),f161(x56341,x56343)))
% 15.02/14.79 [5643]~P54(x56431,x56432,x56433)+P54(x56431,x56432,f857(f285(x56431,x56431),x56433))
% 15.02/14.79 [5644]~P57(x56441,x56442,x56443)+P57(x56441,x56442,f857(f285(x56441,x56441),x56443))
% 15.02/14.79 [5661]~P62(x56611)+E(f44(x56611,f44(x56611,x56612,x56613),x56613),f44(x56611,x56612,x56613))
% 15.02/14.79 [5765]E(x57651,x57652)+~P106(f857(f857(f328(x57653),x57651),f857(a324,x57652)))
% 15.02/14.79 [5811]~P146(x58111)+E(f191(x58111,x58112,f2(a919),x58113),x58113)
% 15.02/14.79 [5833]P54(x58331,x58332,x58333)+~P54(x58331,x58332,f857(f285(x58331,x58331),x58333))
% 15.02/14.79 [5834]P57(x58341,x58342,x58343)+~P57(x58341,x58342,f857(f285(x58341,x58341),x58343))
% 15.02/14.79 [5838]~P109(x58382)+E(f150(x58381,x58382,x58383,f113(x58381)),f113(x58381))
% 15.02/14.79 [5850]E(f170(x58501,x58502,f152(x58501,x58503)),f152(x58501,f170(x58501,x58502,x58503)))+~P106(f857(f137(x58501),x58503))
% 15.02/14.79 [5949]~P106(f857(f857(x59493,x59492),x59492))+P106(f857(f857(f328(x59491),x59492),f269(x59491,x59493)))
% 15.02/14.79 [5951]E(f857(f136(x59511,x59512),x59513),f113(x59511))+P106(f857(x59512,f697(x59513,x59512,x59511)))
% 15.02/14.79 [6010]E(f67(x60101,x60102,x60103),x60102)+P106(f857(x60103,f739(x60102,x60101,x60103)))
% 15.02/14.79 [6106]~P106(f857(f137(x61061),x61062))+P106(f857(f137(x61061),f176(x61061,x61062,x61063)))
% 15.02/14.79 [6107]~P106(f857(f137(x61071),x61073))+P106(f857(f137(x61071),f170(x61071,x61072,x61073)))
% 15.02/14.79 [6108]~P106(f857(f137(x61081),x61083))+P106(f857(f137(x61081),f177(x61081,x61082,x61083)))
% 15.02/14.79 [6109]~P106(f857(f137(x61091),x61093))+P106(f857(f137(x61091),f140(x61091,x61092,x61093)))
% 15.02/14.79 [6110]~P148(x61101,x61103,x61102)+P106(f857(x61101,f44(a1,x61102,x61103)))
% 15.02/14.79 [6126]~P35(x61263,x61261,x61262)+P106(f857(x61261,f751(x61262,x61261,x61263)))
% 15.02/14.79 [6127]~P37(x61273,x61271,x61272)+P106(f857(x61271,f758(x61272,x61271,x61273)))
% 15.02/14.79 [6128]~P37(x61283,x61281,x61282)+P106(f857(x61281,f768(x61282,x61281,x61283)))
% 15.02/14.79 [6129]~P35(x61293,x61291,x61292)+P106(f857(x61291,f795(x61292,x61291,x61293)))
% 15.02/14.79 [6130]~P35(x61303,x61301,x61302)+P106(f857(x61301,f796(x61301,x61302,x61303)))
% 15.02/14.79 [6135]P106(f857(f857(x61351,x61352),x61352))+~P106(f857(f857(f328(x61353),x61352),f269(x61353,x61351)))
% 15.02/14.79 [6150]E(f857(f136(x61501,x61502),x61503),f177(x61501,x61502,x61503))+P106(f857(x61502,f723(x61503,x61502,x61501)))
% 15.02/14.79 [6190]~P106(f857(f137(x61901),x61903))+P106(f857(f137(f920(x61901)),f54(x61901,x61902,x61903)))
% 15.02/14.79 [6226]~P110(x62261)+E(f857(f857(f101(f927(x62261,a915)),f857(f281(x62261),x62262)),f302(x62261,x62262,x62263)),f189(f927(x62261,a915)))
% 15.02/14.79 [6227]~P110(x62271)+E(f857(f857(f101(f927(x62271,a915)),f857(f300(x62271),x62272)),f305(x62271,x62272,x62273)),f189(f927(x62271,a915)))
% 15.02/14.79 [6228]~P110(x62281)+E(f857(f857(f101(f927(x62281,a915)),f857(f300(x62281),x62282)),f304(x62281,x62282,x62283)),f189(f927(x62281,a915)))
% 15.02/14.79 [6462]E(f857(f136(x64621,x64622),x64623),x64623)+~P106(f857(x64622,f698(x64623,x64622,x64621)))
% 15.02/14.79 [6464]E(f857(f857(f308(x64641),f896(x64642,x64643,x64641)),f858(x64642,x64643,x64641)),x64643)+~E(f857(f34(x64641),x64643),f857(a112,x64642))
% 15.02/14.79 [6480]P148(x64801,x64802,x64803)+~P106(f857(x64801,f44(a1,x64803,x64802)))
% 15.02/14.79 [6532]P33(x65321,x65322,x65323)+~P106(f857(x65322,f759(x65323,x65322,x65321)))
% 15.02/14.79 [6533]P33(x65331,x65332,x65333)+~P106(f857(x65332,f765(x65332,x65333,x65331)))
% 15.02/14.79 [6534]P33(x65341,x65342,x65343)+~P106(f857(x65342,f766(x65343,x65342,x65341)))
% 15.02/14.79 [6535]P31(x65351,x65352,x65353)+~P106(f857(x65351,f784(x65353,x65352,x65351)))
% 15.02/14.79 [6536]P32(x65361,x65362,x65363)+~P106(f857(x65361,f827(x65363,x65362,x65361)))
% 15.02/14.79 [6538]E(f177(x65381,x65382,x65383),x65383)+~P106(f857(x65382,f718(x65383,x65382,x65381)))
% 15.02/14.79 [6617]~P106(f857(x66172,f573(x66173,x66172,x66171)))+P106(f857(f247(x66171,x66172),x66173))
% 15.02/14.79 [6618]~P106(f857(x66182,f674(x66183,x66182,x66181)))+P106(f857(f160(x66181,x66182),x66183))
% 15.02/14.79 [6868]~P106(f857(f314(x68681,x68682),f380(x68683,x68682,x68681)))+P106(f857(f314(x68681,x68682),x68683))
% 15.02/14.79 [6869]~P106(f857(f314(x68691,x68692),f391(x68693,x68692,x68691)))+P106(f857(f314(x68691,x68692),x68693))
% 15.02/14.79 [7488]~P62(x74881)+E(f857(f857(f79(x74881),f857(f857(f80(x74881),x74882),f857(f857(f35(x74881),x74883),x74882))),f44(x74881,x74883,x74882)),x74883)
% 15.02/14.79 [7518]P31(x75181,x75182,x75183)+P106(f857(f857(f328(a1),f784(x75183,x75182,x75181)),f302(a1,x75182,x75183)))
% 15.02/14.79 [7945]E(f857(f857(f251(x79451,x79451),f455(x79452,x79453,x79451)),f455(x79452,x79453,x79451)),x79453)+~P106(f857(f857(f328(f926(x79451,x79451)),x79453),f262(x79451,x79452)))
% 15.02/14.79 [8061]~P106(f857(f857(f328(x80611),f509(x80613,x80612,x80611)),f315(x80611,x80613)))+P106(f857(f857(f328(x80611),x80612),f315(x80611,x80613)))
% 15.02/14.79 [8062]~P106(f857(f857(f328(x80621),f602(x80623,x80622,x80621)),f315(x80621,x80623)))+P106(f857(f857(f328(x80621),x80622),f315(x80621,x80623)))
% 15.02/14.79 [8063]~P106(f857(f857(f328(x80631),f604(x80633,x80632,x80631)),f315(x80631,x80633)))+P106(f857(f857(f328(x80631),x80632),f315(x80631,x80633)))
% 15.02/14.79 [8156]P35(a1,x81561,f178(x81562,x81563))+P31(f857(f72(a915,a915,a1,a321),x81561),x81562,x81563)
% 15.02/14.79 [8245]~P62(x82451)+E(f857(f857(f79(x82451),f857(f857(f80(x82451),f857(f857(f35(x82451),x82452),x82453)),x82453)),f44(x82451,x82452,x82453)),x82452)
% 15.02/14.79 [8291]~E(f857(f34(x82911),x82912),f857(a112,x82913))+~P106(f857(f857(f328(x82911),f896(x82913,x82912,x82911)),f858(x82913,x82912,x82911)))
% 15.02/14.79 [8727]~P35(a1,x87271,f178(x87272,x87273))+~P31(f857(f72(a915,a915,a1,a321),x87271),x87272,x87273)
% 15.02/14.79 [8914]P106(f857(f857(f234(f927(f926(x89141,x89141),a915)),f306(x89141,x89142)),f306(x89141,x89143)))+~P106(f857(f857(f234(f927(f926(x89141,x89141),a915)),x89142),f306(x89141,x89143)))
% 15.02/14.79 [9194]E(x91941,f113(x91942))+~P106(f857(f857(f328(f926(f920(x91942),f920(x91942))),f857(f857(f251(f920(x91942),f920(x91942)),x91941),f113(x91942))),f158(x91942,x91943)))
% 15.02/14.79 [9218]E(x92181,f113(x92182))+~P106(f857(f857(f328(f926(f920(x92182),f920(x92182))),f857(f857(f251(f920(x92182),f920(x92182)),f113(x92182)),x92181)),f158(x92182,x92183)))
% 15.02/14.79 [9343]E(f857(f857(f151(x93431),f691(x93432,x93433,x93431)),f692(x93432,x93433,x93431)),x93433)+~P106(f857(f857(f328(f926(f920(x93431),f920(x93431))),f857(f857(f251(f920(x93431),f920(x93431)),f113(x93431)),x93433)),f147(x93431,x93432)))
% 15.02/14.79 [9582]~P128(x95821)+~P106(f857(f857(f235(x95821),f857(f857(f79(x95821),f857(f857(f80(x95821),x95822),x95822)),f857(f857(f80(x95821),x95823),x95823))),f2(x95821)))
% 15.02/14.79 [9633]P106(f857(f60(x96331),x96332))+~P106(f857(f857(f328(f926(f927(x96331,a915),f927(x96331,a915))),f857(f857(f251(f927(x96331,a915),f927(x96331,a915)),x96333),x96332)),f313(x96331)))
% 15.02/14.79 [9935]~P49(x99351,x99352,x99353)+P106(f857(f857(f234(a1),f857(f857(f72(f926(a1,a1),a1,x99351,f250(a1,a1)),f213(x99351)),f231(x99351,x99352,f228(x99351,x99353)))),f2(a1)))
% 15.02/14.79 [9936]~P50(x99361,x99362,x99363)+P106(f857(f857(f235(a1),f857(f857(f72(f926(a1,a1),a1,x99361,f250(a1,a1)),f213(x99361)),f231(x99361,x99362,f228(x99361,x99363)))),f2(a1)))
% 15.02/14.79 [10055]P50(x100551,x100552,x100553)+~P106(f857(f857(f235(a1),f857(f857(f72(f926(a1,a1),a1,x100551,f250(a1,a1)),f213(x100551)),f231(x100551,x100552,f228(x100551,x100553)))),f2(a1)))
% 15.02/14.79 [10056]P49(x100561,x100562,x100563)+~P106(f857(f857(f234(a1),f857(f857(f72(f926(a1,a1),a1,x100561,f250(a1,a1)),f213(x100561)),f231(x100561,x100562,f228(x100561,x100563)))),f2(a1)))
% 15.02/14.79 [10410]~P120(x104101)+~P106(f857(f857(f235(x104101),f857(f857(f79(x104101),f857(f857(f243(x104101),x104102),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x104101),x104103),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f2(x104101)))
% 15.02/14.79 [4928]~E(x49283,f113(x49281))+E(f857(f857(f134(x49281),x49282),x49283),x49282)
% 15.02/14.79 [4929]~E(x49292,f113(x49291))+E(f857(f857(f134(x49291),x49292),x49293),x49293)
% 15.02/14.79 [4935]~E(x49352,f2(a919))+E(f857(f857(f175(x49351),x49352),x49353),f113(x49351))
% 15.02/14.79 [4944]~E(x49443,f113(x49441))+E(f857(f857(f175(x49441),x49442),x49443),f113(x49441))
% 15.02/14.79 [4983]~E(x49831,x49833)+E(x49831,f857(f857(f134(x49832),f113(x49832)),x49833))
% 15.02/14.79 [5074]~P1(x50742)+E(f857(f189(f927(x50741,x50742)),x50743),f189(x50742))
% 15.02/14.79 [5075]~P117(x50752)+E(f857(f241(f927(x50751,x50752)),x50753),f241(x50752))
% 15.02/14.79 [5093]E(x50931,f113(x50932))+~E(f857(f857(f134(x50932),x50933),x50931),x50933)
% 15.02/14.79 [5094]E(x50941,f113(x50942))+~E(f857(f857(f134(x50942),x50941),x50943),x50943)
% 15.02/14.79 [5102]E(x51021,f113(x51022))+~E(f857(f857(f134(x51022),x51023),x51021),f113(x51022))
% 15.02/14.79 [5103]E(x51031,f113(x51032))+~E(f857(f857(f134(x51032),x51031),x51033),f113(x51032))
% 15.02/14.79 [5128]~E(x51282,f2(a919))+E(f857(f857(f80(a919),x51281),x51282),f857(f857(f80(a919),x51283),x51282))
% 15.02/14.79 [5130]~E(x51301,f2(a919))+E(f857(f857(f80(a919),x51301),x51302),f857(f857(f80(a919),x51301),x51303))
% 15.02/14.79 [5187]~P2(x51871)+E(f857(f857(f110(x51871),x51872),x51873),f857(f857(f110(x51871),x51873),x51872))
% 15.02/14.79 [5189]~P101(x51891)+E(f857(f857(f110(x51891),x51892),x51893),f857(f857(f110(x51891),x51893),x51892))
% 15.02/14.79 [5190]~P113(x51901)+E(f857(f857(f80(x51901),x51902),x51903),f857(f857(f80(x51901),x51903),x51902))
% 15.02/14.79 [5191]~P2(x51911)+E(f857(f857(f101(x51911),x51912),x51913),f857(f857(f101(x51911),x51913),x51912))
% 15.02/14.79 [5193]~P102(x51931)+E(f857(f857(f101(x51931),x51932),x51933),f857(f857(f101(x51931),x51933),x51932))
% 15.02/14.79 [5194]~P113(x51941)+E(f857(f857(f79(x51941),x51942),x51943),f857(f857(f79(x51941),x51943),x51942))
% 15.02/14.79 [5196]~P109(x51961)+E(f857(f857(f188(x51961),x51962),x51963),f857(f857(f188(x51961),x51963),x51962))
% 15.02/14.79 [5198]~P109(x51981)+E(f857(f857(f233(x51981),x51982),x51983),f857(f857(f233(x51981),x51983),x51982))
% 15.02/14.79 [5261]E(f44(a919,x52611,x52612),f2(a919))+~E(x52611,f857(f857(f80(a919),x52612),x52613))
% 15.02/14.79 [5262]E(f44(a1,x52621,x52622),f2(a1))+~E(x52621,f857(f857(f80(a1),x52622),x52623))
% 15.02/14.79 [5326]E(x53261,x53262)+~E(f857(f857(f79(a919),x53263),x53261),f857(f857(f79(a919),x53263),x53262))
% 15.02/14.79 [5327]E(x53271,x53272)+~E(f857(f857(f79(a919),x53271),x53273),f857(f857(f79(a919),x53272),x53273))
% 15.02/14.79 [5337]~P96(x53371)+E(f857(f857(f101(x53371),x53372),f857(f78(x53371),x53373)),f857(f857(f3(x53371),x53372),x53373))
% 15.02/14.79 [5338]~P69(x53381)+E(f857(f857(f79(x53381),x53382),f857(f78(x53381),x53383)),f857(f857(f3(x53381),x53382),x53383))
% 15.02/14.79 [5339]~P76(x53391)+E(f857(f857(f79(x53391),x53392),f857(f78(x53391),x53393)),f857(f857(f3(x53391),x53392),x53393))
% 15.02/14.79 [5340]~P115(x53401)+E(f857(f857(f79(x53401),x53402),f857(f78(x53401),x53403)),f857(f857(f3(x53401),x53402),x53403))
% 15.02/14.79 [5341]~P76(x53411)+E(f857(f857(f3(x53411),x53412),f857(f78(x53411),x53413)),f857(f857(f79(x53411),x53412),x53413))
% 15.02/14.79 [5379]~P106(f857(x53793,x53792))+P106(f857(f857(f328(x53791),x53792),x53793))
% 15.02/14.79 [5381]~P72(x53812)+E(f857(f857(f8(x53811,x53812),x53813),f189(f927(x53811,a915))),f2(x53812))
% 15.02/14.79 [5383]~P77(x53832)+E(f857(f857(f11(x53831,x53832),x53833),f189(f927(x53831,a915))),f77(x53832))
% 15.02/14.79 [5435]~E(x54352,f857(f857(f79(a919),x54351),x54353))+P106(f857(f857(f234(a919),x54351),x54352))
% 15.02/14.79 [5438]~E(x54382,f189(f927(x54381,a915)))+E(f857(f857(f59(x54381),x54382),x54383),f189(f927(f927(x54381,a915),a915)))
% 15.02/14.79 [5439]~E(x54392,f189(f927(x54391,a915)))+E(f189(f927(f927(x54391,a915),a915)),f857(f857(f59(x54391),x54392),x54393))
% 15.02/14.79 [5512]~E(f857(f283(x55122,x55123),x55121),f189(f927(x55123,a915)))+E(x55121,f189(f927(f926(x55122,x55123),a915)))
% 15.02/14.79 [5513]~E(f857(f263(x55132,x55133),x55131),f189(f927(x55132,a915)))+E(x55131,f189(f927(f926(x55132,x55133),a915)))
% 15.02/14.79 [5545]E(f857(f283(x55451,x55452),x55453),f189(f927(x55452,a915)))+~E(x55453,f189(f927(f926(x55451,x55452),a915)))
% 15.02/14.79 [5546]E(f857(f263(x55461,x55462),x55463),f189(f927(x55461,a915)))+~E(x55463,f189(f927(f926(x55461,x55462),a915)))
% 15.02/14.79 [5549]E(f273(x55491,x55492,x55493),f857(f857(f3(a99),x55492),x55493))+P106(f857(f857(f235(a99),x55492),x55493))
% 15.02/14.79 [5565]P106(f857(x55651,x55652))+~P106(f857(f857(f328(x55653),x55652),x55651))
% 15.02/14.79 [5604]E(x56041,x56042)+~E(f857(f78(f927(x56043,a915)),x56041),f857(f78(f927(x56043,a915)),x56042))
% 15.02/14.79 [5615]~E(x56151,f189(f927(x56152,a915)))+~P106(f857(f857(f328(x56152),x56153),x56151))
% 15.02/14.79 [5645]~E(x56452,f857(f857(f79(a1),x56451),f857(f100(a1),x56453)))+P106(f857(f857(f234(a1),x56451),x56452))
% 15.02/14.79 [5659]E(f857(f857(f308(x56591),x56592),x56593),x56593)+~P106(f857(f857(f328(x56591),x56592),x56593))
% 15.02/14.79 [5670]E(x56701,f189(f927(x56702,a915)))+~E(f857(f857(f59(x56702),x56701),x56703),f189(f927(f927(x56702,a915),a915)))
% 15.02/14.79 [5671]E(x56711,f189(f927(x56712,a915)))+~E(f189(f927(f927(x56712,a915),a915)),f857(f857(f59(x56712),x56711),x56713))
% 15.02/14.79 [5678]~P111(x56781)+E(f857(f857(f80(x56781),f857(f78(x56781),x56782)),f857(f78(x56781),x56783)),f857(f857(f80(x56781),x56782),x56783))
% 15.02/14.79 [5679]~P65(x56791)+E(f857(f857(f290(x56791),f857(f78(x56791),x56792)),f857(f78(x56791),x56793)),f857(f857(f290(x56791),x56792),x56793))
% 15.02/14.79 [5711]~P106(f857(x57113,x57112))+P106(f857(f857(f328(x57111),x57112),f857(f261(x57111),x57113)))
% 15.02/14.79 [5738]E(x57381,f2(a919))+E(f857(f172(x57382),f169(x57382,x57381,x57383)),f857(f857(f308(x57382),x57383),f189(f927(x57382,a915))))
% 15.02/14.79 [5758]E(f170(x57581,x57582,x57583),x57583)+P106(f857(f857(f328(x57581),x57582),f857(f172(x57581),x57583)))
% 15.02/14.79 [5842]~P106(f857(f137(x58421),x58423))+P106(f857(f137(x58421),f857(f136(x58421,x58422),x58423)))
% 15.02/14.79 [5885]~P62(x58851)+E(f857(f857(f35(x58851),f44(x58851,x58852,x58853)),x58853),f2(x58851))
% 15.02/14.79 [5904]E(f176(x59041,f857(f857(f151(x59041),x59042),f113(x59041)),x59043),f113(x59041))+P106(f857(f857(f328(a919),f2(a919)),x59043))
% 15.02/14.79 [5910]E(x59101,f2(a919))+E(f857(f171(x59102),f169(x59102,x59101,x59103)),f169(x59102,f857(f857(f3(a919),x59101),f77(a919)),x59103))
% 15.02/14.79 [5961]E(f857(f857(f151(x59611),x59612),x59613),f140(x59611,x59612,x59613))+P106(f857(f857(f328(x59611),x59612),f857(f172(x59611),x59613)))
% 15.02/14.79 [5970]E(x59701,x59702)+~E(f857(f857(f80(a919),f857(a112,x59703)),x59701),f857(f857(f80(a919),f857(a112,x59703)),x59702))
% 15.02/14.79 [5971]~E(x59712,f857(f857(f79(a1),x59711),f857(f100(a1),f857(a112,x59713))))+P106(f857(f857(f235(a1),x59711),x59712))
% 15.02/14.79 [6032]~P32(x60321,x60322,x60323)+P33(a919,x60321,f139(a919,f857(f301(a919,x60322),x60323)))
% 15.02/14.79 [6085]~E(x60853,f113(x60851))+E(f857(f857(f857(f183(f920(x60851),f920(x60851)),x60852),f167(x60851)),x60853),f113(x60851))
% 15.02/14.79 [6089]P106(f857(x60891,x60892))+~P106(f857(f857(f328(x60893),x60892),f857(f261(x60893),x60891)))
% 15.02/14.79 [6121]E(x61211,x61212)+~E(f857(f857(f308(x61213),x61211),f189(f927(x61213,a915))),f857(f857(f308(x61213),x61212),f189(f927(x61213,a915))))
% 15.02/14.79 [6137]~P110(x61371)+E(f857(f857(f101(f927(x61371,a915)),f857(f281(x61371),x61372)),f857(f301(x61371,x61372),x61373)),f189(f927(x61371,a915)))
% 15.02/14.79 [6176]E(f140(x61761,x61762,x61763),x61763)+~P106(f857(f857(f328(x61761),x61762),f857(f172(x61761),x61763)))
% 15.02/14.79 [6198]~P80(x61981)+E(f857(f309(x61981,x61981,f78(x61981)),f857(f301(x61981,x61982),x61983)),f304(x61981,f857(f78(x61981),x61983),f857(f78(x61981),x61982)))
% 15.02/14.79 [6209]E(f857(f190(f920(x62091)),f170(x62091,x62092,x62093)),f857(f190(f920(x62091)),x62093))+P106(f857(f857(f328(x62091),x62092),f857(f172(x62091),x62093)))
% 15.02/14.79 [6267]~P110(x62671)+E(f857(f857(f101(f927(x62671,a915)),f857(f301(x62671,x62672),x62673)),f857(f282(x62671),x62673)),f189(f927(x62671,a915)))
% 15.02/14.79 [6287]~P80(x62871)+E(f857(f309(x62871,x62871,f78(x62871)),f302(x62871,x62872,x62873)),f302(x62871,f857(f78(x62871),x62873),f857(f78(x62871),x62872)))
% 15.02/14.79 [6288]~P80(x62881)+E(f857(f309(x62881,x62881,f78(x62881)),f305(x62881,x62882,x62883)),f305(x62881,f857(f78(x62881),x62883),f857(f78(x62881),x62882)))
% 15.02/14.79 [6353]E(f176(x63531,f857(f857(f151(x63531),x63532),f113(x63531)),x63533),f857(f857(f151(x63531),x63532),f113(x63531)))+~P106(f857(f857(f328(a919),f2(a919)),x63533))
% 15.02/14.79 [6358]P32(x63581,x63582,x63583)+~P33(a919,x63581,f139(a919,f857(f301(a919,x63582),x63583)))
% 15.02/14.79 [6361]~P80(x63611)+E(f857(f309(x63611,x63611,f78(x63611)),f304(x63611,x63612,x63613)),f857(f301(x63611,f857(f78(x63611),x63613)),f857(f78(x63611),x63612)))
% 15.02/14.79 [6383]~P63(x63831)+E(f44(x63831,f857(f78(x63831),f44(x63831,x63832,x63833)),x63833),f44(x63831,f857(f78(x63831),x63832),x63833))
% 15.02/14.79 [6478]~P106(f857(f60(f926(x64782,x64781)),x64783))+P106(f857(f60(x64781),f857(f283(x64782,x64781),x64783)))
% 15.02/14.79 [6479]~P106(f857(f60(f926(x64791,x64792)),x64793))+P106(f857(f60(x64791),f857(f263(x64791,x64792),x64793)))
% 15.02/14.79 [6484]~P110(x64841)+E(f857(f857(f101(f927(x64841,a915)),f302(x64841,x64842,x64843)),f857(f303(x64841),x64843)),f189(f927(x64841,a915)))
% 15.02/14.79 [6485]~P110(x64851)+E(f857(f857(f101(f927(x64851,a915)),f305(x64851,x64852,x64853)),f857(f282(x64851),x64853)),f189(f927(x64851,a915)))
% 15.02/14.79 [6486]~P110(x64861)+E(f857(f857(f101(f927(x64861,a915)),f304(x64861,x64862,x64863)),f857(f303(x64861),x64863)),f189(f927(x64861,a915)))
% 15.02/14.79 [6559]E(f857(f857(f164(x65591),x65592),f638(x65592,x65593,x65591)),x65593)+~P106(f857(f857(f328(x65591),x65593),f857(f172(x65591),x65592)))
% 15.02/14.79 [6701]E(x67011,f113(x67012))+~E(f857(f857(f857(f183(f920(x67012),f920(x67012)),x67013),f167(x67012)),x67011),f113(x67012))
% 15.02/14.79 [6806]~P106(f857(f60(f926(x68062,x68061)),x68063))+P106(f857(f60(f926(x68061,x68062)),f857(f285(x68062,x68061),x68063)))
% 15.02/14.79 [6829]E(x68291,x68292)+~E(f289(a919,f286(a919),x68293,x68291),f857(f857(f308(a919),x68292),f189(f927(a919,a915))))
% 15.02/14.79 [6830]E(x68301,x68302)+~E(f289(a919,f286(a919),x68301,x68302),f857(f857(f308(a919),x68303),f189(f927(a919,a915))))
% 15.02/14.79 [6960]P57(x69601,x69602,x69603)+P106(f857(f857(f328(x69601),f615(x69603,x69602,x69601)),x69602))
% 15.02/14.79 [6961]P57(x69611,x69612,x69613)+P106(f857(f857(f328(x69611),f614(x69613,x69612,x69611)),x69612))
% 15.02/14.79 [6971]P106(f857(f314(x69711,x69712),x69713))+P106(f857(f857(x69712,f380(x69713,x69712,x69711)),x69713))
% 15.02/14.79 [6972]P106(f857(f314(x69721,x69722),x69723))+P106(f857(f857(x69722,f391(x69723,x69722,x69721)),x69723))
% 15.02/14.79 [7003]E(f857(f190(f920(x70031)),f170(x70031,x70032,x70033)),f857(f857(f3(a919),f857(f190(f920(x70031)),x70033)),f77(a919)))+~P106(f857(f857(f328(x70031),x70032),f857(f172(x70031),x70033)))
% 15.02/14.79 [7042]P106(f857(f247(x70421,x70422),x70423))+P106(f857(f857(f328(x70421),f573(x70423,x70422,x70421)),x70423))
% 15.02/14.79 [7051]~P106(f857(f60(f926(x70512,x70511)),f857(f285(x70511,x70512),x70513)))+P106(f857(f60(f926(x70511,x70512)),x70513))
% 15.02/14.79 [7109]~P106(f857(f857(f328(x71091),x71092),f857(f172(x71091),f114(x71091,x71093))))+P106(f857(f857(f328(x71091),x71092),f857(f172(x71091),x71093)))
% 15.02/14.79 [7144]E(f857(f136(x71441,x71442),x71443),x71443)+P106(f857(f857(f328(x71441),f698(x71443,x71442,x71441)),f857(f172(x71441),x71443)))
% 15.02/14.79 [7159]E(f857(f136(x71591,x71592),x71593),f113(x71591))+P106(f857(f857(f328(x71591),f697(x71593,x71592,x71591)),f857(f172(x71591),x71593)))
% 15.02/14.79 [7183]P33(x71831,x71832,x71833)+P106(f857(f857(f328(x71831),f759(x71833,x71832,x71831)),f857(f172(x71831),x71833)))
% 15.02/14.79 [7184]P33(x71841,x71842,x71843)+P106(f857(f857(f328(x71841),f766(x71843,x71842,x71841)),f857(f172(x71841),x71843)))
% 15.02/14.79 [7185]P33(x71851,x71852,x71853)+P106(f857(f857(f328(x71851),f765(x71852,x71853,x71851)),f857(f172(x71851),x71853)))
% 15.02/14.79 [7188]E(f177(x71881,x71882,x71883),x71883)+P106(f857(f857(f328(x71881),f718(x71883,x71882,x71881)),f857(f172(x71881),x71883)))
% 15.02/14.79 [7265]P106(f857(f160(x72651,x72652),x72653))+P106(f857(f857(f328(x72651),f674(x72653,x72652,x72651)),f857(f172(x72651),x72653)))
% 15.02/14.79 [7274]~P35(x72741,x72743,x72742)+P106(f857(f857(f328(x72741),f751(x72742,x72743,x72741)),f857(f172(x72741),x72742)))
% 15.02/14.79 [7275]~P37(x72751,x72753,x72752)+P106(f857(f857(f328(x72751),f758(x72752,x72753,x72751)),f857(f172(x72751),x72752)))
% 15.02/14.79 [7276]~P37(x72761,x72763,x72762)+P106(f857(f857(f328(x72761),f768(x72762,x72763,x72761)),f857(f172(x72761),x72762)))
% 15.02/14.79 [7277]~P35(x72771,x72773,x72772)+P106(f857(f857(f328(x72771),f795(x72772,x72773,x72771)),f857(f172(x72771),x72772)))
% 15.02/14.79 [7278]~P35(x72781,x72782,x72783)+P106(f857(f857(f328(x72781),f796(x72782,x72783,x72781)),f857(f172(x72781),x72783)))
% 15.02/14.79 [7312]P106(f857(f857(f328(x73121),x73122),f340(x73123,x73122,x73121)))+~P106(f857(f857(f328(x73121),x73122),f36(f927(x73121,a915),x73123)))
% 15.02/14.79 [7313]~P72(x73131)+E(f857(f857(f79(x73131),f857(f857(f8(a919,x73131),x73132),f857(f281(a919),x73133))),f857(x73132,x73133)),f857(f857(f8(a919,x73131),x73132),f857(f281(a919),f857(a112,x73133))))
% 15.02/14.79 [7325]P32(x73251,x73252,x73253)+P106(f857(f857(f328(a919),f827(x73253,x73252,x73251)),f857(f301(a919,x73252),x73253)))
% 15.02/14.79 [7405]~P35(x74052,x74051,x74053)+P106(f857(x74051,f857(f857(f164(x74052),x74053),f754(x74053,x74051,x74052))))
% 15.02/14.79 [7418]~P106(f857(f857(f328(x74181),x74182),f382(x74182,x74183,x74181)))+P106(f857(f857(f328(x74181),x74182),f37(f927(x74181,a915),x74183)))
% 15.02/14.79 [7451]~P72(x74511)+E(f857(f857(f79(x74511),f857(f857(f8(a919,x74511),x74512),f857(f300(a919),x74513))),f857(x74512,f857(a112,x74513))),f857(f857(f8(a919,x74511),x74512),f857(f300(a919),f857(a112,x74513))))
% 15.02/14.79 [7589]P106(f857(f857(f328(f920(x75891)),x75892),f161(x75891,x75893)))+P106(f857(f857(f328(x75891),f659(x75893,x75892,x75891)),f857(f172(x75891),x75892)))
% 15.02/14.79 [7604]~P106(f857(f857(f328(f920(x76041)),x76042),f161(x76041,f315(x76041,x76043))))+P106(f857(f857(f328(f920(x76041)),x76042),f315(f920(x76041),f157(x76041,x76043))))
% 15.02/14.79 [7629]~P106(f857(f857(f328(f920(x76291)),x76292),f315(f920(x76291),f157(x76291,x76293))))+P106(f857(f857(f328(f920(x76291)),x76292),f161(x76291,f315(x76291,x76293))))
% 15.02/14.79 [7662]E(f857(f857(f857(f183(f920(x76621),f920(x76621)),x76622),f167(x76621)),x76623),x76623)+~P106(f857(f857(f234(a919),f857(f190(f920(x76621)),x76623)),f77(a919)))
% 15.02/14.79 [7695]E(f857(f857(f134(x76951),f755(x76952,x76953,x76951)),f857(f857(f151(x76951),x76953),f757(x76952,x76953,x76951))),x76952)+~P106(f857(f857(f328(x76951),x76953),f857(f172(x76951),x76952)))
% 15.02/14.79 [7696]E(f857(f857(f134(x76961),f761(x76962,x76963,x76961)),f857(f857(f151(x76961),x76963),f762(x76962,x76963,x76961))),x76962)+~P106(f857(f857(f328(x76961),x76963),f857(f172(x76961),x76962)))
% 15.02/14.79 [7697]E(f857(f857(f134(x76971),f763(x76972,x76973,x76971)),f857(f857(f151(x76971),x76973),f764(x76972,x76973,x76971))),x76972)+~P106(f857(f857(f328(x76971),x76973),f857(f172(x76971),x76972)))
% 15.02/14.79 [7718]~P26(x77181,x77182,x77183,f241(f927(x77181,a915)))+P26(f920(x77181),f920(x77182),f857(f154(x77181,x77182),x77183),f241(f927(f920(x77181),a915)))
% 15.02/14.79 [7868]E(x78681,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x78682)),x78683)),f857(f255(a919,a919),x78682)))+~P106(f857(f47(x78681,x78683),x78682))
% 15.02/14.79 [7876]P26(x78761,x78762,x78763,f241(f927(x78761,a915)))+~P26(f920(x78761),f920(x78762),f857(f154(x78761,x78762),x78763),f241(f927(f920(x78761),a915)))
% 15.02/14.79 [7920]P106(f857(f857(f328(f927(x79201,a915)),f382(x79202,x79203,x79201)),x79203))+P106(f857(f857(f328(x79201),x79202),f37(f927(x79201,a915),x79203)))
% 15.02/14.79 [8009]P106(f857(f857(f328(f920(x80091)),x80092),f161(x80091,x80093)))+~P106(f857(f857(f328(x80091),f659(x80093,x80092,x80091)),x80093))
% 15.02/14.79 [8110]P33(x81101,x81102,x81103)+~P106(f857(x81102,f857(f857(f164(x81101),x81103),f760(x81103,x81102,x81101))))
% 15.02/14.79 [8135]E(x81351,x81352)+~E(f857(f857(f9(x81353,f927(x81353,a915),a915),f328(x81353)),x81351),f857(f857(f9(x81353,f927(x81353,a915),a915),f328(x81353)),x81352))
% 15.02/14.79 [8143]~P106(f857(f857(f328(f926(x81431,x81431)),x81433),f262(x81431,x81432)))+P106(f857(f857(f328(x81431),f455(x81432,x81433,x81431)),x81432))
% 15.02/14.79 [8145]~P106(f857(f857(f328(x81451),x81453),f36(f927(x81451,a915),x81452)))+P106(f857(f857(f328(f927(x81451,a915)),f340(x81452,x81453,x81451)),x81452))
% 15.02/14.79 [8265]P26(x82651,x82652,f91(x82652,x82651,f241(f927(x82652,a915)),x82653),f241(f927(x82651,a915)))+~E(f857(f309(x82652,x82651,x82653),f241(f927(x82652,a915))),f241(f927(x82651,a915)))
% 15.02/14.79 [8318]~P106(f857(f857(f328(x83181),x83182),f857(f172(x83181),f761(x83183,x83182,x83181))))+~P106(f857(f857(f328(x83181),x83182),f857(f172(x83181),x83183)))
% 15.02/14.79 [8319]~P106(f857(f857(f328(x83191),x83192),f857(f172(x83191),f764(x83193,x83192,x83191))))+~P106(f857(f857(f328(x83191),x83192),f857(f172(x83191),x83193)))
% 15.02/14.79 [8348]P32(f857(f72(a915,a915,a919,a321),x83481),x83482,x83483)+P35(a919,x83481,f139(a919,f857(f301(a919,x83482),x83483)))
% 15.02/14.79 [8508]E(x85081,f113(x85082))+P106(f857(f857(f328(x85082),f857(f250(x85082,f926(a99,a99)),f857(f274(x85082,x85081),x85083))),f857(f172(x85082),x85081)))
% 15.02/14.79 [8606]~P71(x86061)+E(f857(f142(x86061,x86061,f857(f9(x86061,x86061,x86061),f79(x86061)),x86062),f857(f168(x86061),x86063)),f857(f142(x86061,x86061,f79(x86061),x86062),x86063))
% 15.02/14.79 [8797]~P26(x87972,x87971,x87973,f241(f927(x87972,a915)))+E(f857(f309(x87971,x87972,f91(x87972,x87971,f241(f927(x87972,a915)),x87973)),f241(f927(x87971,a915))),f241(f927(x87972,a915)))
% 15.02/14.79 [8867]~P32(f857(f72(a915,a915,a919,a321),x88671),x88672,x88673)+~P35(a919,x88671,f139(a919,f857(f301(a919,x88672),x88673)))
% 15.02/14.79 [9114]~P109(x91141)+E(f857(f172(x91141),f149(x91141,x91141,f7(x91141),x91142,x91143)),f857(f857(f308(x91141),x91142),f857(f172(x91141),x91143)))
% 15.02/14.79 [9123]~E(f857(x91233,f857(f91(x91231,x91232,f241(f927(x91231,a915)),x91233),f811(x91233,x91232,x91231))),f811(x91233,x91232,x91231))+E(f857(f309(x91231,x91232,x91233),f241(f927(x91231,a915))),f241(f927(x91232,a915)))
% 15.02/14.79 [9125]P106(f857(f857(f235(a919),f2(a919)),f622(x91251,x91252,x91253)))+~P106(f857(f857(f328(f926(x91253,x91253)),x91252),f857(f857(f288(x91253,x91253,x91253),x91251),f306(x91253,x91251))))
% 15.02/14.79 [9400]~P59(x94001,x94002)+~P106(f857(f857(f328(f926(x94001,x94001)),f857(f857(f251(x94001,x94001),x94003),x94003)),f857(f857(f288(x94001,x94001,x94001),x94002),f306(x94001,x94002))))
% 15.02/14.79 [9537]~E(f857(f857(f101(f927(f926(x95371,x95371),a915)),f857(f285(x95371,x95371),x95372)),f306(x95371,x95372)),f189(f927(f926(x95371,x95371),a915)))+~P106(f857(f857(f328(f926(x95371,x95371)),f857(f857(f251(x95371,x95371),x95373),x95373)),f857(f857(f288(x95371,x95371,x95371),x95372),f306(x95371,x95372))))
% 15.02/14.79 [9727]~P106(f857(f60(x97271),x97272))+P106(f857(f857(f234(a919),f857(f34(x97271),f857(f857(f3(f927(x97271,a915)),x97272),f857(f857(f308(x97271),x97273),f189(f927(x97271,a915)))))),f857(f34(x97271),x97272)))
% 15.02/14.79 [5249]~E(x52493,f113(x52491))+E(f144(x52491,f857(f857(f151(x52491),x52492),x52493)),x52492)
% 15.02/14.79 [5258]~E(x52583,f113(x52581))+E(f114(x52581,f857(f857(f151(x52581),x52582),x52583)),f113(x52581))
% 15.02/14.79 [5288]E(x52881,f113(x52882))+E(f144(x52882,f857(f857(f151(x52882),x52883),x52881)),f144(x52882,x52881))
% 15.02/14.79 [5290]E(x52901,f113(x52902))+E(f144(x52902,f857(f857(f134(x52902),x52903),x52901)),f144(x52902,x52901))
% 15.02/14.79 [5295]~E(x52953,f113(x52951))+E(f114(x52951,f857(f857(f134(x52951),x52952),x52953)),f114(x52951,x52952))
% 15.02/14.79 [5297]~E(x52973,f113(x52971))+E(f144(x52971,f857(f857(f134(x52971),x52972),x52973)),f144(x52971,x52972))
% 15.02/14.79 [5331]E(x53311,f113(x53312))+E(f857(f141(x53312),f857(f857(f134(x53312),x53311),x53313)),f857(f141(x53312),x53311))
% 15.02/14.79 [5359]~E(x53592,f113(x53591))+E(f857(f141(x53591),f857(f857(f134(x53591),x53592),x53593)),f857(f141(x53591),x53593))
% 15.02/14.79 [5411]~P2(x54111)+E(f857(f857(f110(x54111),x54112),f857(f857(f101(x54111),x54112),x54113)),x54112)
% 15.02/14.79 [5412]~P2(x54121)+E(f857(f857(f101(x54121),x54122),f857(f857(f110(x54121),x54122),x54123)),x54122)
% 15.02/14.79 [5413]~P109(x54131)+E(f857(f857(f188(x54131),x54132),f857(f857(f233(x54131),x54132),x54133)),x54132)
% 15.02/14.79 [5414]~P109(x54141)+E(f857(f857(f233(x54141),x54142),f857(f857(f188(x54141),x54142),x54143)),x54142)
% 15.02/14.79 [5433]~P62(x54331)+E(f44(x54331,f857(f857(f80(x54331),x54332),x54333),x54333),f2(x54331))
% 15.02/14.79 [5434]~P62(x54341)+E(f44(x54341,f857(f857(f80(x54341),x54342),x54343),x54342),f2(x54341))
% 15.02/14.79 [5507]~P69(x55071)+E(f857(f78(x55071),f857(f857(f3(x55071),x55072),x55073)),f857(f857(f3(x55071),x55073),x55072))
% 15.02/14.79 [5569]E(x55691,f113(x55692))+E(f114(x55692,f857(f857(f151(x55692),x55693),x55691)),f857(f857(f151(x55692),x55693),f114(x55692,x55691)))
% 15.02/14.79 [5570]E(x55701,f113(x55702))+E(f114(x55702,f857(f857(f134(x55702),x55703),x55701)),f857(f857(f134(x55702),x55703),f114(x55702,x55701)))
% 15.02/14.79 [5573]~P6(x55731)+E(f36(x55731,f857(f857(f308(x55731),x55732),x55733)),f857(f857(f110(x55731),x55732),f36(x55731,x55733)))
% 15.02/14.79 [5574]~P6(x55741)+E(f37(x55741,f857(f857(f308(x55741),x55742),x55743)),f857(f857(f101(x55741),x55742),f37(x55741,x55743)))
% 15.02/14.79 [5620]~P2(x56201)+E(f857(f857(f110(x56201),x56202),f857(f857(f110(x56201),x56202),x56203)),f857(f857(f110(x56201),x56202),x56203))
% 15.02/14.79 [5622]~P101(x56221)+E(f857(f857(f110(x56221),x56222),f857(f857(f110(x56221),x56222),x56223)),f857(f857(f110(x56221),x56222),x56223))
% 15.02/14.79 [5623]~P97(x56231)+E(f857(f857(f80(x56231),x56232),f857(f857(f80(x56231),x56232),x56233)),f857(f857(f80(x56231),x56232),x56233))
% 15.02/14.79 [5624]~P2(x56241)+E(f857(f857(f101(x56241),x56242),f857(f857(f101(x56241),x56242),x56243)),f857(f857(f101(x56241),x56242),x56243))
% 15.02/14.79 [5626]~P102(x56261)+E(f857(f857(f101(x56261),x56262),f857(f857(f101(x56261),x56262),x56263)),f857(f857(f101(x56261),x56262),x56263))
% 15.02/14.79 [5628]~P109(x56281)+E(f857(f857(f188(x56281),x56282),f857(f857(f188(x56281),x56282),x56283)),f857(f857(f188(x56281),x56282),x56283))
% 15.02/14.79 [5630]~P109(x56301)+E(f857(f857(f233(x56301),x56302),f857(f857(f233(x56301),x56302),x56303)),f857(f857(f233(x56301),x56302),x56303))
% 15.02/14.79 [5637]~P62(x56371)+E(f44(x56371,f857(f857(f79(x56371),x56372),x56373),x56373),f44(x56371,x56372,x56373))
% 15.02/14.79 [5638]~P62(x56381)+E(f44(x56381,f857(f857(f79(x56381),x56382),x56383),x56382),f44(x56381,x56383,x56382))
% 15.02/14.79 [5646]~P111(x56461)+E(f857(f857(f80(x56461),x56462),f857(f78(x56461),x56463)),f857(f78(x56461),f857(f857(f80(x56461),x56462),x56463)))
% 15.02/14.79 [5647]~P65(x56471)+E(f857(f857(f290(x56471),x56472),f857(f78(x56471),x56473)),f857(f78(x56471),f857(f857(f290(x56471),x56472),x56473)))
% 15.02/14.79 [5648]~P83(x56481)+E(f857(f857(f79(x56481),x56482),f857(f165(x56481),x56483)),f857(f165(x56481),f857(f857(f151(x56481),x56482),x56483)))
% 15.02/14.79 [5676]~P111(x56761)+E(f857(f857(f80(x56761),f857(f78(x56761),x56762)),x56763),f857(f857(f80(x56761),x56762),f857(f78(x56761),x56763)))
% 15.02/14.79 [5682]~P9(x56821,x56822,x56823)+E(f36(f927(x56821,a915),f857(f857(f59(x56821),x56822),x56823)),x56822)
% 15.02/14.79 [5750]~P116(x57501)+E(f857(f857(f80(x57501),x57502),f857(f857(f243(x57501),x57502),x57503)),f857(f857(f243(x57501),x57502),f857(a112,x57503)))
% 15.02/14.79 [5751]~P113(x57511)+E(f857(f857(f80(x57511),x57512),f857(f857(f243(x57511),x57512),x57513)),f857(f857(f243(x57511),x57512),f857(a112,x57513)))
% 15.02/14.79 [5761]~P76(x57611)+E(f857(f857(f79(x57611),f857(f78(x57611),x57612)),f857(f857(f79(x57611),x57612),x57613)),x57613)
% 15.02/14.79 [5784]~P146(x57841)+E(f857(f857(f243(x57841),f857(f100(x57841),x57842)),x57843),f857(f100(x57841),f857(f857(f243(a919),x57842),x57843)))
% 15.02/14.79 [5785]~P143(x57851)+E(f857(f857(f243(x57851),f857(f102(x57851),x57852)),x57853),f857(f102(x57851),f857(f857(f243(a1),x57852),x57853)))
% 15.02/14.79 [5791]~P87(x57911)+E(f857(f75(x57911),f857(f857(f3(x57911),x57912),x57913)),f857(f75(x57911),f857(f857(f3(x57911),x57913),x57912)))
% 15.02/14.79 [5793]~P120(x57931)+E(f857(f857(f80(x57931),f81(x57931,x57932)),f81(x57931,x57933)),f81(x57931,f857(f857(f80(x57931),x57932),x57933)))
% 15.02/14.79 [5797]E(x57971,f113(x57972))+E(f857(f857(f134(x57972),f857(f171(x57972),x57971)),x57973),f857(f171(x57972),f857(f857(f134(x57972),x57971),x57973)))
% 15.02/14.79 [5802]~E(x58022,f857(a112,f857(f857(f79(a919),x58021),x58023)))+P106(f857(f857(f235(a919),x58021),x58022))
% 15.02/14.79 [5803]~P120(x58031)+E(f857(f857(f243(x58031),f857(f75(x58031),x58032)),x58033),f857(f75(x58031),f857(f857(f243(x58031),x58032),x58033)))
% 15.02/14.79 [5804]~P111(x58041)+E(f857(f857(f80(x58041),f857(f78(x58041),x58042)),x58043),f857(f78(x58041),f857(f857(f80(x58041),x58042),x58043)))
% 15.02/14.79 [5805]~P124(x58051)+E(f857(f857(f290(x58051),f857(f78(x58051),x58052)),x58053),f857(f78(x58051),f857(f857(f290(x58051),x58052),x58053)))
% 15.02/14.79 [5903]E(f597(x59031,x59032,x59033),f600(x59031,x59032,x59033))+E(f857(f857(f101(f927(x59033,a915)),x59032),x59031),f189(f927(x59033,a915)))
% 15.02/14.79 [5918]~P72(x59182)+E(f857(f857(f8(x59181,x59182),f857(f18(x59182,x59181),f2(x59182))),x59183),f2(x59182))
% 15.02/14.79 [5919]~P77(x59192)+E(f857(f857(f11(x59191,x59192),f857(f18(x59192,x59191),f77(x59192))),x59193),f77(x59192))
% 15.02/14.79 [5921]~P94(x59211)+E(f857(f857(f3(x59211),f857(f103(x59211),x59212)),f857(f103(x59211),x59213)),f857(f103(x59211),f857(f857(f3(a1),x59212),x59213)))
% 15.02/14.79 [5924]~P146(x59241)+E(f857(f857(f80(x59241),f857(f100(x59241),x59242)),f857(f100(x59241),x59243)),f857(f100(x59241),f857(f857(f80(a919),x59242),x59243)))
% 15.02/14.79 [5925]~P146(x59251)+E(f857(f857(f79(x59251),f857(f100(x59251),x59252)),f857(f100(x59251),x59253)),f857(f100(x59251),f857(f857(f79(a919),x59252),x59253)))
% 15.02/14.79 [5926]~P143(x59261)+E(f857(f857(f3(x59261),f857(f102(x59261),x59262)),f857(f102(x59261),x59263)),f857(f102(x59261),f857(f857(f3(a1),x59262),x59263)))
% 15.02/14.79 [5927]~P143(x59271)+E(f857(f857(f80(x59271),f857(f102(x59271),x59272)),f857(f102(x59271),x59273)),f857(f102(x59271),f857(f857(f80(a1),x59272),x59273)))
% 15.02/14.79 [5928]~P143(x59281)+E(f857(f857(f79(x59281),f857(f102(x59281),x59282)),f857(f102(x59281),x59283)),f857(f102(x59281),f857(f857(f79(a1),x59282),x59283)))
% 15.02/14.79 [5929]~P94(x59291)+E(f857(f857(f80(x59291),f857(f103(x59291),x59292)),f857(f103(x59291),x59293)),f857(f103(x59291),f857(f857(f80(a1),x59292),x59293)))
% 15.02/14.79 [5930]~P94(x59301)+E(f857(f857(f79(x59301),f857(f103(x59301),x59302)),f857(f103(x59301),x59303)),f857(f103(x59301),f857(f857(f79(a1),x59302),x59303)))
% 15.02/14.79 [5978]~E(x59783,x59782)+P106(f857(f857(f234(f927(x59781,a915)),x59782),x59783))
% 15.02/14.79 [5984]~E(x59842,x59843)+P106(f857(f857(f234(f927(x59841,a915)),x59842),x59843))
% 15.02/14.79 [5989]~P120(x59891)+E(f857(f857(f80(x59891),f857(f75(x59891),x59892)),f857(f75(x59891),x59893)),f857(f75(x59891),f857(f857(f80(x59891),x59892),x59893)))
% 15.02/14.79 [5990]~P67(x59901)+E(f857(f857(f290(x59901),f857(f75(x59901),x59902)),f857(f75(x59901),x59903)),f857(f75(x59901),f857(f857(f290(x59901),x59902),x59903)))
% 15.02/14.79 [5991]~P96(x59911)+E(f857(f857(f101(x59911),f857(f78(x59911),x59912)),f857(f78(x59911),x59913)),f857(f78(x59911),f857(f857(f110(x59911),x59912),x59913)))
% 15.02/14.79 [5992]~P96(x59921)+E(f857(f857(f110(x59921),f857(f78(x59921),x59922)),f857(f78(x59921),x59923)),f857(f78(x59921),f857(f857(f101(x59921),x59922),x59923)))
% 15.02/14.79 [5993]~P76(x59931)+E(f857(f857(f79(x59931),f857(f78(x59931),x59932)),f857(f78(x59931),x59933)),f857(f78(x59931),f857(f857(f79(x59931),x59933),x59932)))
% 15.02/14.79 [5994]~P69(x59941)+E(f857(f857(f79(x59941),f857(f78(x59941),x59942)),f857(f78(x59941),x59943)),f857(f78(x59941),f857(f857(f79(x59941),x59942),x59943)))
% 15.02/14.79 [5995]~P78(x59951)+E(f857(f857(f233(x59951),f857(f78(x59951),x59952)),f857(f78(x59951),x59953)),f857(f78(x59951),f857(f857(f188(x59951),x59952),x59953)))
% 15.02/14.79 [5996]~P78(x59961)+E(f857(f857(f188(x59961),f857(f78(x59961),x59962)),f857(f78(x59961),x59963)),f857(f78(x59961),f857(f857(f233(x59961),x59962),x59963)))
% 15.02/14.79 [5997]~P83(x59971)+E(f857(f857(f79(x59971),f857(f165(x59971),x59972)),f857(f165(x59971),x59973)),f857(f165(x59971),f857(f857(f134(x59971),x59972),x59973)))
% 15.02/14.79 [5998]E(x59981,f189(f927(x59982,a915)))+~E(f857(f857(f110(f927(x59982,a915)),x59983),x59981),f189(f927(x59982,a915)))
% 15.02/14.79 [5999]E(x59991,f189(f927(x59992,a915)))+~E(f857(f857(f110(f927(x59992,a915)),x59991),x59993),f189(f927(x59992,a915)))
% 15.02/14.79 [6000]~P149(x60001,x60003,x60002)+P106(f857(x60001,f857(f857(f35(a1),x60002),x60003)))
% 15.02/14.79 [6056]~P106(f857(f60(x60561),x60563))+P106(f857(f60(x60561),f857(f857(f308(x60561),x60562),x60563)))
% 15.02/14.79 [6057]~P106(f857(f137(x60571),x60573))+P106(f857(f137(x60571),f857(f857(f175(x60571),x60572),x60573)))
% 15.02/14.79 [6058]~P106(f857(f137(x60581),x60583))+P106(f857(f137(x60581),f857(f857(f138(x60581),x60582),x60583)))
% 15.02/14.79 [6090]~P2(x60901)+P106(f857(f857(f234(x60901),x60902),f857(f857(f110(x60901),x60903),x60902)))
% 15.02/14.79 [6091]~P101(x60911)+P106(f857(f857(f234(x60911),x60912),f857(f857(f110(x60911),x60913),x60912)))
% 15.02/14.79 [6092]~P2(x60921)+P106(f857(f857(f234(x60921),x60922),f857(f857(f110(x60921),x60922),x60923)))
% 15.02/14.79 [6093]~P101(x60931)+P106(f857(f857(f234(x60931),x60932),f857(f857(f110(x60931),x60932),x60933)))
% 15.02/14.79 [6094]~P109(x60941)+P106(f857(f857(f234(x60941),x60942),f857(f857(f233(x60941),x60943),x60942)))
% 15.02/14.79 [6095]~P109(x60951)+P106(f857(f857(f234(x60951),x60952),f857(f857(f233(x60951),x60952),x60953)))
% 15.02/14.79 [6096]~P113(x60961)+P106(f857(f857(f286(x60961),x60962),f857(f857(f80(x60961),x60963),x60962)))
% 15.02/14.79 [6097]~P113(x60971)+P106(f857(f857(f286(x60971),x60972),f857(f857(f80(x60971),x60972),x60973)))
% 15.02/14.79 [6111]~E(x61111,f2(a919))+E(f857(f857(f35(a919),f857(f857(f80(a919),x61111),x61112)),f857(f857(f80(a919),x61111),x61113)),f2(a919))
% 15.02/14.79 [6192]~P94(x61921)+E(f857(f857(f3(x61921),f857(f103(x61921),x61922)),f857(f103(x61921),x61923)),f857(f103(x61921),f857(f857(f79(a1),x61922),f857(f78(a1),x61923))))
% 15.02/14.79 [6252]E(x62521,f2(a919))+E(f857(f857(f35(a919),f857(f857(f80(a919),x62521),x62522)),f857(f857(f80(a919),x62521),x62523)),f857(f857(f35(a919),x62522),x62523))
% 15.02/14.79 [6285]E(f152(x62851,f857(f857(f151(x62851),x62852),x62853)),f857(f857(f151(x62851),x62852),f152(x62851,x62853)))+P106(f857(f857(f328(x62851),x62852),f857(f172(x62851),x62853)))
% 15.02/14.79 [6322]P149(x63221,x63222,x63223)+~P106(f857(x63221,f857(f857(f35(a1),x63223),x63222)))
% 15.02/14.79 [6396]E(x63961,f113(x63962))+E(f857(f857(f151(x63962),f857(f141(x63962),x63961)),f857(f857(f175(x63962),x63963),f857(f171(x63962),x63961))),f857(f857(f175(x63962),f857(a112,x63963)),x63961))
% 15.02/14.79 [6403]E(f857(f857(f3(f927(x64031,a915)),x64032),x64033),x64032)+~E(f857(f857(f101(f927(x64031,a915)),x64032),x64033),f189(f927(x64031,a915)))
% 15.02/14.79 [6417]E(f152(x64171,f857(f857(f151(x64171),x64172),x64173)),f152(x64171,x64173))+~P106(f857(f857(f328(x64171),x64172),f857(f172(x64171),x64173)))
% 15.02/14.79 [6447]~P106(f857(f857(f234(a919),x64471),x64473))+P106(f857(f857(f234(a919),x64471),f857(f857(f79(a919),x64472),x64473)))
% 15.02/14.79 [6449]~P106(f857(f857(f234(a919),x64491),x64492))+P106(f857(f857(f234(a919),x64491),f857(f857(f79(a919),x64492),x64493)))
% 15.02/14.79 [6451]~P106(f857(f857(f235(a919),x64511),x64513))+P106(f857(f857(f235(a919),x64511),f857(f857(f79(a919),x64512),x64513)))
% 15.02/14.79 [6453]~P106(f857(f857(f235(a919),x64531),x64532))+P106(f857(f857(f235(a919),x64531),f857(f857(f79(a919),x64532),x64533)))
% 15.02/14.79 [6492]P106(f857(f60(x64921),x64922))+~P106(f857(f60(x64921),f857(f857(f308(x64921),x64923),x64922)))
% 15.02/14.79 [6493]P106(f857(f137(x64931),x64932))+~P106(f857(f137(x64931),f857(f857(f151(x64931),x64933),x64932)))
% 15.02/14.79 [6494]P106(f857(f137(x64941),x64942))+~P106(f857(f137(x64941),f857(f857(f134(x64941),x64943),x64942)))
% 15.02/14.79 [6495]P106(f857(f137(x64951),x64952))+~P106(f857(f137(x64951),f857(f857(f134(x64951),x64952),x64953)))
% 15.02/14.79 [6549]~P113(x65491)+E(f857(f857(f79(x65491),x65492),f857(f857(f80(x65491),x65493),x65492)),f857(f857(f80(x65491),f857(f857(f79(x65491),x65493),f77(x65491))),x65492))
% 15.02/14.79 [6596]~E(x65961,x65962)+~P106(f857(f857(f235(f927(x65963,a915)),x65961),x65962))
% 15.02/14.79 [6639]P106(f857(f857(f328(x66391),x66392),x66393))+P106(f857(f857(f328(x66391),x66392),f857(f78(f927(x66391,a915)),x66393)))
% 15.02/14.79 [6645]E(f144(x66451,f857(f857(f138(x66451),x66452),x66453)),f144(x66451,x66453))+~P106(f857(f857(f235(a919),x66452),f857(f190(f920(x66451)),x66453)))
% 15.02/14.79 [6646]E(f857(f857(f175(x66461),x66462),f114(x66461,x66463)),f857(f857(f175(x66461),x66462),x66463))+~P106(f857(f857(f235(a919),x66462),f857(f190(f920(x66461)),x66463)))
% 15.02/14.79 [6703]E(f857(f857(f857(f183(f920(x67031),f920(x67031)),x67032),f167(x67031)),x67033),x67033)+~E(f44(a919,x67032,f857(f190(f920(x67031)),x67033)),f2(a919))
% 15.02/14.79 [6710]~P9(x67101,x67103,x67102)+E(f857(f857(f288(x67101,x67101,x67101),f857(f285(x67101,x67101),x67102)),x67102),x67102)
% 15.02/14.79 [6753]~E(f857(f857(f110(f927(x67531,a915)),x67532),x67533),x67533)+P106(f857(f857(f234(f927(x67531,a915)),x67532),x67533))
% 15.02/14.79 [6758]~P56(x67581,x67581,x67583)+P56(x67581,x67581,f857(f857(f183(f926(x67581,x67581),a915),x67582),x67583))
% 15.02/14.79 [6761]~P106(f857(f857(f328(x67611),x67613),f857(f172(x67611),x67612)))+P106(f857(f857(f235(a919),f2(a919)),f857(f190(f920(x67611)),x67612)))
% 15.02/14.79 [6789]~P87(x67891)+E(f857(f75(x67891),f857(f857(f79(x67891),f857(f75(x67891),x67892)),f857(f75(x67891),x67893))),f857(f857(f79(x67891),f857(f75(x67891),x67892)),f857(f75(x67891),x67893)))
% 15.02/14.79 [6799]E(f857(f857(f35(a919),f857(f857(f80(a919),x67991),x67992)),f857(f857(f80(a919),x67991),x67993)),f857(f857(f35(a919),x67992),x67993))+~P106(f857(f857(f235(a919),f2(a919)),x67991))
% 15.02/14.79 [6939]~P106(f857(f60(x69391),x69393))+E(f857(f857(f63(x69391,f927(x69391,a915),f308(x69391)),x69392),x69393),f857(f857(f110(f927(x69391,a915)),x69393),x69392))
% 15.02/14.79 [6996]E(f857(f857(f110(f927(x69961,a915)),x69962),x69963),x69962)+~P106(f857(f857(f234(f927(x69961,a915)),x69963),x69962))
% 15.02/14.79 [6998]E(f857(f857(f110(f927(x69981,a915)),x69982),x69983),x69983)+~P106(f857(f857(f234(f927(x69981,a915)),x69982),x69983))
% 15.02/14.79 [6999]E(f857(f857(f101(f927(x69991,a915)),x69992),x69993),x69993)+~P106(f857(f857(f234(f927(x69991,a915)),x69993),x69992))
% 15.02/14.79 [7000]E(f857(f857(f101(f927(x70001,a915)),x70002),x70003),x70002)+~P106(f857(f857(f234(f927(x70001,a915)),x70002),x70003))
% 15.02/14.79 [7049]~P106(f857(f137(x70491),x70492))+E(f857(f857(f3(f927(x70491,a915)),f857(f172(x70491),x70492)),f857(f857(f308(x70491),x70493),f189(f927(x70491,a915)))),f857(f172(x70491),f170(x70491,x70493,x70492)))
% 15.02/14.79 [7104]P39(x71041,x71042)+~P39(x71041,f857(f857(f183(f926(x71041,x71041),a915),x71043),x71042))
% 15.02/14.79 [7121]~E(x71211,f2(a919))+P106(f857(f857(f286(a919),f857(f857(f80(a919),x71211),x71212)),f857(f857(f80(a919),x71211),x71213)))
% 15.02/14.79 [7171]P106(f857(f48(x71711,x71712),f857(a50,x71713)))+~P106(f857(f48(f857(f78(a1),x71711),f857(f78(a1),x71712)),x71713))
% 15.02/14.79 [7176]E(f857(f857(f3(f927(x71761,a915)),f857(f857(f308(x71761),x71762),x71763)),f857(f857(f308(x71761),x71762),f189(f927(x71761,a915)))),x71763)+P106(f857(f857(f328(x71761),x71762),x71763))
% 15.02/14.79 [7197]E(f857(f857(f101(f927(x71971,a915)),f857(f172(x71971),x71972)),f857(f172(x71971),x71973)),f189(f927(x71971,a915)))+~P106(f857(f137(x71971),f857(f857(f134(x71971),x71972),x71973)))
% 15.02/14.79 [7212]~P106(f857(f857(f328(x72121),x72122),f857(f172(x72121),x72123)))+~P106(f857(f137(x72121),f857(f857(f151(x72121),x72122),x72123)))
% 15.02/14.79 [7284]P33(x72841,x72842,x72843)+P106(f857(f857(f235(a919),f760(x72843,x72842,x72841)),f857(f190(f920(x72841)),x72843)))
% 15.02/14.79 [7294]E(f857(f857(f101(f927(x72941,a915)),x72942),x72943),f189(f927(x72941,a915)))+P106(f857(f857(f328(x72941),f597(x72943,x72942,x72941)),x72942))
% 15.02/14.79 [7295]E(f857(f857(f101(f927(x72951,a915)),x72952),x72953),f189(f927(x72951,a915)))+P106(f857(f857(f328(x72951),f600(x72953,x72952,x72951)),x72953))
% 15.02/14.79 [7298]E(f114(x72981,f857(f857(f175(x72981),x72982),x72983)),f857(f857(f175(x72981),f857(f857(f3(a919),x72982),f77(a919))),x72983))+~P106(f857(f857(f234(a919),x72982),f857(f190(f920(x72981)),x72983)))
% 15.02/14.79 [7358]~P35(x73583,x73582,x73581)+P106(f857(f857(f235(a919),f754(x73581,x73582,x73583)),f857(f190(f920(x73583)),x73581)))
% 15.02/14.79 [7378]P106(f857(f857(f235(a919),f2(a919)),x73781))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x73782),x73781)),f857(f857(f80(a919),x73783),x73781)))
% 15.02/14.79 [7379]P106(f857(f857(f235(a919),f2(a919)),x73791))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x73791),x73792)),f857(f857(f80(a919),x73791),x73793)))
% 15.02/14.79 [7382]~P106(f857(f857(f328(x73821),x73822),x73823))+~P106(f857(f857(f328(x73821),x73822),f857(f78(f927(x73821,a915)),x73823)))
% 15.02/14.79 [7388]~P106(f857(f857(f235(f927(x73881,a915)),x73882),x73883))+P106(f857(f857(f234(f927(x73881,a915)),x73882),x73883))
% 15.02/14.79 [7496]~P106(f857(f857(f234(a919),x74963),x74962))+P106(f857(f857(f234(a919),f857(f857(f3(a919),x74961),x74962)),f857(f857(f3(a919),x74961),x74963)))
% 15.02/14.79 [7497]~P106(f857(f857(f234(a919),x74971),x74973))+P106(f857(f857(f234(a919),f857(f857(f3(a919),x74971),x74972)),f857(f857(f3(a919),x74973),x74972)))
% 15.02/14.79 [7499]~P106(f857(f857(f234(a919),x74992),x74993))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x74991),x74992)),f857(f857(f80(a919),x74991),x74993)))
% 15.02/14.79 [7501]~P106(f857(f857(f234(a919),x75011),x75013))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x75011),x75012)),f857(f857(f80(a919),x75013),x75012)))
% 15.02/14.79 [7502]~P106(f857(f857(f234(a919),x75022),x75023))+P106(f857(f857(f234(a919),f857(f857(f79(a919),x75021),x75022)),f857(f857(f79(a919),x75021),x75023)))
% 15.02/14.79 [7503]~P106(f857(f857(f234(a919),x75031),x75033))+P106(f857(f857(f234(a919),f857(f857(f79(a919),x75031),x75032)),f857(f857(f79(a919),x75033),x75032)))
% 15.02/14.79 [7504]~P106(f857(f857(f234(a919),x75041),x75043))+P106(f857(f857(f234(a919),f857(f857(f35(a919),x75041),x75042)),f857(f857(f35(a919),x75043),x75042)))
% 15.02/14.79 [7505]~P106(f857(f857(f234(a1),x75052),x75053))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x75051),x75052)),f857(f857(f79(a1),x75051),x75053)))
% 15.02/14.79 [7508]~P106(f857(f857(f235(a919),x75082),x75083))+P106(f857(f857(f235(a919),f857(f857(f79(a919),x75081),x75082)),f857(f857(f79(a919),x75081),x75083)))
% 15.02/14.79 [7509]~P106(f857(f857(f235(a919),x75091),x75093))+P106(f857(f857(f235(a919),f857(f857(f79(a919),x75091),x75092)),f857(f857(f79(a919),x75093),x75092)))
% 15.02/14.79 [7510]~P106(f857(f857(f235(a1),x75101),x75103))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x75101),x75102)),f857(f857(f79(a1),x75103),x75102)))
% 15.02/14.79 [7513]~P106(f857(f857(f286(a919),x75132),x75133))+P106(f857(f857(f286(a919),f857(f857(f80(a919),x75131),x75132)),f857(f857(f80(a919),x75131),x75133)))
% 15.02/14.79 [7588]E(x75881,x75882)+~P106(f857(f857(f328(x75883),x75881),f857(f857(f308(x75883),x75882),f189(f927(x75883,a915)))))
% 15.02/14.79 [7590]~E(f857(f857(f101(f927(x75901,a915)),x75902),x75903),f189(f927(x75901,a915)))+P106(f857(f857(f234(f927(x75901,a915)),x75902),f857(f78(f927(x75901,a915)),x75903)))
% 15.02/14.79 [7595]P106(f857(f857(f328(f927(x75951,a915)),x75952),f857(f307(x75951),x75953)))+~P106(f857(f857(f234(f927(x75951,a915)),x75952),x75953))
% 15.02/14.79 [7600]P106(f857(f857(f328(x76001),f444(x76002,x76003,x76001)),x76003))+P106(f857(f857(f234(f927(x76001,a915)),x76003),x76002))
% 15.02/14.79 [7646]E(f857(f857(f151(x76461),f857(f857(f164(x76461),x76462),x76463)),f857(f857(f138(x76461),f857(a112,x76463)),x76462)),f857(f857(f138(x76461),x76463),x76462))+~P106(f857(f857(f235(a919),x76463),f857(f190(f920(x76461)),x76462)))
% 15.02/14.79 [7672]P106(f857(f857(f328(f926(x76721,x76721)),x76722),f306(x76721,x76723)))+~P106(f857(f857(f328(f926(x76721,x76721)),x76722),x76723))
% 15.02/14.79 [7681]~P106(f857(f857(f328(f927(x76811,a915)),x76812),f857(f307(x76811),x76813)))+P106(f857(f857(f234(f927(x76811,a915)),x76812),x76813))
% 15.02/14.79 [7724]P106(f857(f857(f234(f927(x77241,a915)),x77242),f36(f927(x77241,a915),x77243)))+~P106(f857(f857(f328(f927(x77241,a915)),x77242),x77243))
% 15.02/14.79 [7748]~P143(x77481)+E(f857(f857(f80(x77481),f857(f857(f243(x77481),f857(f78(x77481),f77(x77481))),x77482)),f857(f857(f243(x77481),x77483),x77482)),f857(f857(f243(x77481),f857(f78(x77481),x77483)),x77482))
% 15.02/14.79 [7770]E(f857(f857(f164(x77701),x77702),f857(f857(f3(a919),f857(f190(f920(x77701)),x77702)),f857(a112,x77703))),f857(f857(f164(x77701),f857(f168(x77701),x77702)),x77703))+~P106(f857(f857(f235(a919),x77703),f857(f190(f920(x77701)),x77702)))
% 15.02/14.79 [7787]~E(f857(f857(f101(f927(x77871,a915)),f880(x77873,x77872,x77871)),x77873),f189(f927(x77871,a915)))+E(f857(f857(f101(f927(x77871,a915)),f36(f927(x77871,a915),x77872)),x77873),f189(f927(x77871,a915)))
% 15.02/14.79 [7851]~P106(f857(f857(f328(x78513),x78512),f857(f172(x78513),x78511)))+P106(f857(f857(f235(a919),f638(x78511,x78512,x78513)),f857(f190(f920(x78513)),x78511)))
% 15.02/14.79 [7859]P106(f857(f857(f328(x78591),f857(f857(f164(x78591),x78592),x78593)),f857(f172(x78591),x78592)))+~P106(f857(f857(f235(a919),x78593),f857(f190(f920(x78591)),x78592)))
% 15.02/14.79 [7956]~P106(f857(x79562,f720(x79563,x79562,x79561)))+E(f857(f857(f138(x79561),f857(f190(f920(x79561)),f177(x79561,x79562,x79563))),x79563),f113(x79561))
% 15.02/14.79 [7969]P106(f857(f857(f234(f927(f920(x79691),a915)),f161(x79691,x79692)),f161(x79691,x79693)))+~P106(f857(f857(f234(f927(x79691,a915)),x79692),x79693))
% 15.02/14.79 [7970]P106(f857(f857(f234(f927(f920(x79701),a915)),f160(x79701,x79702)),f160(x79701,x79703)))+~P106(f857(f857(f234(f927(x79701,a915)),x79702),x79703))
% 15.02/14.79 [7996]E(f857(f857(f101(f927(x79961,a915)),f36(f927(x79961,a915),x79962)),x79963),f189(f927(x79961,a915)))+P106(f857(f857(f328(f927(x79961,a915)),f880(x79963,x79962,x79961)),x79962))
% 15.02/14.79 [7998]~P106(f857(f857(f328(f927(x79981,a915)),x79983),x79982))+P106(f857(f857(f234(f927(x79981,a915)),f37(f927(x79981,a915),x79982)),x79983))
% 15.02/14.79 [8000]E(f857(f857(f101(f927(x80001,a915)),x80002),x80003),f189(f927(x80001,a915)))+~P106(f857(f857(f234(f927(x80001,a915)),x80002),f857(f78(f927(x80001,a915)),x80003)))
% 15.02/14.79 [8048]E(f857(f857(f3(a919),f857(f857(f79(a919),f857(f165(a919),x80481)),x80482)),f857(f857(f164(a919),x80481),x80483)),f857(f165(a919),f857(f857(f159(a919,x80481),x80483),x80482)))+~P106(f857(f857(f235(a919),x80483),f857(f190(f920(a919)),x80481)))
% 15.02/14.79 [8099]P106(f857(f857(f234(a919),x80991),x80992))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x80993),x80991)),f857(f857(f79(a919),x80993),x80992)))
% 15.02/14.79 [8102]P106(f857(f857(f235(a919),x81021),x81022))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),x81023),x81021)),f857(f857(f79(a919),x81023),x81022)))
% 15.02/14.79 [8103]P106(f857(f857(f235(a919),x81031),x81032))+~P106(f857(f857(f235(a919),f857(f857(f80(a919),x81033),x81031)),f857(f857(f80(a919),x81033),x81032)))
% 15.02/14.79 [8104]P106(f857(f857(f235(a919),x81041),x81042))+~P106(f857(f857(f235(a919),f857(f857(f80(a919),x81041),x81043)),f857(f857(f80(a919),x81042),x81043)))
% 15.02/14.79 [8133]P106(f857(f857(f235(a919),f2(a919)),x81331))+~P106(f857(f857(f235(a919),f857(f857(f80(a919),x81332),x81331)),f857(f857(f80(a919),x81333),x81331)))
% 15.02/14.79 [8134]P106(f857(f857(f235(a919),f2(a919)),x81341))+~P106(f857(f857(f235(a919),f857(f857(f80(a919),x81341),x81342)),f857(f857(f80(a919),x81341),x81343)))
% 15.02/14.79 [8172]~P106(f857(f857(f328(x81721),f444(x81723,x81722,x81721)),x81723))+P106(f857(f857(f234(f927(x81721,a915)),x81722),x81723))
% 15.02/14.79 [8208]E(f246(x82081,x82082,x82083),x82082)+~P106(f857(f857(f234(f927(x82081,a915)),x82083),f857(f857(f308(x82081),x82082),f189(f927(x82081,a915)))))
% 15.02/14.79 [8258]~P106(f857(f137(x82581),x82583))+E(f857(f136(x82581,f857(f857(f10(a915,a915,x82581),a321),f857(a324,x82582))),x82583),f170(x82581,x82582,x82583))
% 15.02/14.79 [8283]E(f857(f857(f138(x82831),f857(f190(f920(x82831)),f177(x82831,x82832,x82833))),x82833),f113(x82831))+P106(f857(f857(f328(x82831),f720(x82833,x82832,x82831)),f857(f172(x82831),x82833)))
% 15.02/14.79 [8287]E(f857(f857(f134(x82871),f857(f857(f175(x82871),x82872),x82873)),f857(f857(f151(x82871),f857(f857(f164(x82871),x82873),x82872)),f113(x82871))),f857(f857(f175(x82871),f857(a112,x82872)),x82873))+~P106(f857(f857(f235(a919),x82872),f857(f190(f920(x82871)),x82873)))
% 15.02/14.79 [8353]E(f857(f136(x83531,f857(f857(f10(a915,a915,x83531),a321),f857(a324,x83532))),x83533),x83533)+P106(f857(f857(f328(x83531),x83532),f857(f172(x83531),x83533)))
% 15.02/14.79 [8359]P106(f857(f857(f234(f927(f927(x83591,a915),a915)),f247(x83591,x83592)),f247(x83591,x83593)))+~P106(f857(f857(f234(f927(x83591,a915)),x83592),x83593))
% 15.02/14.79 [8398]~P106(f857(f137(x83981),x83983))+P106(f857(f137(x83981),f857(f857(f857(f183(f920(x83981),f920(x83981)),x83982),f167(x83981)),x83983)))
% 15.02/14.79 [8404]~P106(f857(f857(f235(a919),x84042),x84043))+P106(f857(f857(f235(a919),f857(f857(f80(a919),f857(a112,x84041)),x84042)),f857(f857(f80(a919),f857(a112,x84041)),x84043)))
% 15.02/14.79 [8424]P106(f857(f857(f234(f927(f927(x84241,a915),a915)),f857(f307(x84241),x84242)),f857(f307(x84241),x84243)))+~P106(f857(f857(f234(f927(x84241,a915)),x84242),x84243))
% 15.02/14.79 [8493]~E(f857(f309(x84931,x84932,x84933),f241(f927(x84931,a915))),f241(f927(x84932,a915)))+E(f857(f72(x84931,x84932,x84932,x84933),f91(x84931,x84932,f241(f927(x84931,a915)),x84933)),f31(x84932))
% 15.02/14.79 [8586]~P106(f857(f857(f234(f927(x85861,a915)),x85863),x85862))+P106(f857(f857(f234(f927(x85861,a915)),f857(f78(f927(x85861,a915)),x85862)),f857(f78(f927(x85861,a915)),x85863)))
% 15.02/14.79 [8619]E(f857(f309(a919,a919,f857(f857(f9(a919,a919,a919),f3(a919)),x86191)),f857(f301(a919,x86192),x86193)),f857(f301(a919,f857(f857(f3(a919),x86192),x86191)),f857(f857(f3(a919),x86193),x86191)))+~P106(f857(f857(f235(a919),x86191),x86193))
% 15.02/14.80 [8645]~P83(x86451)+E(f857(f857(f79(x86451),x86452),f857(f142(x86451,x86451,f79(x86451),f2(x86451)),x86453)),f857(f142(x86451,x86451,f79(x86451),x86452),x86453))
% 15.02/14.80 [8721]~P87(x87211)+P106(f857(f857(f234(x87211),f857(f75(x87211),f857(f857(f3(x87211),x87212),x87213))),f857(f857(f79(x87211),f857(f75(x87211),x87212)),f857(f75(x87211),x87213))))
% 15.02/14.80 [8722]~P87(x87221)+P106(f857(f857(f234(x87221),f857(f75(x87221),f857(f857(f79(x87221),x87222),x87223))),f857(f857(f79(x87221),f857(f75(x87221),x87222)),f857(f75(x87221),x87223))))
% 15.02/14.80 [8733]E(f857(f857(f79(a1),f857(f857(f80(a1),x87331),f44(a1,f857(f857(f35(a1),x87332),x87331),x87333))),f44(a1,x87332,x87331)),f44(a1,x87332,f857(f857(f80(a1),x87331),x87333)))+~P106(f857(f857(f235(a1),f2(a1)),x87333))
% 15.02/14.80 [8739]E(f857(f857(f134(x87391),f857(f857(f175(x87391),x87392),x87393)),f857(f857(f151(x87391),f857(f141(x87391),f857(f857(f138(x87391),x87392),x87393))),f113(x87391))),f857(f857(f175(x87391),f857(a112,x87392)),x87393))+~P106(f857(f857(f235(a919),x87392),f857(f190(f920(x87391)),x87393)))
% 15.02/14.80 [8759]E(f857(f267(x87591,f857(f857(f154(x87591,f926(a99,x87591)),f857(f251(a99,x87591),f77(a99))),x87592)),f857(a5,x87593)),f857(f857(f164(x87591),x87592),x87593))+~P106(f857(f857(f235(a919),x87593),f857(f190(f920(x87591)),x87592)))
% 15.02/14.80 [8827]P106(f857(f857(f328(f926(x88271,x88271)),x88272),f857(f857(f288(x88271,x88271,x88271),x88273),f306(x88271,x88273))))+~P106(f857(f857(f328(f926(x88271,x88271)),x88272),x88273))
% 15.02/14.80 [8838]E(f857(f309(x88381,x88382,x88383),f241(f927(x88381,a915))),f241(f927(x88382,a915)))+~E(f857(f72(x88381,x88382,x88382,x88383),f91(x88381,x88382,f241(f927(x88381,a915)),x88383)),f31(x88382))
% 15.02/14.80 [8847]P106(f857(f857(f234(a919),x88471),x88472))+~P106(f857(f857(f234(a919),f857(f857(f80(a919),f857(a112,x88473)),x88471)),f857(f857(f80(a919),f857(a112,x88473)),x88472)))
% 15.02/14.80 [8863]P106(f857(f857(f234(f927(x88631,a915)),x88632),x88633))+~P106(f857(f857(f234(f927(x88631,a915)),f857(f78(f927(x88631,a915)),x88633)),f857(f78(f927(x88631,a915)),x88632)))
% 15.02/14.80 [8886]P106(f857(f137(x88861),x88862))+~P106(f857(f137(x88861),f857(f857(f857(f183(f920(x88861),f920(x88861)),x88863),f167(x88861)),x88862)))
% 15.02/14.80 [8959]E(f857(f284(x89591,x89591,f306(x89591,x89592)),x89593),x89593)+~P106(f857(f857(f234(f927(x89591,a915)),f857(f284(x89591,x89591,x89592),x89593)),x89593))
% 15.02/14.80 [9007]~P109(x90071)+P14(x90071,f857(f136(x90071,f857(f857(f9(x90071,x90071,a915),a324),f857(x90072,x90073))),x90073))
% 15.02/14.80 [9014]~P106(f857(f857(f234(a919),x90141),x90142))+P106(f857(f857(f234(a919),x90141),f857(f142(a919,a919,f79(a919),x90142),x90143)))
% 15.02/14.80 [9100]~P106(f857(f857(f328(f926(x91001,x91001)),x91002),f306(x91001,x91003)))+P106(f857(f857(f328(f926(x91001,x91001)),x91002),f857(f857(f183(f926(x91001,x91001),a915),f620(x91003,x91002,x91001)),x91003)))
% 15.02/14.80 [9181]~P83(x91811)+E(f857(f857(f79(x91811),x91812),f857(f142(x91811,x91811,f857(f9(x91811,x91811,x91811),f79(x91811)),f2(x91811)),f857(f168(x91811),x91813))),f857(f142(x91811,x91811,f79(x91811),x91812),x91813))
% 15.02/14.80 [9298]~P27(x92982,x92981,x92983,f241(f927(x92982,a915)),f241(f927(x92981,a915)))+E(f91(x92981,x92982,f241(f927(x92981,a915)),f91(x92982,x92981,f241(f927(x92982,a915)),x92983)),x92983)
% 15.02/14.80 [9451]P56(x94511,x94512,x94513)+P106(f857(f857(f328(f926(x94511,x94512)),f857(f857(f251(x94511,x94512),f612(x94513,x94512,x94511)),f599(x94513,x94512,x94511))),x94513))
% 15.02/14.80 [9452]P56(x94521,x94522,x94523)+P106(f857(f857(f328(f926(x94521,x94522)),f857(f857(f251(x94521,x94522),f612(x94523,x94522,x94521)),f598(x94523,x94522,x94521))),x94523))
% 15.02/14.80 [9522]~P106(f857(f857(f328(f926(x95221,x95221)),x95222),f857(f857(f288(x95221,x95221,x95221),x95223),f306(x95221,x95223))))+P106(f857(f857(f328(f926(x95221,x95221)),x95222),f857(f857(f183(f926(x95221,x95221),a915),f622(x95223,x95222,x95221)),x95223)))
% 15.02/14.80 [9523]~P106(f857(x95231,f857(f857(f164(x95232),x95233),f857(f190(f920(x95232)),f177(x95232,x95231,x95233)))))+~P106(f857(f857(f235(a919),f857(f190(f920(x95232)),f177(x95232,x95231,x95233))),f857(f190(f920(x95232)),x95233)))
% 15.02/14.80 [9614]~P106(f857(f857(f234(f927(x96141,a915)),x96142),x96143))+P106(f857(f857(f234(f927(x96141,a915)),f857(f857(f9(x96141,f927(x96141,a915),a915),f328(x96141)),x96142)),f857(f857(f9(x96141,f927(x96141,a915),a915),f328(x96141)),x96143)))
% 15.02/14.80 [9674]~P106(f857(f857(f328(f926(f927(x96741,a915),f927(x96741,a915))),f857(f857(f251(f927(x96741,a915),f927(x96741,a915)),x96742),x96743)),f313(x96741)))+P106(f857(f857(f235(f927(x96741,a915)),x96742),x96743))
% 15.02/14.80 [9702]P57(x97021,x97022,x97023)+~P106(f857(f857(f328(f926(x97021,x97021)),f857(f857(f251(x97021,x97021),f615(x97023,x97022,x97021)),f614(x97023,x97022,x97021))),x97023))
% 15.02/14.80 [9703]P57(x97031,x97032,x97033)+~P106(f857(f857(f328(f926(x97031,x97031)),f857(f857(f251(x97031,x97031),f614(x97033,x97032,x97031)),f615(x97033,x97032,x97031))),x97033))
% 15.02/14.80 [9741]~P106(f857(f857(f328(f926(f920(x97411),f920(x97411))),f857(f857(f251(f920(x97411),f920(x97411)),x97412),x97412)),f147(x97411,x97413)))+P106(f857(f857(f328(f926(x97411,x97411)),f857(f857(f251(x97411,x97411),f651(x97412,x97413,x97411)),f651(x97412,x97413,x97411))),x97413))
% 15.02/14.80 [9791]P106(f857(f857(f234(f927(x97911,a915)),x97912),x97913))+~P106(f857(f857(f234(f927(x97911,a915)),f857(f857(f9(x97911,f927(x97911,a915),a915),f328(x97911)),x97912)),f857(f857(f9(x97911,f927(x97911,a915),a915),f328(x97911)),x97913)))
% 15.02/14.80 [9872]E(f857(f857(f3(a919),f857(f857(f8(a919,a919),x98721),f857(f281(a919),x98722))),f857(f857(f8(a919,a919),x98723),f857(f281(a919),x98722))),f857(f857(f8(a919,a919),f857(f857(f20(a919,a919,a919),f857(f857(f10(a919,f927(a919,a919),a919),f3(a919)),x98721)),x98723)),f857(f281(a919),x98722)))+~P106(f857(f857(f234(a919),f857(x98723,f417(x98722,x98721,x98723))),f857(x98721,f417(x98722,x98721,x98723))))
% 15.02/14.80 [5839]~P76(x58391)+E(f857(f857(f3(x58391),f857(f857(f79(x58391),x58392),x58393)),x58393),x58392)
% 15.02/14.80 [5840]~P76(x58401)+E(f857(f857(f79(x58401),f857(f857(f3(x58401),x58402),x58403)),x58403),x58402)
% 15.02/14.80 [6065]~P76(x60651)+E(f857(f857(f79(x60651),x60652),f857(f857(f79(x60651),f857(f78(x60651),x60652)),x60653)),x60653)
% 15.02/14.80 [6153]~P82(x61531)+E(f857(f857(f80(x61531),f857(f857(f243(x61531),x61532),x61533)),x61532),f857(f857(f243(x61531),x61532),f857(a112,x61533)))
% 15.02/14.80 [6154]~P113(x61541)+E(f857(f857(f80(x61541),f857(f857(f243(x61541),x61542),x61543)),x61542),f857(f857(f243(x61541),x61542),f857(a112,x61543)))
% 15.02/14.80 [6380]~P120(x63801)+E(f857(f75(x63801),f857(f857(f243(x63801),f857(f78(x63801),x63802)),x63803)),f857(f75(x63801),f857(f857(f243(x63801),x63802),x63803)))
% 15.02/14.80 [6426]~P82(x64261)+E(f857(f857(f80(x64261),f857(f857(f243(x64261),x64262),x64263)),x64262),f857(f857(f80(x64261),x64262),f857(f857(f243(x64261),x64262),x64263)))
% 15.02/14.80 [6483]E(f857(f857(f3(a99),f857(f857(f79(a99),x64831),x64832)),x64833),f273(x64831,x64832,x64833))+~P106(f857(f857(f235(a99),x64832),x64833))
% 15.02/14.80 [6507]~E(f857(f857(f138(x65071),x65073),x65072),f113(x65071))+P106(f857(f857(f234(a919),f857(f190(f920(x65071)),x65072)),x65073))
% 15.02/14.80 [6644]E(f857(f857(f80(a919),f857(f103(a919),x66441)),f857(f857(f80(a919),f857(f103(a919),x66442)),x66443)),f2(a919))+~P106(f857(f857(f235(a1),x66441),a82))
% 15.02/14.80 [6660]~P65(x66601)+E(f857(f857(f243(x66601),f857(f857(f290(x66601),f77(x66601)),x66602)),x66603),f857(f857(f290(x66601),f77(x66601)),f857(f857(f243(x66601),x66602),x66603)))
% 15.02/14.80 [6739]E(f857(f857(f3(a919),f857(f857(f79(a919),x67391),x67392)),x67393),f857(f857(f3(a919),x67391),f857(f857(f3(a919),x67393),x67392)))+~P106(f857(f857(f234(a919),x67392),x67393))
% 15.02/14.80 [6741]E(f857(f857(f3(a919),f857(f857(f79(a919),x67411),x67412)),x67413),f857(f857(f79(a919),x67411),f857(f857(f3(a919),x67412),x67413)))+~P106(f857(f857(f234(a919),x67413),x67412))
% 15.02/14.80 [6780]~P2(x67801)+P106(f857(f857(f234(x67801),f857(f857(f101(x67801),x67802),x67803)),x67803))
% 15.02/14.80 [6781]~P102(x67811)+P106(f857(f857(f234(x67811),f857(f857(f101(x67811),x67812),x67813)),x67813))
% 15.02/14.80 [6782]~P2(x67821)+P106(f857(f857(f234(x67821),f857(f857(f101(x67821),x67822),x67823)),x67822))
% 15.02/14.80 [6783]~P102(x67831)+P106(f857(f857(f234(x67831),f857(f857(f101(x67831),x67832),x67833)),x67832))
% 15.02/14.80 [6784]~P109(x67841)+P106(f857(f857(f234(x67841),f857(f857(f188(x67841),x67842),x67843)),x67843))
% 15.02/14.80 [6785]~P109(x67851)+P106(f857(f857(f234(x67851),f857(f857(f188(x67851),x67852),x67853)),x67852))
% 15.02/14.80 [6798]E(f857(f857(f35(a1),f857(f857(f35(a1),x67981),x67982)),x67983),f857(f857(f35(a1),x67981),f857(f857(f80(a1),x67982),x67983)))+~P106(f857(f857(f235(a1),f2(a1)),x67983))
% 15.02/14.80 [6850]~P113(x68501)+E(f857(f857(f79(x68501),f857(f857(f80(x68501),x68502),x68503)),x68503),f857(f857(f80(x68501),f857(f857(f79(x68501),x68502),f77(x68501))),x68503))
% 15.02/14.80 [6851]~P94(x68511)+E(f857(f857(f80(x68511),f857(f78(x68511),f857(f103(x68511),x68512))),x68513),f857(f857(f80(x68511),f857(f103(x68511),f857(f78(a1),x68512))),x68513))
% 15.02/14.80 [6923]~P83(x69231)+E(f857(f165(x69231),f857(f857(f154(x69232,x69231),f857(f18(x69231,x69232),f2(x69231))),x69233)),f2(x69231))
% 15.02/14.80 [6941]E(f857(f857(f79(a919),f857(f103(a919),x69411)),f857(f857(f79(a919),f857(f103(a919),x69412)),x69413)),f857(f857(f79(a919),f857(f103(a919),x69412)),x69413))+~P106(f857(a194,f857(f103(a1),x69411)))
% 15.02/14.80 [6956]~P6(x69561)+E(f36(x69561,f857(f857(f308(x69561),x69562),f857(f857(f308(x69561),x69563),f189(f927(x69561,a915))))),f857(f857(f110(x69561),x69562),x69563))
% 15.02/14.80 [6957]~P6(x69571)+E(f37(x69571,f857(f857(f308(x69571),x69572),f857(f857(f308(x69571),x69573),f189(f927(x69571,a915))))),f857(f857(f101(x69571),x69572),x69573))
% 15.02/14.80 [6979]E(f857(f857(f175(x69791),x69792),x69793),x69793)+~P106(f857(f857(f234(a919),f857(f190(f920(x69791)),x69793)),x69792))
% 15.02/14.80 [6991]E(f857(f857(f138(x69911),x69912),x69913),f113(x69911))+~P106(f857(f857(f234(a919),f857(f190(f920(x69911)),x69913)),x69912))
% 15.02/14.80 [7002]E(f857(f857(f79(a919),f857(f857(f3(a919),x70021),x70022)),x70023),f857(f857(f3(a919),f857(f857(f79(a919),x70021),x70023)),x70022))+~P106(f857(f857(f234(a919),x70022),x70021))
% 15.02/14.80 [7016]~P106(f857(f857(f235(a919),x70161),x70163))+P106(f857(f857(f235(a919),f857(f857(f3(a919),x70161),x70162)),x70163))
% 15.02/14.80 [7043]~P109(x70431)+E(f170(x70431,x70432,f857(f857(f148(x70431,x70431,f7(x70431)),x70432),x70433)),x70433)
% 15.02/14.80 [7134]E(f857(f857(f3(a919),f857(f857(f79(a919),x71341),x71342)),f857(a112,x71343)),f857(f857(f3(a919),x71341),f857(a112,f857(f857(f3(a919),x71343),x71342))))+~P106(f857(f857(f234(a919),x71342),x71343))
% 15.02/14.80 [7135]~P120(x71351)+P106(f857(f857(f234(x71351),f2(x71351)),f857(f857(f243(x71351),f857(f75(x71351),x71352)),x71353)))
% 15.02/14.80 [7181]P25(x71811,x71812,x71813)+~P106(f857(f857(f234(f927(f918(x71811),a915)),x71813),x71812))
% 15.02/14.80 [7223]~P106(f857(f60(x72231),x72232))+P106(f857(f60(x72231),f857(f857(f3(f927(x72231,a915)),x72232),x72233)))
% 15.02/14.80 [7224]~P106(f857(f60(x72241),x72243))+P106(f857(f60(x72241),f857(f857(f101(f927(x72241,a915)),x72242),x72243)))
% 15.02/14.80 [7225]~P106(f857(f60(x72251),x72252))+P106(f857(f60(x72251),f857(f857(f101(f927(x72251,a915)),x72252),x72253)))
% 15.02/14.80 [7368]~P39(x73681,x73683)+P39(x73681,f857(f857(f101(f927(f926(x73681,x73681),a915)),x73682),x73683))
% 15.02/14.80 [7369]~P39(x73691,x73692)+P39(x73691,f857(f857(f101(f927(f926(x73691,x73691),a915)),x73692),x73693))
% 15.02/14.80 [7492]~P2(x74921)+E(f12(x74921,f857(f172(x74921),f857(f857(f151(x74921),x74922),x74923))),f857(f142(x74921,x74921,f110(x74921),x74922),x74923))
% 15.02/14.80 [7493]~P2(x74931)+E(f13(x74931,f857(f172(x74931),f857(f857(f151(x74931),x74932),x74933))),f857(f142(x74931,x74931,f101(x74931),x74932),x74933))
% 15.02/14.80 [7494]~P109(x74941)+E(f16(x74941,f857(f172(x74941),f857(f857(f151(x74941),x74942),x74943))),f857(f142(x74941,x74941,f188(x74941),x74942),x74943))
% 15.02/14.80 [7495]~P109(x74951)+E(f17(x74951,f857(f172(x74951),f857(f857(f151(x74951),x74952),x74953))),f857(f142(x74951,x74951,f233(x74951),x74952),x74953))
% 15.02/14.80 [7556]~P106(f857(f60(x75561),x75562))+P106(f857(f857(f234(a919),f857(f34(x75561),x75562)),f857(f34(x75561),f857(f857(f308(x75561),x75563),x75562))))
% 15.02/14.80 [7563]E(f857(f857(f110(f927(a919,a915)),f857(f301(a919,x75631),x75632)),f857(f301(a919,x75632),f857(f857(f79(a919),x75632),x75633))),f857(f301(a919,x75631),f857(f857(f79(a919),x75632),x75633)))+~P106(f857(f857(f234(a919),x75631),x75632))
% 15.02/14.80 [7572]P106(f857(f857(f234(a919),x75721),x75722))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x75723),x75721)),x75722))
% 15.02/14.80 [7573]P106(f857(f857(f234(a919),x75731),x75732))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x75731),x75733)),x75732))
% 15.02/14.80 [7574]P106(f857(f857(f235(a919),x75741),x75742))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),x75741),x75743)),x75742))
% 15.02/14.80 [7613]~P109(x76131)+E(f14(x76131,f188(x76131),f857(f172(x76131),f857(f857(f151(x76131),x76132),x76133))),f857(f142(x76131,x76131,f188(x76131),x76132),x76133))
% 15.02/14.80 [7614]~P109(x76141)+E(f15(x76141,f233(x76141),f857(f172(x76141),f857(f857(f151(x76141),x76142),x76143))),f857(f142(x76141,x76141,f233(x76141),x76142),x76143))
% 15.02/14.80 [7618]~E(x76182,f189(f927(f926(x76181,x76181),a915)))+P106(f857(f857(f234(f927(f926(x76181,x76181),a915)),x76182),x76183))
% 15.02/14.80 [7719]E(f857(f857(f110(f927(x77191,a915)),x77192),f857(f857(f3(f927(x77191,a915)),x77193),x77192)),x77193)+~P106(f857(f857(f234(f927(x77191,a915)),x77192),x77193))
% 15.02/14.80 [7720]~P106(f857(f857(f234(a919),x77201),f857(f857(f79(a919),x77203),x77202)))+P106(f857(f857(f234(a919),f857(f857(f3(a919),x77201),x77202)),x77203))
% 15.02/14.80 [7721]~P106(f857(f857(f235(a919),x77211),f857(f857(f3(a919),x77213),x77212)))+P106(f857(f857(f235(a919),f857(f857(f79(a919),x77211),x77212)),x77213))
% 15.02/14.80 [7777]E(x77771,f113(x77772))+E(f857(f141(x77772),f857(f857(f857(f183(f920(x77772),f920(x77772)),x77773),f167(x77772)),x77771)),f857(f857(f164(x77772),x77771),f44(a919,x77773,f857(f190(f920(x77772)),x77771))))
% 15.02/14.80 [7786]E(f857(f857(f308(x77861),x77862),f857(f857(f3(f927(x77861,a915)),x77863),f857(f857(f308(x77861),x77862),f189(f927(x77861,a915))))),x77863)+~P106(f857(f857(f328(x77861),x77862),x77863))
% 15.02/14.80 [7947]P106(f857(f857(f234(a919),x79471),f857(f857(f79(a919),x79472),x79473)))+~P106(f857(f857(f234(a919),f857(f857(f3(a919),x79471),x79473)),x79472))
% 15.02/14.80 [7948]P106(f857(f857(f235(a919),x79481),f857(f857(f3(a919),x79482),x79483)))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),x79481),x79483)),x79482))
% 15.02/14.80 [7973]P106(f857(f60(x79731),x79732))+~P106(f857(f60(x79731),f857(f857(f110(f927(x79731,a915)),x79733),x79732)))
% 15.02/14.80 [7974]P106(f857(f60(x79741),x79742))+~P106(f857(f60(x79741),f857(f857(f110(f927(x79741,a915)),x79742),x79743)))
% 15.02/14.80 [8047]~P48(x80471,x80473)+P106(f857(f857(f328(f926(x80471,x80471)),f857(f857(f251(x80471,x80471),x80472),x80472)),x80473))
% 15.02/14.80 [8181]E(f857(f857(f164(a919),f139(a919,f857(f301(a919,x81811),x81812))),x81813),f857(f857(f79(a919),x81811),x81813))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),x81811),x81813)),x81812))
% 15.02/14.80 [8247]E(f857(f857(f175(a919),x82471),f139(a919,f857(f301(a919,x82472),x82473))),f139(a919,f857(f301(a919,x82472),f857(f857(f79(a919),x82472),x82471))))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x82472),x82471)),x82473))
% 15.02/14.80 [8303]~P94(x83031)+E(f857(f857(f243(x83031),x83032),f857(f103(a919),f857(f857(f79(a1),x83033),x83033))),f857(f857(f85(x83031,x83031),f857(f857(f243(x83031),x83032),f857(f103(a919),x83033))),f857(f857(f20(x83031,x83031,x83031),f80(x83031)),f7(x83031))))
% 15.02/14.80 [8567]E(f857(f857(f134(x85671),f857(f857(f175(x85671),x85672),x85673)),f857(f857(f151(x85671),f857(f857(f164(x85671),x85673),x85672)),f857(f857(f138(x85671),f857(a112,x85672)),x85673))),x85673)+~P106(f857(f857(f235(a919),x85672),f857(f190(f920(x85671)),x85673)))
% 15.02/14.80 [8574]P106(f857(f857(f234(f927(x85741,a915)),f314(x85741,x85742)),f314(x85741,x85743)))+~P106(f857(f857(f234(f927(x85741,f927(x85741,a915))),x85743),x85742))
% 15.02/14.80 [8575]~P57(x85751,x85752,x85753)+P57(x85751,x85752,f857(f857(f3(f927(f926(x85751,x85751),a915)),x85753),f306(x85751,f189(f927(f926(x85751,x85751),a915)))))
% 15.02/14.80 [8594]P106(f857(f857(f234(f927(x85941,a915)),f315(x85941,x85942)),f315(x85941,x85943)))+~P106(f857(f857(f234(f927(f926(x85941,x85941),a915)),x85943),x85942))
% 15.02/14.80 [8601]~P128(x86011)+P106(f857(f857(f234(x86011),f2(x86011)),f857(f857(f79(x86011),f857(f857(f80(x86011),x86012),x86012)),f857(f857(f80(x86011),x86013),x86013))))
% 15.02/14.80 [8634]P106(f857(f857(f234(f927(x86341,a915)),f857(f280(x86341),x86342)),f857(f280(x86341),x86343)))+~P106(f857(f857(f234(f927(f926(x86341,x86341),a915)),x86342),x86343))
% 15.02/14.80 [8663]~P55(x86631,x86632)+~P106(f857(f857(f328(f926(x86631,x86631)),f857(f857(f251(x86631,x86631),x86633),x86633)),x86632))
% 15.02/14.80 [8665]~P39(x86651,x86652)+~P106(f857(f857(f328(f926(x86651,x86651)),f857(f857(f251(x86651,x86651),x86653),x86653)),x86652))
% 15.02/14.80 [8723]P106(f857(f857(f234(f927(x87231,a915)),f36(f927(x87231,a915),x87232)),f36(f927(x87231,a915),x87233)))+~P106(f857(f857(f234(f927(f927(x87231,a915),a915)),x87232),x87233))
% 15.02/14.80 [8724]P106(f857(f857(f234(f927(x87241,a915)),f37(f927(x87241,a915),x87242)),f37(f927(x87241,a915),x87243)))+~P106(f857(f857(f234(f927(f927(x87241,a915),a915)),x87243),x87242))
% 15.02/14.80 [8778]~P9(x87781,x87783,x87782)+P106(f857(f857(f234(f927(f926(x87781,x87781),a915)),x87782),f857(f857(f253(x87781,x87781),x87783),f857(f18(f927(x87781,a915),x87781),x87783))))
% 15.02/14.80 [8779]~P54(x87791,x87793,x87792)+P106(f857(f857(f234(f927(f926(x87791,x87791),a915)),x87792),f857(f857(f253(x87791,x87791),x87793),f857(f18(f927(x87791,a915),x87791),x87793))))
% 15.02/14.80 [8828]~P87(x88281)+P106(f857(f857(f234(x88281),f857(f857(f3(x88281),f857(f75(x88281),x88282)),f857(f75(x88281),x88283))),f857(f75(x88281),f857(f857(f3(x88281),x88283),x88282))))
% 15.02/14.80 [8829]~P87(x88291)+P106(f857(f857(f234(x88291),f857(f857(f3(x88291),f857(f75(x88291),x88292)),f857(f75(x88291),x88293))),f857(f75(x88291),f857(f857(f3(x88291),x88292),x88293))))
% 15.02/14.80 [8861]P106(f857(f857(f234(f927(f926(x88611,x88611),a915)),f306(x88611,x88612)),f306(x88611,x88613)))+~P106(f857(f857(f234(f927(f926(x88611,x88611),a915)),x88612),x88613))
% 15.02/14.80 [8972]~P26(x89722,x89721,x89723,f241(f927(x89722,a915)))+E(f857(f72(x89721,x89722,x89722,f91(x89722,x89721,f241(f927(x89722,a915)),x89723)),x89723),f31(x89722))
% 15.02/14.80 [9032]P57(x90321,x90322,x90323)+~P57(x90321,x90322,f857(f857(f3(f927(f926(x90321,x90321),a915)),x90323),f306(x90321,f189(f927(f926(x90321,x90321),a915)))))
% 15.02/14.80 [9052]P106(f857(f857(f234(f927(f926(f920(x90521),f920(x90521)),a915)),f157(x90521,x90522)),f157(x90521,x90523)))+~P106(f857(f857(f234(f927(f926(x90521,x90521),a915)),x90522),x90523))
% 15.02/14.80 [9053]P106(f857(f857(f234(f927(f926(f920(x90531),f920(x90531)),a915)),f158(x90531,x90532)),f158(x90531,x90533)))+~P106(f857(f857(f234(f927(f926(x90531,x90531),a915)),x90532),x90533))
% 15.02/14.80 [9074]~P54(x90741,x90743,x90742)+P106(f857(f857(f234(f927(f926(x90741,x90741),a915)),x90742),f857(f857(f288(x90741,x90741,x90741),f857(f285(x90741,x90741),x90742)),x90742)))
% 15.02/14.80 [9126]~P106(f857(f137(x91261),x91262))+E(f857(f136(x91261,f857(f857(f9(x91261,f927(x91261,a915),a915),f328(x91261)),f857(f172(x91261),f176(x91261,x91262,x91263)))),x91262),f176(x91261,x91262,x91263))
% 15.02/14.80 [9179]E(x91791,x91792)+~P106(f857(f857(f328(f926(x91793,x91793)),f857(f857(f251(x91793,x91793),x91791),x91792)),f306(x91793,f189(f927(f926(x91793,x91793),a915)))))
% 15.02/14.80 [9261]P106(f857(f857(f328(x92611),x92612),f315(x92611,x92613)))+P106(f857(f857(f328(f926(x92611,x92611)),f857(f857(f251(x92611,x92611),f509(x92613,x92612,x92611)),x92612)),x92613))
% 15.02/14.80 [9262]P106(f857(f857(f328(x92621),x92622),f315(x92621,x92623)))+P106(f857(f857(f328(f926(x92621,x92621)),f857(f857(f251(x92621,x92621),f602(x92623,x92622,x92621)),x92622)),x92623))
% 15.02/14.80 [9263]P106(f857(f857(f328(x92631),x92632),f315(x92631,x92633)))+P106(f857(f857(f328(f926(x92631,x92631)),f857(f857(f251(x92631,x92631),f604(x92633,x92632,x92631)),x92632)),x92633))
% 15.02/14.80 [9299]P26(x92991,x92992,x92993,f241(f927(x92991,a915)))+~E(f857(f72(x92992,x92991,x92991,f91(x92991,x92992,f241(f927(x92991,a915)),x92993)),x92993),f31(x92991))
% 15.02/14.80 [9352]~P106(f857(f857(f328(f920(x93521)),x93523),f161(x93521,x93522)))+P106(f857(f160(x93521,f857(f857(f9(x93521,f927(x93521,a915),a915),f328(x93521)),x93522)),x93523))
% 15.02/14.80 [9375]P106(f857(x93753,x93752))+E(f857(f261(x93751),f857(f857(f20(x93751,a915,a915),f857(f857(f10(a915,f927(a915,a915),x93751),a325),f857(a324,x93752))),x93753)),f189(f927(x93751,a915)))
% 15.02/14.80 [9391]~P87(x93911)+P106(f857(f857(f234(x93911),f857(f75(x93911),f857(f857(f3(x93911),f857(f75(x93911),x93912)),f857(f75(x93911),x93913)))),f857(f75(x93911),f857(f857(f3(x93911),x93912),x93913))))
% 15.02/14.80 [9405]~P106(f857(x94053,x94052))+E(f857(f261(x94051),f857(f857(f20(x94051,a915,a915),f857(f857(f10(a915,f927(a915,a915),x94051),a325),f857(a324,x94052))),x94053)),f857(f857(f308(x94051),x94052),f189(f927(x94051,a915))))
% 15.02/14.80 [9414]~P106(f857(f857(f328(f927(x94141,a915)),x94143),f857(f307(x94141),x94142)))+P106(f857(f247(x94141,f857(f857(f9(x94141,f927(x94141,a915),a915),f328(x94141)),x94142)),x94143))
% 15.02/14.80 [9450]P39(x94501,x94502)+P106(f857(f857(f328(f926(x94501,x94501)),f857(f857(f251(x94501,x94501),f857(f567(x94502,x94501),f857(a112,x94503))),f857(f567(x94502,x94501),x94503))),x94502))
% 15.02/14.80 [9591]P106(f857(f857(f328(f920(x95911)),x95912),f161(x95911,x95913)))+~P106(f857(f160(x95911,f857(f857(f9(x95911,f927(x95911,a915),a915),f328(x95911)),x95913)),x95912))
% 15.02/14.80 [9606]P106(f857(f857(f328(f927(x96061,a915)),x96062),f857(f307(x96061),x96063)))+~P106(f857(f247(x96061,f857(f857(f9(x96061,f927(x96061,a915),a915),f328(x96061)),x96063)),x96062))
% 15.02/14.80 [9669]P106(f857(f857(f328(x96691),f857(f267(x96691,x96692),x96693)),f857(f172(x96691),f857(f857(f154(f926(a99,x96691),x96691),f255(a99,x96691)),x96692))))+~P106(f857(f857(f235(a99),x96693),f857(f165(a99),f857(f857(f154(f926(a99,x96691),a99),f250(a99,x96691)),x96692))))
% 15.02/14.80 [9720]P106(f857(f857(f234(f927(f926(f920(x97201),f920(x97201)),a915)),f158(x97201,x97202)),f857(f857(f253(f920(x97201),f920(x97201)),f161(x97201,x97203)),f857(f18(f927(f920(x97201),a915),f920(x97201)),f161(x97201,x97203)))))+~P106(f857(f857(f234(f927(f926(x97201,x97201),a915)),x97202),f857(f857(f253(x97201,x97201),x97203),f857(f18(f927(x97201,a915),x97201),x97203))))
% 15.02/14.80 [9744]P106(f857(f857(f328(x97441),f857(f250(x97441,f926(a99,a99)),f857(f265(x97441,x97442),x97443))),f857(f172(x97441),f857(f857(f154(f926(a99,x97441),x97441),f255(a99,x97441)),x97442))))+~P106(f857(f857(f235(a99),f2(a99)),f857(f165(a99),f857(f857(f154(f926(a99,x97441),a99),f250(a99,x97441)),x97442))))
% 15.02/14.80 [9759]~P106(f857(f857(f234(f927(f926(x97591,x97591),a915)),x97592),f857(f857(f253(x97591,x97591),x97593),f857(f18(f927(x97591,a915),x97591),x97593))))+P106(f857(f857(f234(f927(f926(x97591,x97591),a915)),f857(f857(f288(x97591,x97591,x97591),x97592),f306(x97591,x97592))),f857(f857(f253(x97591,x97591),x97593),f857(f18(f927(x97591,a915),x97591),x97593))))
% 15.02/14.80 [10058]~P39(x100581,x100582)+~P106(f857(f857(f328(f926(x100581,x100581)),f857(f857(f251(x100581,x100581),f857(x100583,f857(a112,f568(x100582,x100581,x100583)))),f857(x100583,f568(x100582,x100581,x100583)))),x100582))
% 15.02/14.80 [10059]~P39(x100591,x100592)+~P106(f857(f857(f328(f926(x100591,x100591)),f857(f857(f251(x100591,x100591),f857(x100593,f857(a112,f608(x100593,x100592,x100591)))),f857(x100593,f608(x100593,x100592,x100591)))),x100592))
% 15.02/14.80 [10320]P106(f857(f857(f234(f927(f926(f927(x103201,a915),f927(x103201,a915)),a915)),f857(f857(f288(f927(x103201,a915),f927(x103201,a915),f927(x103201,a915)),f319(x103201,x103202)),f857(f857(f110(f927(f926(f927(x103201,a915),f927(x103201,a915)),a915)),f319(x103201,x103203)),f857(f857(f308(f926(f927(x103201,a915),f927(x103201,a915))),f857(f857(f251(f927(x103201,a915),f927(x103201,a915)),f189(f927(x103201,a915))),f189(f927(x103201,a915)))),f189(f927(f926(f927(x103201,a915),f927(x103201,a915)),a915)))))),f319(x103201,x103202)))+~P106(f857(f857(f234(f927(f926(x103201,x103201),a915)),f857(f857(f288(x103201,x103201,x103201),x103202),x103203)),x103202))
% 15.02/14.80 [10321]P106(f857(f857(f234(f927(f926(f927(x103211,a915),f927(x103211,a915)),a915)),f857(f857(f288(f927(x103211,a915),f927(x103211,a915),f927(x103211,a915)),f317(x103211,x103212)),f857(f857(f110(f927(f926(f927(x103211,a915),f927(x103211,a915)),a915)),f317(x103211,x103213)),f857(f857(f308(f926(f927(x103211,a915),f927(x103211,a915))),f857(f857(f251(f927(x103211,a915),f927(x103211,a915)),f189(f927(x103211,a915))),f189(f927(x103211,a915)))),f189(f927(f926(f927(x103211,a915),f927(x103211,a915)),a915)))))),f317(x103211,x103212)))+~P106(f857(f857(f234(f927(f926(x103211,x103211),a915)),f857(f857(f288(x103211,x103211,x103211),x103212),x103213)),x103212))
% 15.02/14.80 [7491]~P106(f857(f857(f234(a919),x74912),x74911))+E(f857(f857(f3(a919),f857(a112,f857(f857(f3(a919),x74911),x74912))),x74913),f857(f857(f3(a919),f857(a112,x74911)),f857(f857(f79(a919),x74912),x74913)))
% 15.02/14.80 [7531]~P62(x75311)+E(f857(f857(f79(x75311),f44(x75311,x75312,x75313)),f857(f857(f80(x75311),f857(f857(f35(x75311),x75312),x75313)),x75313)),x75312)
% 15.02/14.80 [7725]E(f857(f857(f80(a919),f857(f103(a919),x77251)),f857(f857(f80(a919),f857(f103(a919),x77252)),x77253)),f857(f857(f80(a919),f857(f103(a919),f857(f857(f80(a1),x77251),x77252))),x77253))+P106(f857(f857(f235(a1),x77251),a82))
% 15.02/14.80 [8190]~P106(f857(f857(f234(a919),x81903),x81902))+P106(f857(f857(f234(a919),x81901),f857(f857(f3(a919),f857(f857(f79(a919),x81902),x81901)),x81903)))
% 15.02/14.80 [8389]~P106(f857(f857(f234(a919),x83891),x83892))+E(f857(f857(f134(a919),f139(a919,f857(f301(a919,x83891),x83892))),f139(a919,f857(f301(a919,x83892),f857(f857(f79(a919),x83892),x83893)))),f139(a919,f857(f301(a919,x83891),f857(f857(f79(a919),x83892),x83893))))
% 15.02/14.80 [8642]~P106(f857(f60(x86421),x86422))+E(f857(a112,f857(f34(x86421),f857(f857(f3(f927(x86421,a915)),x86422),f857(f857(f308(x86421),x86423),f189(f927(x86421,a915)))))),f857(f34(x86421),f857(f857(f308(x86421),x86423),x86422)))
% 15.02/14.80 [8681]~P106(f857(f60(x86811),x86812))+E(f857(f857(f79(a919),f77(a919)),f857(f34(x86811),f857(f857(f3(f927(x86811,a915)),x86812),f857(f857(f308(x86811),x86813),f189(f927(x86811,a915)))))),f857(f34(x86811),f857(f857(f308(x86811),x86813),x86812)))
% 15.02/14.80 [8870]E(f857(f857(f3(a919),f857(f34(x88701),x88702)),f857(f34(x88701),f857(f857(f101(f927(x88701,a915)),x88702),x88703))),f857(f34(x88701),f857(f857(f3(f927(x88701,a915)),x88702),x88703)))+~P106(f857(f60(x88701),f857(f857(f101(f927(x88701,a915)),x88702),x88703)))
% 15.02/14.80 [9121]~P7(f857(x91212,f403(x91212,x91213,x91211)))+E(f857(f100(a1),f857(f857(f8(x91211,a919),f857(f857(f10(a1,a919,x91211),a104),x91212)),x91213)),f857(f857(f8(x91211,a1),x91212),x91213))
% 15.02/14.80 [9122]~P7(f857(x91222,f396(x91222,x91223,x91221)))+E(f857(f100(a1),f857(f857(f11(x91221,a919),f857(f857(f10(a1,a919,x91221),a104),x91222)),x91223)),f857(f857(f11(x91221,a1),x91222),x91223))
% 15.02/14.80 [9162]~P106(f857(f60(x91621),x91623))+P106(f857(f857(f234(a919),f857(f857(f3(a919),f857(f34(x91621),x91622)),f857(f34(x91621),x91623))),f857(f34(x91621),f857(f857(f3(f927(x91621,a915)),x91622),x91623))))
% 15.02/14.80 [9189]P106(f857(f857(f328(x91891),f403(x91892,x91893,x91891)),x91893))+E(f857(f100(a1),f857(f857(f8(x91891,a919),f857(f857(f10(a1,a919,x91891),a104),x91892)),x91893)),f857(f857(f8(x91891,a1),x91892),x91893))
% 15.02/14.80 [9190]P106(f857(f857(f328(x91901),f396(x91902,x91903,x91901)),x91903))+E(f857(f100(a1),f857(f857(f11(x91901,a919),f857(f857(f10(a1,a919,x91901),a104),x91902)),x91903)),f857(f857(f11(x91901,a1),x91902),x91903))
% 15.02/14.80 [9253]E(f84(x92531,f857(f857(f9(x92531,f927(x92531,a915),a915),f328(x92531)),f857(f857(f3(f927(x92531,a915)),x92532),f857(f857(f308(x92531),x92533),f189(f927(x92531,a915)))))),f246(x92531,x92533,x92532))+P106(f857(f857(f234(f927(x92531,a915)),x92532),f857(f857(f308(x92531),x92533),f189(f927(x92531,a915)))))
% 15.02/14.80 [9607]E(f857(f857(f154(f920(x96071),x96071),f857(f857(f9(f920(x96071),a919,x96071),f164(x96071)),x96072)),f857(f136(f920(x96071),f857(f857(f10(a919,a915,f920(x96071)),f857(f235(a919),x96072)),f190(f920(x96071)))),x96073)),f857(f857(f164(f920(x96071)),f179(x96071,x96073)),x96072))+~P106(f857(f857(f235(a919),x96072),f857(f190(f920(f920(x96071))),f179(x96071,x96073))))
% 15.02/14.80 [9692]E(f857(f136(x96921,x96922),x96923),f177(x96921,x96922,x96923))+P106(f857(f857(f328(x96921),f723(x96923,x96922,x96921)),f857(f172(x96921),f857(f857(f138(x96921),f857(f190(f920(x96921)),f177(x96921,x96922,x96923))),x96923))))
% 15.02/14.80 [9832]E(f857(f857(f138(x98321),f857(f190(f920(x98321)),f177(x98321,x98322,x98323))),x98323),f113(x98321))+~P106(f857(x98322,f857(f141(x98321),f857(f857(f138(x98321),f857(f190(f920(x98321)),f177(x98321,x98322,x98323))),x98323))))
% 15.02/14.80 [9924]~P106(f857(f857(f328(f926(x99241,x99241)),x99242),f306(x99241,x99243)))+P106(f857(f857(f328(f926(x99241,x99241)),x99242),f857(f857(f39(a919,f927(f926(x99241,x99241),a915)),f241(f927(a919,a915))),f857(f857(f9(a919,f927(f926(x99241,x99241),a915),f927(f926(x99241,x99241),a915)),f183(f926(x99241,x99241),a915)),x99243))))
% 15.02/14.80 [9984]~P106(f857(f857(f234(f927(x99841,a915)),f857(f857(f39(a919,f927(x99841,a915)),f857(f301(a919,f2(a919)),f501(x99843,x99842,x99841))),x99842)),x99843))+P106(f857(f857(f234(f927(x99841,a915)),f857(f857(f39(a919,f927(x99841,a915)),f241(f927(a919,a915))),x99842)),x99843))
% 15.02/14.80 [10031]~P106(f857(f857(f235(a1),f2(a1)),x100313))+P106(f857(f857(f235(a1),x100311),f857(f857(f79(a1),x100312),f857(f857(f80(a1),f857(f857(f79(a1),f857(f75(a1),f857(f857(f3(a1),x100312),x100311))),f77(a1))),x100313))))
% 15.02/14.80 [10045]~P39(x100451,f857(f857(f110(f927(f926(x100451,x100451),a915)),x100452),x100453))+P39(x100451,f857(f857(f110(f927(f926(x100451,x100451),a915)),f857(f857(f110(f927(f926(x100451,x100451),a915)),f857(f857(f288(x100451,x100451,x100451),x100452),x100452)),f857(f857(f288(x100451,x100451,x100451),x100453),x100452))),x100453))
% 15.02/14.80 [10120]P39(x101201,f857(f857(f110(f927(f926(x101201,x101201),a915)),x101202),x101203))+~P39(x101201,f857(f857(f110(f927(f926(x101201,x101201),a915)),f857(f857(f110(f927(f926(x101201,x101201),a915)),f857(f857(f288(x101201,x101201,x101201),x101202),x101202)),f857(f857(f288(x101201,x101201,x101201),x101203),x101202))),x101203))
% 15.02/14.80 [9696]~P143(x96961)+E(f857(f102(x96961),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x96962),x96963)),f189(f927(f926(a919,a919),a915)))))),f857(f857(f3(x96961),f857(f100(x96961),x96962)),f857(f100(x96961),x96963)))
% 15.02/14.80 [9779]P106(f857(x97793,x97792))+E(f857(f261(x97791),f857(f857(f20(x97791,a915,a915),f857(f857(f10(a915,f927(a915,a915),x97791),a325),f857(f857(f9(x97791,x97791,a915),a324),x97792))),x97793)),f189(f927(x97791,a915)))
% 15.02/14.80 [9781]~P106(f857(x97813,x97812))+E(f857(f261(x97811),f857(f857(f20(x97811,a915,a915),f857(f857(f10(a915,f927(a915,a915),x97811),a325),f857(f857(f9(x97811,x97811,a915),a324),x97812))),x97813)),f857(f857(f308(x97811),x97812),f189(f927(x97811,a915))))
% 15.02/14.80 [10010]E(x100101,x100102)+P106(f857(f857(f242(x100103,x100103,f857(f857(f10(f927(x100103,a915),f927(x100103,a915),x100103),f857(f10(a915,a915,x100103),a321)),a324)),x100101),x100102))
% 15.02/14.80 [10100]~E(x101001,x101002)+~P106(f857(f857(f242(x101003,x101003,f857(f857(f10(f927(x101003,a915),f927(x101003,a915),x101003),f857(f10(a915,a915,x101003),a321)),a324)),x101001),x101002))
% 15.02/14.80 [10112]~P106(f857(f60(x101121),x101123))+E(f857(f857(f63(x101121,f927(x101121,a915),f857(f857(f10(f927(x101121,a915),f927(f927(x101121,a915),f927(x101121,a915)),x101121),f857(f9(f927(x101121,a915),f927(x101121,a915),f927(x101121,a915)),f3(f927(x101121,a915)))),f857(f857(f9(x101121,f927(x101121,a915),f927(x101121,a915)),f308(x101121)),f189(f927(x101121,a915))))),x101122),x101123),f857(f857(f3(f927(x101121,a915)),x101122),x101123))
% 15.02/14.80 [10144]~P106(f857(f857(f235(a1),f2(a1)),x101443))+P106(f857(f857(f235(a1),f857(f857(f3(a1),x101441),f857(f857(f80(a1),f857(f857(f79(a1),f857(f75(a1),f857(f857(f3(a1),x101441),x101442))),f77(a1))),x101443))),x101442))
% 15.02/14.80 [10406]~P106(f857(f857(f328(x104061),x104063),f315(x104061,x104062)))+P106(f857(f314(x104061,f857(f857(f9(x104061,f927(f926(x104061,x104061),a915),f927(x104061,a915)),f857(f857(f10(f927(x104061,f927(f927(f926(x104061,x104061),a915),a915)),f927(f927(f926(x104061,x104061),a915),f927(x104061,a915)),x104061),f9(x104061,f927(f926(x104061,x104061),a915),a915)),f857(f857(f10(f927(x104061,f926(x104061,x104061)),f927(x104061,f927(f927(f926(x104061,x104061),a915),a915)),x104061),f857(f10(f926(x104061,x104061),f927(f927(f926(x104061,x104061),a915),a915),x104061),f328(f926(x104061,x104061)))),f251(x104061,x104061)))),x104062)),x104063))
% 15.02/14.80 [10420]P106(f857(f857(f328(x104201),x104202),f315(x104201,x104203)))+~P106(f857(f314(x104201,f857(f857(f9(x104201,f927(f926(x104201,x104201),a915),f927(x104201,a915)),f857(f857(f10(f927(x104201,f927(f927(f926(x104201,x104201),a915),a915)),f927(f927(f926(x104201,x104201),a915),f927(x104201,a915)),x104201),f9(x104201,f927(f926(x104201,x104201),a915),a915)),f857(f857(f10(f927(x104201,f926(x104201,x104201)),f927(x104201,f927(f927(f926(x104201,x104201),a915),a915)),x104201),f857(f10(f926(x104201,x104201),f927(f927(f926(x104201,x104201),a915),a915),x104201),f328(f926(x104201,x104201)))),f251(x104201,x104201)))),x104203)),x104202))
% 15.02/14.80 [9982]~P106(f857(f60(x99821),f857(f261(x99821),x99823)))+P106(f857(f60(x99821),f857(f261(x99821),f857(f857(f20(x99821,a915,a915),f857(f857(f10(a915,f927(a915,a915),x99821),a325),x99822)),x99823))))
% 15.02/14.80 [9983]~P106(f857(f60(x99831),f857(f261(x99831),x99832)))+P106(f857(f60(x99831),f857(f261(x99831),f857(f857(f20(x99831,a915,a915),f857(f857(f10(a915,f927(a915,a915),x99831),a325),x99832)),x99833))))
% 15.02/14.80 [10079]P106(f857(f60(x100791),f857(f261(x100791),x100792)))+~P106(f857(f60(x100791),f857(f261(x100791),f857(f857(f20(x100791,a915,a915),f857(f857(f10(a915,f927(a915,a915),x100791),a326),x100793)),x100792))))
% 15.02/14.80 [10080]P106(f857(f60(x100801),f857(f261(x100801),x100802)))+~P106(f857(f60(x100801),f857(f261(x100801),f857(f857(f20(x100801,a915,a915),f857(f857(f10(a915,f927(a915,a915),x100801),a326),x100802)),x100803))))
% 15.02/14.80 [10383]~P106(f857(f60(x103831),x103832))+P106(f857(f60(f920(x103831)),f857(f261(f920(x103831)),f857(f857(f20(f920(x103831),a915,a915),f857(f857(f10(a915,f927(a915,a915),f920(x103831)),a325),f857(f857(f9(f920(x103831),f927(x103831,a915),a915),f857(f857(f10(f927(x103831,a915),f927(f927(x103831,a915),a915),f920(x103831)),f234(f927(x103831,a915))),f172(x103831))),x103832))),f857(f857(f9(f920(x103831),a919,a915),f857(f857(f10(a919,f927(a919,a915),f920(x103831)),a324),f190(f920(x103831)))),x103833)))))
% 15.02/14.80 [10384]~P106(f857(f60(x103841),x103842))+P106(f857(f60(f920(x103841)),f857(f261(f920(x103841)),f857(f857(f20(f920(x103841),a915,a915),f857(f857(f10(a915,f927(a915,a915),f920(x103841)),a325),f857(f857(f9(f920(x103841),f927(x103841,a915),a915),f857(f857(f10(f927(x103841,a915),f927(f927(x103841,a915),a915),f920(x103841)),f234(f927(x103841,a915))),f172(x103841))),x103842))),f857(f857(f9(f920(x103841),a919,a915),f857(f857(f10(a919,f927(a919,a915),f920(x103841)),f234(a919)),f190(f920(x103841)))),x103843)))))
% 15.02/14.80 [10093]~P113(x100931)+E(f857(f857(f243(x100931),x100932),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x100933)),f857(f857(f80(x100931),f857(f857(f243(x100931),x100932),x100933)),f857(f857(f243(x100931),x100932),x100933)))
% 15.02/14.80 [10125]~P82(x101251)+E(f857(f857(f243(x101251),f857(f857(f243(x101251),x101252),x101253)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f243(x101251),x101252),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101253)))
% 15.02/14.80 [10181]~P143(x101811)+E(f857(f857(f243(x101811),f857(f78(x101811),x101812)),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101813)),f857(f857(f243(x101811),x101812),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101813)))
% 15.02/14.80 [10328]~P120(x103281)+P106(f857(f857(f234(x103281),f2(x103281)),f857(f857(f79(x103281),f857(f857(f243(x103281),x103282),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103281),x103283),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))))
% 15.02/14.80 [10191]~P113(x101911)+E(f857(f857(f243(x101911),x101912),f857(a112,f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101913))),f857(f857(f80(x101911),x101912),f857(f857(f80(x101911),f857(f857(f243(x101911),x101912),x101913)),f857(f857(f243(x101911),x101912),x101913))))
% 15.02/14.80 [10241]~P82(x102411)+E(f857(f857(f80(x102411),x102412),f857(f857(f243(x102411),f857(f857(f243(x102411),x102412),x102413)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x102411),x102412),f857(a112,f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x102413))))
% 15.02/14.80 [10282]~P120(x102821)+P106(f857(f857(f234(x102821),f2(x102821)),f857(f857(f243(x102821),x102822),f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x102823))))
% 15.02/14.80 [10359]~P94(x103591)+E(f857(f857(f3(x103591),f857(f857(f79(x103591),f857(f857(f243(x103591),x103592),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103591),x103593),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f857(f857(f80(x103591),f857(f857(f80(x103591),f857(f103(x103591),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103592)),x103593)),f857(f857(f243(x103591),f857(f857(f3(x103591),x103592),x103593)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.80 [10360]~P94(x103601)+E(f857(f857(f79(x103601),f857(f857(f79(x103601),f857(f857(f243(x103601),x103602),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103601),x103603),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f857(f857(f80(x103601),f857(f857(f80(x103601),f857(f103(x103601),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103602)),x103603)),f857(f857(f243(x103601),f857(f857(f79(x103601),x103602),x103603)),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.80 [4871]E(x48711,x48712)+~E(f30(x48713,x48711),f30(x48714,x48712))
% 15.02/14.80 [4872]E(x48721,x48722)+~E(f30(x48721,x48723),f30(x48722,x48724))
% 15.02/14.80 [4873]E(x48731,x48732)+~E(f29(x48733,x48731),f29(x48734,x48732))
% 15.02/14.80 [4874]E(x48741,x48742)+~E(f29(x48741,x48743),f29(x48742,x48744))
% 15.02/14.80 [7990]P26(x79901,x79902,x79903,x79904)+~E(f494(x79904,x79903,x79902,x79901),f495(x79904,x79903,x79902,x79901))
% 15.02/14.80 [8281]P36(x82811,x82812,x82813,x82814,f113(x82812))+~E(x82814,f113(x82811))
% 15.02/14.80 [8282]P36(x82821,x82822,x82823,f113(x82821),x82824)+~E(x82824,f113(x82822))
% 15.02/14.80 [8818]~P36(x88182,x88183,x88184,x88181,f113(x88183))+E(x88181,f113(x88182))
% 15.02/14.80 [8819]~P36(x88193,x88192,x88194,f113(x88193),x88191)+E(x88191,f113(x88192))
% 15.02/14.80 [5254]~P18(x52543,x52541,x52544)+E(f857(f857(x52541,x52542),x52542),x52542)
% 15.02/14.80 [5505]P106(f857(x55052,x55054))+E(f857(f136(x55051,x55052),f169(x55051,x55053,x55054)),f113(x55051))
% 15.02/14.80 [5542]~E(x55424,f189(f927(x55421,a915)))+E(f857(f309(x55421,x55422,x55423),x55424),f189(f927(x55422,a915)))
% 15.02/14.80 [5789]~P106(f857(x57892,x57894))+E(f857(f136(x57891,x57892),f169(x57891,x57893,x57894)),f169(x57891,x57893,x57894))
% 15.02/14.80 [5818]~E(f857(f309(x58182,x58183,x58184),x58181),f189(f927(x58183,a915)))+E(x58181,f189(f927(x58182,a915)))
% 15.02/14.80 [6005]~P8(x60051,x60053)+E(f270(x60051,x60052,f269(x60051,x60053),x60054),x60054)
% 15.02/14.80 [6112]~P109(x61122)+E(f857(f857(f148(x61121,x61122,x61123),x61124),f113(x61121)),f857(f857(f151(x61121),x61124),f113(x61121)))
% 15.02/14.80 [6477]~E(x64771,f189(f927(x64772,a915)))+~P106(f857(f61(x64772,x64773,x64771),x64774))
% 15.02/14.80 [6499]~P60(x64991,x64993,x64994,x64992)+P106(f857(f60(x64991),x64992))
% 15.02/14.80 [6501]~P60(x65011,x65013,x65012,x65014)+P106(f857(f60(x65011),x65012))
% 15.02/14.80 [6509]~P60(x65092,x65093,x65094,x65091)+~E(x65091,f189(f927(x65092,a915)))
% 15.02/14.80 [6543]~P110(x65431)+E(f857(f857(f101(f927(x65431,a915)),f857(f301(x65431,x65432),x65433)),f302(x65431,x65433,x65434)),f189(f927(x65431,a915)))
% 15.02/14.80 [6571]~P106(f857(f857(x65713,x65714),x65712))+P106(f857(f857(f328(x65711),x65712),f293(x65711,x65713,x65714)))
% 15.02/14.80 [6572]~P106(f857(f857(x65723,x65724),x65722))+P106(f857(f857(f328(x65721),x65722),f294(x65721,x65723,x65724)))
% 15.02/14.80 [6573]~P106(f857(f857(x65733,x65732),x65734))+P106(f857(f857(f328(x65731),x65732),f295(x65731,x65733,x65734)))
% 15.02/14.80 [6574]~P106(f857(f857(x65743,x65742),x65744))+P106(f857(f857(f328(x65741),x65742),f297(x65741,x65743,x65744)))
% 15.02/14.80 [6714]~P110(x67141)+E(f857(f857(f101(f927(x67141,a915)),f302(x67141,x67142,x67143)),f305(x67141,x67143,x67144)),f189(f927(x67141,a915)))
% 15.02/14.80 [6715]~P110(x67151)+E(f857(f857(f101(f927(x67151,a915)),f302(x67151,x67152,x67153)),f304(x67151,x67153,x67154)),f189(f927(x67151,a915)))
% 15.02/14.80 [6716]~P110(x67161)+E(f857(f857(f101(f927(x67161,a915)),f305(x67161,x67162,x67163)),f302(x67161,x67163,x67164)),f189(f927(x67161,a915)))
% 15.02/14.80 [6717]~P110(x67171)+E(f857(f857(f101(f927(x67171,a915)),f304(x67171,x67172,x67173)),f305(x67171,x67173,x67174)),f189(f927(x67171,a915)))
% 15.02/14.80 [6718]~P110(x67181)+E(f857(f857(f101(f927(x67181,a915)),f304(x67181,x67182,x67183)),f304(x67181,x67183,x67184)),f189(f927(x67181,a915)))
% 15.02/14.80 [6756]P106(f857(f857(x67561,x67562),f566(x67562,x67561)))+~P106(f857(f248(x67563,x67564,x67561),x67562))
% 15.02/14.80 [6837]~P109(x68372)+E(f857(f172(x68371),f150(x68371,x68372,x68373,x68374)),f857(f172(x68371),x68374))
% 15.02/14.80 [6887]~P146(x68871)+E(f191(x68871,x68872,f857(a112,x68873),x68874),f191(x68871,x68872,x68873,f857(x68872,x68874)))
% 15.02/14.80 [6950]~P106(f857(f857(f328(x69504),x69503),f293(x69504,x69501,x69502)))+P106(f857(f857(x69501,x69502),x69503))
% 15.02/14.80 [6951]~P106(f857(f857(f328(x69514),x69513),f294(x69514,x69511,x69512)))+P106(f857(f857(x69511,x69512),x69513))
% 15.02/14.80 [6952]~P106(f857(f857(f328(x69524),x69522),f295(x69524,x69521,x69523)))+P106(f857(f857(x69521,x69522),x69523))
% 15.02/14.80 [6953]~P106(f857(f857(f328(x69534),x69532),f297(x69534,x69531,x69533)))+P106(f857(f857(x69531,x69532),x69533))
% 15.02/14.80 [7028]E(f857(f34(f925(x70281,x70282)),f312(x70281,x70282,x70283,x70284)),f2(a919))+P106(f857(f60(x70282),x70284))
% 15.02/14.80 [7029]E(f857(f34(f925(x70291,x70292)),f312(x70291,x70292,x70293,x70294)),f2(a919))+P106(f857(f60(x70291),x70293))
% 15.02/14.80 [7232]~P15(x72324,x72321,x72322)+E(f857(f72(x72321,x72321,x72321,f857(x72322,x72323)),f857(x72322,x72323)),f857(x72322,x72323))
% 15.02/14.80 [7476]E(f276(x74761,x74762,x74763,x74764),f857(f251(f927(a99,f927(a915,f923(f921(x74761)))),f926(a99,a99)),f40(x74761)))+~P106(f857(f857(f234(a99),x74763),f2(a99)))
% 15.02/14.80 [8112]~E(x81122,x81123)+P106(f857(f857(f328(f926(x81121,x81121)),f857(f857(f251(x81121,x81121),x81122),x81123)),f306(x81121,x81124)))
% 15.02/14.80 [8141]~P26(x81411,x81412,x81413,f241(f927(x81411,a915)))+E(f857(f76(x81411,x81412,f241(f927(x81411,a915)),x81413),f857(x81413,x81414)),x81414)
% 15.02/14.80 [8142]~P26(x81421,x81422,x81423,f241(f927(x81421,a915)))+E(f857(f91(x81421,x81422,f241(f927(x81421,a915)),x81423),f857(x81423,x81424)),x81424)
% 15.02/14.80 [8230]~P106(f857(f857(f328(f920(x82301)),f857(f857(f151(x82301),x82304),x82302)),f161(x82301,x82303)))+P106(f857(f857(f328(f920(x82301)),x82302),f161(x82301,x82303)))
% 15.02/14.80 [8231]~P106(f857(f857(f328(f920(x82311)),f857(f857(f134(x82311),x82314),x82312)),f161(x82311,x82313)))+P106(f857(f857(f328(f920(x82311)),x82312),f161(x82311,x82313)))
% 15.02/14.80 [8232]~P106(f857(f857(f328(f920(x82321)),f857(f857(f134(x82321),x82322),x82324)),f161(x82321,x82323)))+P106(f857(f857(f328(f920(x82321)),x82322),f161(x82321,x82323)))
% 15.02/14.80 [8243]~P109(x82431)+P14(x82431,f857(f857(f154(x82432,x82431),x82433),f150(x82432,x82431,x82433,x82434)))
% 15.02/14.80 [8347]P26(x83474,x83473,x83471,x83472)+E(f857(x83471,f494(x83472,x83471,x83473,x83474)),f857(x83471,f495(x83472,x83471,x83473,x83474)))
% 15.02/14.80 [8453]~P26(x84532,x84531,x84534,x84533)+P26(x84531,x84532,f76(x84532,x84531,x84533,x84534),f857(f309(x84532,x84531,x84534),x84533))
% 15.02/14.80 [8592]P39(f926(x85922,x85924),f279(x85922,x85924,x85921,x85923))+P106(f857(x85921,f571(x85922,x85923,x85924,x85921)))
% 15.02/14.80 [8706]E(x87061,x87062)+~P106(f857(f857(f328(f926(x87063,x87063)),f857(f857(f251(x87063,x87063),x87061),x87062)),f262(x87063,x87064)))
% 15.02/14.80 [8770]~P106(f857(f60(f925(x87703,x87701)),f312(x87703,x87701,x87704,x87702)))+P106(f857(f60(x87701),x87702))
% 15.02/14.80 [8771]~P106(f857(f60(f925(x87711,x87713)),f312(x87711,x87713,x87712,x87714)))+P106(f857(f60(x87711),x87712))
% 15.02/14.80 [8780]~P26(x87801,x87802,x87803,x87804)+P27(x87801,x87802,x87803,x87804,f857(f309(x87801,x87802,x87803),x87804))
% 15.02/14.80 [8781]P12(x87811,x87812,x87813,x87814)+~E(f857(x87814,f828(x87812,x87814,x87813,x87811)),f857(x87814,f829(x87812,x87814,x87813,x87811)))
% 15.02/14.80 [8871]~P27(x88712,x88713,x88714,x88711,f189(f927(x88713,a915)))+E(x88711,f189(f927(x88712,a915)))
% 15.02/14.80 [8872]~P27(x88723,x88722,x88724,f189(f927(x88723,a915)),x88721)+E(x88721,f189(f927(x88722,a915)))
% 15.02/14.80 [8964]P39(f926(x89641,x89642),f279(x89641,x89642,x89643,x89644))+~P39(x89642,f857(x89644,f571(x89641,x89644,x89642,x89643)))
% 15.02/14.80 [9527]E(f857(f857(f159(x95271,x95272),f670(x95273,x95274,x95272,x95271)),f671(x95273,x95274,x95272,x95271)),x95274)+~P106(f857(f857(f328(f926(f920(x95271),f920(x95271))),f857(f857(f251(f920(x95271),f920(x95271)),x95272),x95274)),f157(x95271,x95273)))
% 15.02/14.80 [9532]~P106(f857(f857(f328(f926(f920(x95321),f920(x95321))),f857(f857(f251(f920(x95321),f920(x95321)),x95322),x95323)),f145(x95321,x95324)))+P106(f857(f857(f328(f926(f920(x95321),f920(x95321))),f857(f857(f251(f920(x95321),f920(x95321)),x95322),x95323)),f147(x95321,x95324)))
% 15.02/14.80 [9644]P106(f857(f60(x96441),x96442))+~P106(f857(f857(f328(f926(f927(x96441,a915),f927(x96441,a915))),f857(f857(f251(f927(x96441,a915),f927(x96441,a915)),x96443),x96442)),f317(x96441,x96444)))
% 15.02/14.80 [9645]P106(f857(f60(x96451),x96452))+~P106(f857(f857(f328(f926(f927(x96451,a915),f927(x96451,a915))),f857(f857(f251(f927(x96451,a915),f927(x96451,a915)),x96452),x96453)),f317(x96451,x96454)))
% 15.02/14.80 [9648]~E(x96481,f189(f927(x96482,a915)))+~P106(f857(f857(f328(f926(f927(x96482,a915),f927(x96482,a915))),f857(f857(f251(f927(x96482,a915),f927(x96482,a915)),x96483),x96481)),f317(x96482,x96484)))
% 15.02/14.80 [10293]P12(x102931,x102932,x102933,x102934)+~P106(f857(f857(f256(x102931,x102931,a915),f857(f857(f9(x102931,f927(x102931,x102932),f927(x102931,a915)),f857(f857(f10(f927(x102932,a915),f927(f927(x102931,x102932),f927(x102931,a915)),x102931),f10(x102932,a915,x102931)),f857(f857(f10(x102932,f927(x102932,a915),x102931),a324),x102934))),x102934)),f578(x102934,x102933,x102932,x102931)))
% 15.02/14.80 [5153]~E(x51532,f113(x51531))+E(f857(f857(f159(x51531,x51532),x51533),x51534),f113(x51531))
% 15.02/14.80 [5154]~E(x51544,f113(x51541))+E(f857(f857(f154(x51541,x51542),x51543),x51544),f113(x51542))
% 15.02/14.80 [5387]E(x53871,f113(x53872))+~E(f857(f857(f154(x53872,x53873),x53874),x53871),f113(x53873))
% 15.02/14.80 [5388]E(x53881,f113(x53882))+~E(f857(f857(f159(x53882,x53881),x53883),x53884),f113(x53882))
% 15.02/14.80 [5425]E(x54251,x54252)+~E(f857(f857(f134(x54253),x54254),x54251),f857(f857(f134(x54253),x54254),x54252))
% 15.02/14.80 [5426]E(x54261,x54262)+~E(f857(f857(f134(x54263),x54261),x54264),f857(f857(f134(x54263),x54262),x54264))
% 15.02/14.80 [5579]P106(f857(x55793,x55792))+E(f170(x55791,x55792,f857(f136(x55791,x55793),x55794)),f857(f136(x55791,x55793),x55794))
% 15.02/14.80 [5581]~P106(f857(x55812,x55813))+P35(x55811,x55812,f857(f857(f151(x55811),x55813),x55814))
% 15.02/14.80 [5591]E(x55911,x55912)+~E(f139(a919,f857(f301(a919,x55911),x55913)),f857(f857(f151(a919),x55912),x55914))
% 15.02/14.80 [5639]~P28(x56392,x56393)+P28(x56391,f857(f857(f73(x56392,x56391),x56393),x56394))
% 15.02/14.80 [5640]~P39(x56402,x56403)+P39(x56401,f857(f857(f287(x56402,x56401),x56403),x56404))
% 15.02/14.80 [5641]~P40(x56412,x56413)+P40(x56411,f857(f857(f287(x56412,x56411),x56413),x56414))
% 15.02/14.80 [5642]~P53(x56422,x56423)+P53(x56421,f857(f857(f287(x56422,x56421),x56423),x56424))
% 15.02/14.80 [5773]~P35(x57731,x57732,x57734)+P35(x57731,x57732,f857(f857(f151(x57731),x57733),x57734))
% 15.02/14.80 [5774]~P35(x57741,x57742,x57744)+P35(x57741,x57742,f857(f857(f134(x57741),x57743),x57744))
% 15.02/14.80 [5775]~P35(x57751,x57752,x57753)+P35(x57751,x57752,f857(f857(f134(x57751),x57753),x57754))
% 15.02/14.80 [5861]~E(x58611,f113(x58612))+~E(f857(f857(f134(x58612),x58613),f857(f857(f151(x58612),x58614),f113(x58612))),x58611)
% 15.02/14.80 [5886]~P33(x58863,x58861,f857(f857(f151(x58863),x58862),x58864))+P106(f857(x58861,x58862))
% 15.02/14.80 [5896]E(f114(x58961,x58962),x58963)+~E(f857(f857(f134(x58961),x58963),f857(f857(f151(x58961),x58964),f113(x58961))),x58962)
% 15.02/14.80 [5897]E(f144(x58971,x58972),x58973)+~E(f857(f857(f134(x58971),x58974),f857(f857(f151(x58971),x58973),f113(x58971))),x58972)
% 15.02/14.80 [6007]~E(f139(a919,f857(f301(a919,x60071),x60072)),f857(f857(f151(a919),x60073),x60074))+P106(f857(f857(f235(a919),x60071),x60072))
% 15.02/14.80 [6016]P33(x60161,x60162,x60163)+~P33(x60161,x60162,f857(f857(f151(x60161),x60164),x60163))
% 15.02/14.80 [6017]P33(x60171,x60172,x60173)+~P33(x60171,x60172,f857(f857(f134(x60171),x60174),x60173))
% 15.02/14.80 [6018]P33(x60181,x60182,x60183)+~P33(x60181,x60182,f857(f857(f134(x60181),x60183),x60184))
% 15.02/14.80 [6216]E(x62161,f857(f857(f134(x62162),f857(f168(x62162),x62163)),f857(f857(f151(x62162),x62164),f113(x62162))))+~E(f857(f168(x62162),x62161),f857(f857(f151(x62162),x62164),x62163))
% 15.02/14.80 [6398]~P110(x63981)+E(f857(f857(f101(f927(x63981,a915)),f857(f301(x63981,x63982),x63983)),f857(f301(x63981,x63983),x63984)),f189(f927(x63981,a915)))
% 15.02/14.80 [6409]E(f857(f857(f164(x64091),f169(x64091,x64092,x64093)),x64094),x64093)+~P106(f857(f857(f235(a919),x64094),x64092))
% 15.02/14.80 [6436]~P72(x64361)+E(f857(f165(x64361),f857(f857(f154(a1,x64361),x64362),f178(x64363,x64364))),f857(f857(f8(a1,x64361),x64362),f857(f172(a1),f178(x64363,x64364))))
% 15.02/14.80 [6437]~P72(x64371)+E(f857(f857(f8(a1,x64371),x64372),f857(f172(a1),f178(x64373,x64374))),f857(f165(x64371),f857(f857(f154(a1,x64371),x64372),f178(x64373,x64374))))
% 15.02/14.80 [6584]~E(x65842,f857(f857(f134(x65841),f857(f168(x65841),x65844)),f857(f857(f151(x65841),x65843),f113(x65841))))+E(f857(f168(x65841),x65842),f857(f857(f151(x65841),x65843),x65844))
% 15.02/14.80 [6600]~P20(x66002,x66003,x66004,x66001)+E(f857(x66001,f189(f927(x66002,a915))),f31(x66003))
% 15.02/14.80 [6625]~P110(x66251)+E(f857(f857(f101(f927(x66251,a915)),f305(x66251,x66252,x66253)),f857(f301(x66251,x66253),x66254)),f189(f927(x66251,a915)))
% 15.02/14.80 [6838]E(x68381,f189(f927(x68382,a915)))+~E(f312(x68383,x68382,x68384,x68381),f189(f927(f925(x68383,x68382),a915)))
% 15.02/14.80 [6839]E(x68391,f189(f927(x68392,a915)))+~E(f312(x68392,x68393,x68391,x68394),f189(f927(f925(x68392,x68393),a915)))
% 15.02/14.80 [6907]~P109(x69072)+E(f857(f190(f920(x69071)),f150(x69071,x69072,x69073,x69074)),f857(f190(f920(x69071)),x69074))
% 15.02/14.80 [6918]~P106(f857(f249(x69183,x69184,x69181),x69182))+P106(f857(f857(x69181,f556(x69182,x69181)),x69182))
% 15.02/14.80 [6962]~P106(f857(f60(x69622),x69624))+P106(f857(f60(x69621),f857(f309(x69622,x69621,x69623),x69624)))
% 15.02/14.80 [7193]~P26(x71932,x71931,x71933,x71934)+E(f857(f34(x71931),f857(f309(x71932,x71931,x71933),x71934)),f857(f34(x71932),x71934))
% 15.02/14.80 [7211]E(f857(f309(x72111,x72112,x72113),f857(f310(x72111,x72112,x72113),x72114)),x72114)+~E(f857(f309(x72111,x72112,x72113),f241(f927(x72111,a915))),f241(f927(x72112,a915)))
% 15.02/14.80 [7627]~P26(x76271,x76272,x76273,f241(f927(x76271,a915)))+E(f857(f310(x76271,x76272,x76273),f857(f309(x76271,x76272,x76273),x76274)),x76274)
% 15.02/14.80 [7908]E(x79081,x79082)+~P106(f857(f857(f328(x79083),x79081),f857(f172(x79083),f169(x79083,x79084,x79082))))
% 15.02/14.80 [7917]~E(x79171,f2(a919))+~P106(f857(f857(f328(x79172),x79173),f857(f172(x79172),f169(x79172,x79171,x79174))))
% 15.02/14.80 [7950]P106(f857(x79501,x79502))+~P106(f857(f857(f328(x79503),x79502),f857(f172(x79503),f177(x79503,x79501,x79504))))
% 15.02/14.80 [8058]~P106(f857(f857(f328(f920(x80581)),f857(f857(f151(x80581),x80582),x80584)),f161(x80581,x80583)))+P106(f857(f857(f328(x80581),x80582),x80583))
% 15.02/14.80 [8187]~P106(f857(f857(f328(x81871),x81872),f857(f172(x81871),f176(x81871,x81873,x81874))))+P106(f857(f857(f328(x81871),x81872),f857(f172(x81871),x81873)))
% 15.02/14.80 [8188]~P106(f857(f857(f328(x81881),x81882),f857(f172(x81881),f170(x81881,x81884,x81883))))+P106(f857(f857(f328(x81881),x81882),f857(f172(x81881),x81883)))
% 15.02/14.80 [8189]~P106(f857(f857(f328(x81891),x81892),f857(f172(x81891),f177(x81891,x81894,x81893))))+P106(f857(f857(f328(x81891),x81892),f857(f172(x81891),x81893)))
% 15.02/14.80 [8199]E(f857(f190(f920(x81991)),x81992),x81993)+~P106(f857(f857(f328(f920(x81991)),x81992),f857(f172(f920(x81991)),f54(x81991,x81993,x81994))))
% 15.02/14.80 [8294]P106(f857(x82943,x82942))+E(f857(f136(x82941,f857(f857(f10(a915,a915,x82941),a321),f857(a324,x82942))),f857(f136(x82941,x82943),x82944)),f857(f136(x82941,x82943),x82944))
% 15.02/14.80 [8405]E(f857(f857(f164(x84051),f177(x84051,x84052,x84053)),x84054),f857(f857(f164(x84051),x84053),x84054))+~P106(f857(f857(f235(a919),x84054),f857(f190(f920(x84051)),f177(x84051,x84052,x84053))))
% 15.02/14.80 [8491]~P72(x84911)+E(f857(f857(f8(a919,x84911),f857(f857(f10(a919,x84911,a919),x84912),a112)),f857(f301(a919,x84913),x84914)),f857(f857(f8(a919,x84911),x84912),f857(f301(a919,f857(a112,x84913)),f857(a112,x84914))))
% 15.02/14.80 [8500]~P72(x85001)+E(f857(f857(f8(a919,x85001),f857(f857(f10(a919,x85001,a919),x85002),a112)),f302(a919,x85003,x85004)),f857(f857(f8(a919,x85001),x85002),f302(a919,f857(a112,x85003),f857(a112,x85004))))
% 15.02/14.80 [8627]~P26(x86271,x86273,x86274,f241(f927(x86271,a915)))+P26(x86271,f927(x86272,x86273),f857(f857(f10(x86273,f927(x86272,x86273),x86271),f18(x86273,x86272)),x86274),f241(f927(x86271,a915)))
% 15.02/14.80 [8712]~P26(x87122,x87121,x87124,x87123)+E(f857(f309(x87121,x87122,f76(x87122,x87121,x87123,x87124)),f857(f309(x87122,x87121,x87124),x87123)),x87123)
% 15.02/14.80 [8772]~P106(f857(f857(f328(f926(x87721,x87721)),f857(f857(f251(x87721,x87721),x87722),x87724)),f262(x87721,x87723)))+P106(f857(f857(f328(x87721),x87722),x87723))
% 15.02/14.80 [8895]~P26(x88952,x88951,x88953,f241(f927(x88952,a915)))+E(f857(f309(x88951,x88952,f91(x88952,x88951,f241(f927(x88952,a915)),x88953)),f857(f309(x88952,x88951,x88953),x88954)),x88954)
% 15.02/14.80 [8970]~P27(x89701,x89702,x89703,x89704,f241(f927(x89702,a915)))+E(f857(f309(x89701,x89702,x89703),f241(f927(x89701,a915))),f241(f927(x89702,a915)))
% 15.02/14.80 [9003]~E(f857(f857(f8(x90031,a919),x90034),x90033),f857(a112,x90032))+P106(f857(f857(f328(x90031),f912(x90032,x90033,x90034,x90031)),x90033))
% 15.02/14.80 [9024]~E(f857(f857(f8(x90244,a919),x90241),x90243),f857(a112,x90242))+P106(f857(f857(f235(a919),f2(a919)),f857(x90241,f912(x90242,x90243,x90241,x90244))))
% 15.02/14.80 [9035]~P106(f857(f60(x90352),x90354))+P106(f857(f857(f234(a919),f857(f34(x90351),f857(f309(x90352,x90351,x90353),x90354))),f857(f34(x90352),x90354)))
% 15.02/14.80 [9036]E(f857(f857(f251(x90361,x90362),f643(x90363,x90364,x90362,x90361)),f644(x90363,x90364,x90362,x90361)),x90364)+~P106(f857(f857(f328(f926(x90361,x90362)),x90364),f857(f285(x90362,x90361),x90363)))
% 15.02/14.80 [9044]P26(x90441,x90442,x90443,x90444)+P106(f857(f857(f328(x90441),f494(x90444,x90443,x90442,x90441)),x90444))
% 15.02/14.80 [9045]P26(x90451,x90452,x90453,x90454)+P106(f857(f857(f328(x90451),f495(x90454,x90453,x90452,x90451)),x90454))
% 15.02/14.80 [9113]P12(x91131,x91132,x91133,x91134)+P106(f857(f857(f328(f926(x91131,x91131)),f578(x91134,x91133,x91132,x91131)),x91133))
% 15.02/14.80 [9167]P106(f857(x91671,x91672))+~P106(f857(x91671,f857(f857(f251(x91673,x91674),f397(x91674,x91673,x91671)),f398(x91674,x91673,x91671))))
% 15.02/14.80 [9184]E(f857(f190(f920(x91841)),x91842),f857(f190(f920(x91841)),x91843))+~P106(f857(f857(f328(f926(f920(x91841),f920(x91841))),f857(f857(f251(f920(x91841),f920(x91841)),x91842),x91843)),f145(x91841,x91844)))
% 15.02/14.80 [9185]E(f857(f190(f920(x91851)),x91852),f857(f190(f920(x91851)),x91853))+~P106(f857(f857(f328(f926(f920(x91851),f920(x91851))),f857(f857(f251(f920(x91851),f920(x91851)),x91852),x91853)),f157(x91851,x91854)))
% 15.02/14.80 [9188]E(f857(f190(f920(x91881)),x91882),f857(f190(f920(x91881)),x91883))+~P106(f857(f857(f328(f926(f920(x91881),f920(x91881))),f857(f857(f251(f920(x91881),f920(x91881)),x91882),x91883)),f158(x91881,x91884)))
% 15.02/14.80 [9257]P106(f857(f857(f234(a919),f155(x92571,x92572,x92573)),f155(x92571,x92574,x92573)))+P106(f857(f857(f328(x92571),f669(x92574,x92572,x92573,x92571)),f857(f172(x92571),x92573)))
% 15.02/14.80 [9260]E(f857(f190(f920(x92601)),x92602),f857(f190(f920(x92601)),x92603))+~P106(f857(f857(f328(f926(f920(x92601),f920(x92601))),f857(f857(f251(f920(x92601),f920(x92601)),x92602),x92603)),f306(f920(x92601),f157(x92601,x92604))))
% 15.02/14.80 [9498]~P26(x94981,x94982,x94983,x94984)+~P106(f857(f857(f235(a919),f857(f34(x94982),f857(f309(x94981,x94982,x94983),x94984))),f857(f34(x94981),x94984)))
% 15.02/14.80 [9545]~P106(f857(f857(f328(f926(f920(x95451),f920(x95451))),f857(f857(f251(f920(x95451),f920(x95451)),x95452),x95453)),f157(x95451,x95454)))+P106(f857(f857(f328(f926(f920(x95451),f920(x95451))),f857(f857(f251(f920(x95451),f920(x95451)),x95452),x95453)),f158(x95451,f306(x95451,x95454))))
% 15.02/14.80 [9549]~P106(f857(f857(f328(f926(f920(x95491),f920(x95491))),f857(f857(f251(f920(x95491),f920(x95491)),x95492),x95493)),f158(x95491,x95494)))+P106(f857(f857(f328(f926(f920(x95491),f920(x95491))),f857(f857(f251(f920(x95491),f920(x95491)),x95492),x95493)),f306(f920(x95491),f157(x95491,x95494))))
% 15.02/14.80 [9565]P106(f857(f857(f328(f926(x95651,x95651)),f857(f857(f251(x95651,x95651),x95652),x95653)),f306(x95651,x95654)))+~P106(f857(f857(f328(f926(x95651,x95651)),f857(f857(f251(x95651,x95651),x95652),x95653)),f857(f857(f288(x95651,x95651,x95651),x95654),f306(x95651,x95654))))
% 15.02/14.80 [9639]P106(f857(f857(f286(a919),x96391),x96392))+~P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x96393,x96394)),f289(a919,f286(a919),x96391,x96392)))
% 15.02/14.80 [9760]E(f857(f857(f134(x97601),f685(x97602,x97603,x97604,x97601)),f857(f857(f151(x97601),f686(x97602,x97603,x97604,x97601)),f688(x97602,x97603,x97604,x97601))),x97604)+~P106(f857(f857(f328(f926(f920(x97601),f920(x97601))),f857(f857(f251(f920(x97601),f920(x97601)),x97604),x97603)),f157(x97601,x97602)))
% 15.02/14.80 [9761]E(f857(f857(f134(x97611),f685(x97612,x97613,x97614,x97611)),f857(f857(f151(x97611),f687(x97612,x97613,x97614,x97611)),f688(x97612,x97613,x97614,x97611))),x97613)+~P106(f857(f857(f328(f926(f920(x97611),f920(x97611))),f857(f857(f251(f920(x97611),f920(x97611)),x97614),x97613)),f157(x97611,x97612)))
% 15.02/14.80 [9839]P106(f857(f857(f328(f926(x98391,x98391)),f857(f857(f251(x98391,x98391),x98392),f637(x98393,x98394,x98392,x98391))),f306(x98391,x98393)))+~P106(f857(f857(f328(f926(x98391,x98391)),f857(f857(f251(x98391,x98391),x98392),x98394)),f857(f857(f288(x98391,x98391,x98391),x98393),f306(x98391,x98393))))
% 15.02/14.80 [9907]P106(f857(f857(f234(a919),f155(x99071,x99072,x99073)),f155(x99071,x99074,x99073)))+~P106(f857(f857(f235(a919),f857(x99072,f669(x99074,x99072,x99073,x99071))),f857(x99074,f669(x99074,x99072,x99073,x99071))))
% 15.02/14.80 [9978]P106(f857(f857(f328(f926(x99781,x99781)),f857(f857(f251(x99781,x99781),f628(x99782,x99783,x99784,x99781)),x99783)),f306(x99781,x99782)))+~P106(f857(f857(f328(f926(x99781,x99781)),f857(f857(f251(x99781,x99781),x99784),x99783)),f857(f857(f288(x99781,x99781,x99781),x99782),f306(x99781,x99782))))
% 15.02/14.80 [5407]~E(x54072,x54073)+E(f170(x54071,x54072,f857(f857(f151(x54071),x54073),x54074)),x54074)
% 15.02/14.80 [5535]P106(f857(x55352,x55353))+E(f177(x55351,x55352,f857(f857(f151(x55351),x55353),x55354)),f113(x55351))
% 15.02/14.80 [5603]~P90(x56032)+E(f857(f857(f78(f927(x56031,x56032)),x56033),x56034),f857(f78(x56032),f857(x56033,x56034)))
% 15.02/14.80 [5616]~E(x56162,f2(a919))+E(f857(f857(f138(x56161),x56162),f857(f857(f151(x56161),x56163),x56164)),f857(f857(f151(x56161),x56163),x56164))
% 15.02/14.80 [5617]P106(f857(x56172,x56173))+E(f857(f136(x56171,x56172),f857(f857(f151(x56171),x56173),x56174)),f857(f136(x56171,x56172),x56174))
% 15.02/14.80 [5756]~E(x57562,x57564)+P106(f857(f857(f857(f308(x57561),x57562),x57563),x57564))
% 15.02/14.80 [5764]E(x57641,f113(x57642))+E(f144(x57643,f857(f857(f154(x57642,x57643),x57644),x57641)),f857(x57644,f144(x57642,x57641)))
% 15.02/14.80 [5778]~E(x57781,f62(x57782,x57784))+E(f857(x57781,f857(f857(f308(x57782),x57783),f189(f927(x57782,a915)))),x57783)
% 15.02/14.80 [5813]E(x58131,f113(x58132))+E(f857(f141(x58133),f857(f857(f154(x58132,x58133),x58134),x58131)),f857(x58134,f857(f141(x58132),x58131)))
% 15.02/14.80 [5916]~P106(f857(x59163,x59164))+P106(f857(f857(f857(f308(x59161),x59162),x59163),x59164))
% 15.02/14.80 [6035]~P19(x60352,x60354,x60351)+E(f857(x60351,f857(f857(f308(x60352),x60353),f189(f927(x60352,a915)))),x60353)
% 15.02/14.80 [6061]~E(x60612,x60613)+P106(f857(f857(f328(x60611),x60612),f857(f857(f308(x60611),x60613),x60614)))
% 15.02/14.80 [6066]~P2(x60661)+E(f857(f857(f110(x60661),x60662),f857(f857(f110(x60661),x60663),x60664)),f857(f857(f110(x60661),x60663),f857(f857(f110(x60661),x60662),x60664)))
% 15.02/14.80 [6068]~P101(x60681)+E(f857(f857(f110(x60681),x60682),f857(f857(f110(x60681),x60683),x60684)),f857(f857(f110(x60681),x60683),f857(f857(f110(x60681),x60682),x60684)))
% 15.02/14.80 [6069]~P113(x60691)+E(f857(f857(f80(x60691),x60692),f857(f857(f80(x60691),x60693),x60694)),f857(f857(f80(x60691),x60693),f857(f857(f80(x60691),x60692),x60694)))
% 15.02/14.80 [6070]~P2(x60701)+E(f857(f857(f101(x60701),x60702),f857(f857(f101(x60701),x60703),x60704)),f857(f857(f101(x60701),x60703),f857(f857(f101(x60701),x60702),x60704)))
% 15.02/14.80 [6072]~P102(x60721)+E(f857(f857(f101(x60721),x60722),f857(f857(f101(x60721),x60723),x60724)),f857(f857(f101(x60721),x60723),f857(f857(f101(x60721),x60722),x60724)))
% 15.02/14.80 [6073]~P113(x60731)+E(f857(f857(f79(x60731),x60732),f857(f857(f79(x60731),x60733),x60734)),f857(f857(f79(x60731),x60733),f857(f857(f79(x60731),x60732),x60734)))
% 15.02/14.80 [6075]~P109(x60751)+E(f857(f857(f188(x60751),x60752),f857(f857(f188(x60751),x60753),x60754)),f857(f857(f188(x60751),x60753),f857(f857(f188(x60751),x60752),x60754)))
% 15.02/14.80 [6077]~P109(x60771)+E(f857(f857(f233(x60771),x60772),f857(f857(f233(x60771),x60773),x60774)),f857(f857(f233(x60771),x60773),f857(f857(f233(x60771),x60772),x60774)))
% 15.02/14.80 [6084]E(x60841,x60842)+E(f170(x60843,x60841,f857(f857(f151(x60843),x60842),x60844)),f857(f857(f151(x60843),x60842),f170(x60843,x60841,x60844)))
% 15.02/14.80 [6099]~P106(f857(x60992,x60993))+E(f857(f136(x60991,x60992),f857(f857(f151(x60991),x60993),x60994)),f857(f857(f151(x60991),x60993),f857(f136(x60991,x60992),x60994)))
% 15.02/14.80 [6238]~P106(f857(x62382,x62383))+E(f177(x62381,x62382,f857(f857(f151(x62381),x62383),x62384)),f857(f857(f151(x62381),x62383),f177(x62381,x62382,x62384)))
% 15.02/14.80 [6290]P25(x62901,x62902,x62903)+~P25(x62901,x62902,f857(f857(f308(f918(x62901)),x62904),x62903))
% 15.02/14.80 [6306]E(x63061,f189(f927(x63062,a915)))+E(f857(f857(f38(x63062,f927(x63063,a915)),x63061),f857(f18(f927(x63063,a915),x63062),x63064)),x63064)
% 15.02/14.80 [6307]E(x63071,f189(f927(x63072,a915)))+E(f857(f857(f39(x63072,f927(x63073,a915)),x63071),f857(f18(f927(x63073,a915),x63072),x63074)),x63074)
% 15.02/14.80 [6316]~E(x63164,f189(f927(x63162,a915)))+E(f857(f857(f253(x63161,x63162),x63163),f857(f18(f927(x63162,a915),x63161),x63164)),f189(f927(f926(x63161,x63162),a915)))
% 15.02/14.80 [6317]~E(x63173,f189(f927(x63171,a915)))+E(f857(f857(f253(x63171,x63172),x63173),f857(f18(f927(x63172,a915),x63171),x63174)),f189(f927(f926(x63171,x63172),a915)))
% 15.02/14.80 [6371]E(x63711,f2(a919))+E(f857(f857(f138(x63712),x63711),f857(f857(f151(x63712),x63713),x63714)),f857(f857(f138(x63712),f857(f857(f3(a919),x63711),f77(a919))),x63714))
% 15.02/14.80 [6392]E(x63921,f189(f927(x63922,a915)))+E(f857(f309(x63922,x63923,f857(f18(x63923,x63922),x63924)),x63921),f857(f857(f308(x63923),x63924),f189(f927(x63923,a915))))
% 15.02/14.80 [6395]E(f857(f310(x63951,x63952,f857(f18(x63952,x63951),x63953)),x63954),f189(f927(x63951,a915)))+P106(f857(f857(f328(x63952),x63953),x63954))
% 15.02/14.80 [6460]~E(x64603,f189(f927(x64601,a915)))+E(f857(f857(f38(x64601,f927(x64602,a915)),x64603),f857(f18(f927(x64602,a915),x64601),x64604)),f241(f927(x64602,a915)))
% 15.02/14.80 [6461]~E(x64613,f189(f927(x64611,a915)))+E(f857(f857(f39(x64611,f927(x64612,a915)),x64613),f857(f18(f927(x64612,a915),x64611),x64614)),f189(f927(x64612,a915)))
% 15.02/14.80 [6463]~P62(x64631)+E(f44(x64631,f857(f857(f80(x64631),x64632),x64633),f857(f857(f80(x64631),x64632),x64634)),f857(f857(f80(x64631),x64632),f44(x64631,x64633,x64634)))
% 15.02/14.80 [6635]E(f857(f310(x66351,x66352,f857(f18(x66352,x66351),x66353)),x66354),f241(f927(x66351,a915)))+~P106(f857(f857(f328(x66352),x66353),x66354))
% 15.02/14.80 [6658]~P106(f857(f857(f328(x66581),x66582),x66584))+P106(f857(f857(f328(x66581),x66582),f857(f857(f308(x66581),x66583),x66584)))
% 15.02/14.80 [6663]P106(f857(x66631,x66632))+~P106(f857(f160(x66633,x66631),f857(f857(f151(x66633),x66632),x66634)))
% 15.02/14.80 [6672]~E(x66723,f857(f857(f3(a919),f857(f190(f920(x66721)),x66722)),f77(a919)))+E(f114(x66721,f857(f857(f159(x66721,x66722),x66723),x66724)),f114(x66721,x66722))
% 15.02/14.80 [6692]~P109(x66921)+E(f857(f857(f101(f927(x66921,a915)),f857(f300(x66921),x66922)),f302(x66921,x66923,x66924)),f302(x66921,x66923,f857(f857(f188(x66921),x66922),x66924)))
% 15.02/14.80 [6693]~P109(x66931)+E(f857(f857(f101(f927(x66931,a915)),f857(f282(x66931),x66932)),f302(x66931,x66933,x66934)),f302(x66931,f857(f857(f233(x66931),x66932),x66933),x66934))
% 15.02/14.80 [6709]E(f857(f857(f101(f927(x67091,a915)),x67092),f857(f857(f308(x67091),x67093),x67094)),f857(f857(f101(f927(x67091,a915)),x67092),x67094))+P106(f857(f857(f328(x67091),x67093),x67092))
% 15.02/14.80 [6721]E(f170(x67211,x67212,f857(f857(f134(x67211),x67213),x67214)),f857(f857(f134(x67211),x67213),f170(x67211,x67212,x67214)))+P106(f857(f857(f328(x67211),x67212),f857(f172(x67211),x67213)))
% 15.02/14.80 [6726]~P82(x67261)+E(f857(f857(f80(x67261),f857(f857(f243(x67261),x67262),x67263)),f857(f857(f243(x67261),x67262),x67264)),f857(f857(f243(x67261),x67262),f857(f857(f79(a919),x67263),x67264)))
% 15.02/14.80 [6727]~P113(x67271)+E(f857(f857(f80(x67271),f857(f857(f243(x67271),x67272),x67273)),f857(f857(f243(x67271),x67272),x67274)),f857(f857(f243(x67271),x67272),f857(f857(f79(a919),x67273),x67274)))
% 15.02/14.80 [6764]~P99(x67641)+E(f857(f857(f101(x67641),f857(f857(f110(x67641),x67642),x67643)),f857(f857(f110(x67641),x67642),x67644)),f857(f857(f110(x67641),x67642),f857(f857(f101(x67641),x67643),x67644)))
% 15.02/14.80 [6765]~P113(x67651)+E(f857(f857(f79(x67651),f857(f857(f80(x67651),x67652),x67653)),f857(f857(f80(x67651),x67652),x67654)),f857(f857(f80(x67651),x67652),f857(f857(f79(x67651),x67653),x67654)))
% 15.02/14.80 [6766]~P99(x67661)+E(f857(f857(f110(x67661),f857(f857(f101(x67661),x67662),x67663)),f857(f857(f101(x67661),x67662),x67664)),f857(f857(f101(x67661),x67662),f857(f857(f110(x67661),x67663),x67664)))
% 15.02/14.80 [6767]~P109(x67671)+E(f857(f857(f233(x67671),f857(f857(f188(x67671),x67672),x67673)),f857(f857(f188(x67671),x67672),x67674)),f857(f857(f188(x67671),x67672),f857(f857(f233(x67671),x67673),x67674)))
% 15.02/14.80 [6768]~P109(x67681)+E(f857(f857(f188(x67681),f857(f857(f233(x67681),x67682),x67683)),f857(f857(f233(x67681),x67682),x67684)),f857(f857(f233(x67681),x67682),f857(f857(f188(x67681),x67683),x67684)))
% 15.02/14.80 [6801]~P62(x68011)+E(f44(x68011,f857(f857(f80(x68011),x68012),x68013),f857(f857(f80(x68011),x68014),x68013)),f857(f857(f80(x68011),f44(x68011,x68012,x68014)),x68013))
% 15.02/14.80 [6804]~E(f857(f190(f920(x68041)),x68043),f857(f190(f920(x68042)),x68044))+E(f857(f857(f154(f926(x68041,x68042),x68042),f255(x68041,x68042)),f857(f857(f181(x68041,x68042),x68043),x68044)),x68044)
% 15.02/14.80 [6805]~E(f857(f190(f920(x68051)),x68053),f857(f190(f920(x68052)),x68054))+E(f857(f857(f154(f926(x68051,x68052),x68051),f250(x68051,x68052)),f857(f857(f181(x68051,x68052),x68053),x68054)),x68053)
% 15.02/14.80 [6810]P106(f857(f160(x68101,x68102),x68103))+~P106(f857(f160(x68101,x68102),f857(f857(f151(x68101),x68104),x68103)))
% 15.02/14.80 [6811]P106(f857(f160(x68111,x68112),x68113))+~P106(f857(f160(x68111,x68112),f857(f857(f134(x68111),x68114),x68113)))
% 15.02/14.80 [6812]P106(f857(f160(x68121,x68122),x68123))+~P106(f857(f160(x68121,x68122),f857(f857(f134(x68121),x68123),x68124)))
% 15.02/14.80 [6817]~P63(x68171)+E(f44(x68171,f857(f857(f3(x68171),x68172),f44(x68171,x68173,x68174)),x68174),f44(x68171,f857(f857(f3(x68171),x68172),x68173),x68174))
% 15.02/14.80 [6818]~P62(x68181)+E(f44(x68181,f857(f857(f80(x68181),x68182),f44(x68181,x68183,x68184)),x68184),f44(x68181,f857(f857(f80(x68181),x68182),x68183),x68184))
% 15.02/14.80 [6820]~P62(x68201)+E(f44(x68201,f857(f857(f79(x68201),x68202),f44(x68201,x68203,x68204)),x68204),f44(x68201,f857(f857(f79(x68201),x68202),x68203),x68204))
% 15.02/14.80 [6900]~P109(x69001)+E(f857(f857(f101(f927(x69001,a915)),f302(x69001,x69002,x69003)),f857(f300(x69001),x69004)),f302(x69001,x69002,f857(f857(f188(x69001),x69003),x69004)))
% 15.02/14.80 [6901]~P109(x69011)+E(f857(f857(f101(f927(x69011,a915)),f302(x69011,x69012,x69013)),f857(f282(x69011),x69014)),f302(x69011,f857(f857(f233(x69011),x69012),x69014),x69013))
% 15.02/14.80 [6904]~E(f857(f190(f920(x69041)),x69043),f857(f190(f920(x69042)),x69044))+E(f857(f857(f181(x69041,x69042),f857(f168(x69041),x69043)),f857(f168(x69042),x69044)),f857(f168(f926(x69041,x69042)),f857(f857(f181(x69041,x69042),x69043),x69044)))
% 15.02/14.80 [6915]E(x69151,f857(f857(f3(a919),f857(f190(f920(x69152)),x69153)),f77(a919)))+E(f114(x69152,f857(f857(f159(x69152,x69153),x69151),x69154)),f857(f857(f159(x69152,f114(x69152,x69153)),x69151),x69154))
% 15.02/14.80 [6930]~P106(f857(f137(x69302),x69304))+P106(f857(f137(f926(x69301,x69302)),f857(f857(f181(x69301,x69302),x69303),x69304)))
% 15.02/14.80 [6931]~P106(f857(f137(x69311),x69313))+P106(f857(f137(f926(x69311,x69312)),f857(f857(f181(x69311,x69312),x69313),x69314)))
% 15.02/14.80 [7196]E(f857(f857(f35(a919),x71961),x71962),x71963)+~P106(f857(f47(x71961,x71962),f857(f857(f251(a919,a919),x71963),x71964)))
% 15.02/14.80 [7219]E(f44(a919,x72191,x72192),x72193)+~P106(f857(f47(x72191,x72192),f857(f857(f251(a919,a919),x72194),x72193)))
% 15.02/14.80 [7222]P106(f857(f137(x72221),x72222))+~P106(f857(f137(x72223),f857(f857(f154(x72221,x72223),x72224),x72222)))
% 15.02/14.80 [7230]~P25(x72301,x72302,f857(f857(f308(f918(x72301)),x72303),x72304))+P25(x72301,x72302,f857(f857(f308(f918(x72301)),x72303),f189(f927(f918(x72301),a915))))
% 15.02/14.80 [7307]E(f170(x73071,x73072,f857(f857(f134(x73071),x73073),x73074)),f857(f857(f134(x73071),f170(x73071,x73072,x73073)),x73074))+~P106(f857(f857(f328(x73071),x73072),f857(f172(x73071),x73073)))
% 15.02/14.80 [7400]~P63(x74001)+E(f44(x74001,f857(f857(f3(x74001),f44(x74001,x74002,x74003)),x74004),x74003),f44(x74001,f857(f857(f3(x74001),x74002),x74004),x74003))
% 15.02/14.80 [7403]~P62(x74031)+E(f44(x74031,f857(f857(f80(x74031),f44(x74031,x74032,x74033)),x74034),x74033),f44(x74031,f857(f857(f80(x74031),x74032),x74034),x74033))
% 15.02/14.80 [7404]~P62(x74041)+E(f44(x74041,f857(f857(f79(x74041),f44(x74041,x74042,x74043)),x74044),x74043),f44(x74041,f857(f857(f79(x74041),x74042),x74044),x74043))
% 15.02/14.80 [7597]~E(x75971,f857(f857(f151(x75972),x75973),x75974))+~P106(f857(f857(f234(a919),f857(f190(f920(x75972)),x75971)),f857(f190(f920(x75972)),x75974)))
% 15.02/14.80 [7799]P26(x77991,x77992,x77993,f857(f172(x77991),x77994))+~P106(f857(f137(x77992),f857(f857(f154(x77991,x77992),x77993),x77994)))
% 15.02/14.80 [7874]~P106(f857(f857(f234(f927(x78741,a915)),x78742),x78744))+P106(f857(f857(f234(f927(x78741,a915)),x78742),f857(f857(f308(x78741),x78743),x78744)))
% 15.02/14.80 [7909]~P63(x79091)+E(f44(x79091,f857(f857(f3(x79091),f44(x79091,x79092,x79093)),f44(x79091,x79094,x79093)),x79093),f44(x79091,f857(f857(f3(x79091),x79092),x79094),x79093))
% 15.02/14.80 [7910]~P62(x79101)+E(f44(x79101,f857(f857(f80(x79101),f44(x79101,x79102,x79103)),f44(x79101,x79104,x79103)),x79103),f44(x79101,f857(f857(f80(x79101),x79102),x79104),x79103))
% 15.02/14.80 [7911]~P62(x79111)+E(f44(x79111,f857(f857(f79(x79111),f44(x79111,x79112,x79113)),f44(x79111,x79114,x79113)),x79113),f44(x79111,f857(f857(f79(x79111),x79112),x79114),x79113))
% 15.02/14.80 [8013]~E(f857(x80134,f422(x80134,x80133,x80131,x80132)),f189(f927(x80132,a915)))+E(f857(f857(f39(x80131,f927(x80132,a915)),x80133),x80134),f189(f927(x80132,a915)))
% 15.02/14.80 [8014]~E(f857(x80144,f425(x80144,x80143,x80141,x80142)),f241(f927(x80142,a915)))+E(f857(f857(f38(x80141,f927(x80142,a915)),x80143),x80144),f241(f927(x80142,a915)))
% 15.02/14.80 [8015]~E(f857(x80154,f430(x80154,x80153,x80152,x80151)),f241(f927(x80152,a915)))+E(f857(f857(f38(x80151,f927(x80152,a915)),x80153),x80154),f241(f927(x80152,a915)))
% 15.02/14.80 [8016]~E(f857(x80164,f423(x80164,x80163,x80162,x80161)),f189(f927(x80162,a915)))+E(f857(f857(f39(x80161,f927(x80162,a915)),x80163),x80164),f189(f927(x80162,a915)))
% 15.02/14.80 [8406]P106(f857(x84061,x84062))+~P106(f857(f857(f328(x84063),x84062),f857(f857(f101(f927(x84063,a915)),x84064),f857(f261(x84063),x84061))))
% 15.02/14.80 [8443]~P106(f857(f857(f234(f927(x84431,a915)),x84433),x84434))+P106(f857(f857(f234(f927(x84431,a915)),f857(f857(f308(x84431),x84432),x84433)),f857(f857(f308(x84431),x84432),x84434)))
% 15.02/14.80 [8620]P106(f857(x86202,x86203))+E(f857(f857(f138(x86201),f857(f190(f920(x86201)),f177(x86201,x86202,f857(f857(f151(x86201),x86203),x86204)))),f857(f857(f151(x86201),x86203),x86204)),f857(f857(f151(x86201),x86203),x86204))
% 15.02/14.80 [8726]~P106(f857(f857(f235(a919),f857(x87264,x87262)),f857(x87264,x87263)))+P106(f857(f857(f328(f926(x87261,x87261)),f857(f857(f251(x87261,x87261),x87262),x87263)),f857(f857(f287(a919,x87261),a239),x87264)))
% 15.02/14.80 [8822]~P106(f857(x88222,f742(x88224,x88222,x88223,x88221)))+E(f177(x88221,x88222,f857(f857(f134(x88221),x88223),x88224)),f857(f857(f134(x88221),x88223),f177(x88221,x88222,x88224)))
% 15.02/14.80 [8899]P26(f920(x88991),f920(x88992),f857(f154(x88991,x88992),x88993),x88994)+~P26(x88991,x88992,x88993,f36(f927(x88991,a915),f857(f309(f920(x88991),f927(x88991,a915),f172(x88991)),x88994)))
% 15.02/14.80 [8974]~P106(f857(x89742,x89743))+E(f857(f857(f138(x89741),f857(f190(f920(x89741)),f177(x89741,x89742,f857(f857(f151(x89741),x89743),x89744)))),f857(f857(f151(x89741),x89743),x89744)),f857(f857(f138(x89741),f857(f190(f920(x89741)),f177(x89741,x89742,x89744))),x89744))
% 15.02/14.80 [9015]~E(x90152,x90153)+E(f857(f136(x90151,f857(f857(f10(a915,a915,x90151),a321),f857(a324,x90152))),f857(f857(f151(x90151),x90153),x90154)),f857(f136(x90151,f857(f857(f10(a915,a915,x90151),a321),f857(a324,x90152))),x90154))
% 15.02/14.80 [9025]E(f857(f857(f39(x90251,f927(x90252,a915)),x90253),x90254),f189(f927(x90252,a915)))+P106(f857(f857(f328(x90251),f422(x90254,x90253,x90251,x90252)),x90253))
% 15.02/14.80 [9026]E(f857(f857(f38(x90261,f927(x90262,a915)),x90263),x90264),f241(f927(x90262,a915)))+P106(f857(f857(f328(x90261),f425(x90264,x90263,x90261,x90262)),x90263))
% 15.02/14.80 [9027]E(f857(f857(f38(x90271,f927(x90272,a915)),x90273),x90274),f241(f927(x90272,a915)))+P106(f857(f857(f328(x90271),f430(x90274,x90273,x90272,x90271)),x90273))
% 15.02/14.80 [9028]E(f857(f857(f39(x90281,f927(x90282,a915)),x90283),x90284),f189(f927(x90282,a915)))+P106(f857(f857(f328(x90281),f423(x90284,x90283,x90282,x90281)),x90283))
% 15.02/14.80 [9066]P106(f857(f857(f235(a919),f857(x90661,x90662)),f857(x90661,x90663)))+~P106(f857(f857(f328(f926(x90664,x90664)),f857(f857(f251(x90664,x90664),x90662),x90663)),f857(f857(f287(a919,x90664),a239),x90661)))
% 15.02/14.80 [9092]E(f177(x90921,x90922,f857(f857(f134(x90921),x90923),x90924)),f857(f857(f134(x90921),x90923),f177(x90921,x90922,x90924)))+P106(f857(f857(f328(x90921),f742(x90924,x90922,x90923,x90921)),f857(f172(x90921),x90923)))
% 15.02/14.80 [9143]~P27(x91431,x91432,x91433,f241(f927(x91431,a915)),f241(f927(x91432,a915)))+E(f857(f309(x91431,x91432,x91433),f857(f78(f927(x91431,a915)),x91434)),f857(f78(f927(x91432,a915)),f857(f309(x91431,x91432,x91433),x91434)))
% 15.02/14.80 [9246]P106(f857(f857(f328(x92461),f480(x92462,x92463,x92464,x92461)),x92463))+~P106(f857(f857(f328(f927(x92461,a915)),x92464),f857(f857(f59(x92461),x92463),x92462)))
% 15.02/14.80 [9249]E(x92491,x92492)+~P106(f857(f857(f328(f926(x92493,x92493)),f857(f857(f251(x92493,x92493),x92491),x92492)),f857(f857(f183(f926(x92493,x92493),a915),f2(a919)),x92494)))
% 15.02/14.80 [9330]E(f857(f284(x93301,x93301,x93302),f857(f857(f308(x93301),f480(x93302,x93303,x93304,x93301)),f189(f927(x93301,a915)))),x93304)+~P106(f857(f857(f328(f927(x93301,a915)),x93304),f857(f857(f59(x93301),x93303),x93302)))
% 15.02/14.80 [9335]~P106(f857(f857(f328(f926(x93351,x93351)),f857(f857(f251(x93351,x93351),x93353),x93352)),f306(x93351,x93354)))+P106(f857(f857(f328(f926(x93351,x93351)),f857(f857(f251(x93351,x93351),x93352),x93353)),f306(x93351,f857(f285(x93351,x93351),x93354))))
% 15.02/14.80 [9348]~P62(x93481)+E(f857(f857(f79(x93481),f857(f857(f79(x93481),f857(f857(f80(x93481),x93482),f857(f857(f35(x93481),x93483),x93482))),f44(x93481,x93483,x93482))),x93484),f857(f857(f79(x93481),x93483),x93484))
% 15.02/14.80 [9359]~P106(f857(f857(f328(x93591),x93593),x93594))+P106(f857(f857(f328(f927(x93591,a915)),f857(f284(x93591,x93591,x93592),f857(f857(f308(x93591),x93593),f189(f927(x93591,a915))))),f857(f857(f59(x93591),x93594),x93592)))
% 15.02/14.80 [9371]P106(f857(f857(f328(f926(x93711,x93711)),f857(f857(f251(x93711,x93711),x93712),x93713)),f306(x93711,x93714)))+~P106(f857(f857(f328(f926(x93711,x93711)),f857(f857(f251(x93711,x93711),x93713),x93712)),f306(x93711,f857(f285(x93711,x93711),x93714))))
% 15.02/14.80 [9457]E(f857(f857(f159(x94571,f857(f168(x94571),x94572)),f857(f857(f3(a919),f857(f857(f3(a919),f857(f190(f920(x94571)),x94572)),x94573)),f77(a919))),x94574),f857(f168(x94571),f857(f857(f159(x94571,x94572),x94573),x94574)))+~P106(f857(f857(f235(a919),x94573),f857(f190(f920(x94571)),x94572)))
% 15.02/14.80 [9460]~P106(f857(x94602,f736(x94604,x94602,x94603,x94601)))+E(f857(f857(f138(x94601),f857(f190(f920(x94601)),f177(x94601,x94602,f857(f857(f134(x94601),x94603),x94604)))),f857(f857(f134(x94601),x94603),x94604)),f857(f857(f138(x94601),f857(f190(f920(x94601)),f177(x94601,x94602,x94604))),x94604))
% 15.02/14.80 [9506]~P26(x95062,x95061,x95063,f241(f927(x95062,a915)))+P106(f857(f857(f234(f927(x95061,a915)),f857(f309(x95062,x95061,x95063),f857(f78(f927(x95062,a915)),x95064))),f857(f78(f927(x95061,a915)),f857(f309(x95062,x95061,x95063),x95064))))
% 15.02/14.80 [9518]~P6(x95181)+E(f857(f142(x95181,x95182,f857(f9(x95182,x95181,x95181),f857(f857(f10(x95181,f927(x95181,x95181),x95182),f101(x95181)),x95183)),f241(x95181)),x95184),f857(f857(f38(x95182,x95181),f857(f172(x95182),x95184)),x95183))
% 15.02/14.80 [9519]~P6(x95191)+E(f857(f142(x95191,x95192,f857(f9(x95192,x95191,x95191),f857(f857(f10(x95191,f927(x95191,x95191),x95192),f110(x95191)),x95193)),f189(x95191)),x95194),f857(f857(f39(x95192,x95191),f857(f172(x95192),x95194)),x95193))
% 15.02/14.80 [9529]E(f857(f857(f138(x95291),f857(f190(f920(x95291)),f177(x95291,x95292,f857(f857(f134(x95291),x95293),x95294)))),f857(f857(f134(x95291),x95293),x95294)),f857(f857(f138(x95291),f857(f190(f920(x95291)),f177(x95291,x95292,x95294))),x95294))+P106(f857(f857(f328(x95291),f736(x95294,x95292,x95293,x95291)),f857(f172(x95291),x95293)))
% 15.02/14.80 [9599]~P106(f857(f857(f328(f926(f920(x95994),f920(x95994))),f857(f857(f251(f920(x95994),f920(x95994)),x95993),x95992)),f157(x95994,x95991)))+P106(f857(f857(f235(a919),f670(x95991,x95992,x95993,x95994)),f857(f190(f920(x95994)),x95993)))
% 15.02/14.80 [9600]~P62(x96001)+E(f857(f857(f79(x96001),f857(f857(f79(x96001),f857(f857(f80(x96001),f857(f857(f35(x96001),x96002),x96003)),x96003)),f44(x96001,x96002,x96003))),x96004),f857(f857(f79(x96001),x96002),x96004))
% 15.02/14.80 [9629]~P106(f857(f857(f328(f926(f920(x96291),f920(x96291))),f857(f857(f251(f920(x96291),f920(x96291)),x96292),x96293)),f857(f285(f920(x96291),f920(x96291)),f157(x96291,x96294))))+P106(f857(f857(f328(f926(f920(x96291),f920(x96291))),f857(f857(f251(f920(x96291),f920(x96291)),x96292),x96293)),f157(x96291,f857(f285(x96291,x96291),x96294))))
% 15.02/14.80 [9630]P106(f857(f857(f328(f926(f920(x96301),f920(x96301))),f857(f857(f251(f920(x96301),f920(x96301)),x96302),x96303)),f857(f285(f920(x96301),f920(x96301)),f157(x96301,x96304))))+~P106(f857(f857(f328(f926(f920(x96301),f920(x96301))),f857(f857(f251(f920(x96301),f920(x96301)),x96302),x96303)),f157(x96301,f857(f285(x96301,x96301),x96304))))
% 15.02/14.80 [9672]~P106(f857(f857(f328(x96721),x96723),f857(f263(x96721,x96722),x96724)))+P106(f857(f857(f328(f926(x96721,x96722)),f857(f857(f251(x96721,x96722),x96723),f569(x96724,x96722,x96723,x96721))),x96724))
% 15.02/14.80 [9673]~P106(f857(f857(f328(x96731),x96733),f857(f263(x96731,x96732),x96734)))+P106(f857(f857(f328(f926(x96731,x96732)),f857(f857(f251(x96731,x96732),x96733),f570(x96734,x96732,x96733,x96731))),x96734))
% 15.02/14.80 [9834]~P106(f857(f857(f328(f926(x98341,x98341)),f857(f857(f251(x98341,x98341),x98342),x98344)),f857(f857(f288(x98341,x98341,x98341),x98343),f306(x98341,x98343))))+P106(f857(f857(f328(f926(x98341,x98341)),f857(f857(f251(x98341,x98341),x98342),f628(x98343,x98344,x98342,x98341))),x98343))
% 15.02/14.80 [9992]P12(x99921,x99922,x99923,x99924)+P106(f857(f857(f328(f926(x99921,x99921)),f857(f857(f251(x99921,x99921),f829(x99922,x99924,x99923,x99921)),f828(x99922,x99924,x99923,x99921))),x99923))
% 15.02/14.80 [9999]~P106(f857(f857(f328(f926(x99992,x99991)),x99994),f857(f285(x99991,x99992),x99993)))+P106(f857(f857(f328(f926(x99991,x99992)),f857(f857(f251(x99991,x99992),f644(x99993,x99994,x99991,x99992)),f643(x99993,x99994,x99991,x99992))),x99993))
% 15.02/14.80 [10023]~P106(f857(f857(f328(f926(f920(x100231),f920(x100231))),f857(f857(f251(f920(x100231),f920(x100231)),x100234),x100233)),f157(x100231,x100232)))+P106(f857(f857(f328(f926(x100231,x100231)),f857(f857(f251(x100231,x100231),f686(x100232,x100233,x100234,x100231)),f687(x100232,x100233,x100234,x100231))),x100232))
% 15.02/14.80 [10114]~P106(f857(f857(f328(f926(f920(x101141),f920(x101141))),f857(f857(f251(f920(x101141),f920(x101141)),x101142),x101144)),f157(x101141,x101143)))+P106(f857(f857(f328(f926(x101141,x101141)),f857(f857(f251(x101141,x101141),f857(f857(f164(x101141),x101142),f670(x101143,x101144,x101142,x101141))),f671(x101143,x101144,x101142,x101141))),x101143))
% 15.02/14.80 [10136]~P106(f857(f60(x101362),x101364))+E(f857(f857(f857(f64(f927(x101361,a915),x101362,f110(f927(x101361,a915))),f857(f857(f9(x101362,f927(x101361,a915),f927(x101361,a915)),f857(f857(f10(x101361,f927(f927(x101361,a915),f927(x101361,a915)),x101362),f308(x101361)),x101363)),f189(f927(x101361,a915)))),f189(f927(x101361,a915))),x101364),f857(f309(x101362,x101361,x101363),x101364))
% 15.02/14.80 [10246]~P26(x102461,x102462,x102463,f241(f927(x102461,a915)))+P106(f857(f857(f234(f927(x102461,a915)),f857(f310(x102461,x102462,x102463),f857(f857(f308(x102462),x102464),f189(f927(x102462,a915))))),f857(f857(f308(x102461),f84(x102461,f857(f857(f9(x102461,x102462,a915),f857(f857(f10(x102462,f927(x102462,a915),x102461),a324),x102463)),x102464))),f189(f927(x102461,a915)))))
% 15.02/14.80 [5824]~E(f857(f857(f134(x58241),x58242),x58244),x58243)+E(f857(f857(f175(x58241),f857(f190(f920(x58241)),x58242)),x58243),x58242)
% 15.02/14.80 [5825]~E(f857(f857(f134(x58252),x58253),x58251),x58254)+E(x58251,f857(f857(f138(x58252),f857(f190(f920(x58252)),x58253)),x58254))
% 15.02/14.80 [5836]~E(x58364,f2(a919))+E(f857(f857(f164(x58361),f857(f857(f151(x58361),x58362),x58363)),x58364),x58362)
% 15.02/14.80 [6384]~P113(x63841)+E(f857(f857(f243(x63841),f857(f857(f243(x63841),x63842),x63843)),x63844),f857(f857(f243(x63841),x63842),f857(f857(f80(a919),x63843),x63844)))
% 15.02/14.80 [6385]~P82(x63851)+E(f857(f857(f243(x63851),f857(f857(f243(x63851),x63852),x63853)),x63854),f857(f857(f243(x63851),x63852),f857(f857(f80(a919),x63853),x63854)))
% 15.02/14.80 [6393]E(x63931,f2(a919))+E(f857(f857(f164(x63932),f857(f857(f151(x63932),x63933),x63934)),x63931),f857(f857(f164(x63932),x63934),f857(f857(f3(a919),x63931),f77(a919))))
% 15.02/14.80 [6419]~P124(x64191)+E(f857(f857(f290(x64191),f857(f857(f80(x64191),x64192),x64193)),x64194),f857(f857(f80(x64191),x64192),f857(f857(f290(x64191),x64193),x64194)))
% 15.02/14.80 [6421]~P2(x64211)+E(f857(f857(f110(x64211),f857(f857(f110(x64211),x64212),x64213)),x64214),f857(f857(f110(x64211),x64212),f857(f857(f110(x64211),x64213),x64214)))
% 15.02/14.80 [6423]~P101(x64231)+E(f857(f857(f110(x64231),f857(f857(f110(x64231),x64232),x64233)),x64234),f857(f857(f110(x64231),x64232),f857(f857(f110(x64231),x64233),x64234)))
% 15.02/14.80 [6424]~P70(x64241)+E(f857(f857(f80(x64241),f857(f857(f80(x64241),x64242),x64243)),x64244),f857(f857(f80(x64241),x64242),f857(f857(f80(x64241),x64243),x64244)))
% 15.02/14.80 [6425]~P113(x64251)+E(f857(f857(f80(x64251),f857(f857(f80(x64251),x64252),x64253)),x64254),f857(f857(f80(x64251),x64252),f857(f857(f80(x64251),x64253),x64254)))
% 15.02/14.80 [6427]~P2(x64271)+E(f857(f857(f101(x64271),f857(f857(f101(x64271),x64272),x64273)),x64274),f857(f857(f101(x64271),x64272),f857(f857(f101(x64271),x64273),x64274)))
% 15.02/14.80 [6429]~P102(x64291)+E(f857(f857(f101(x64291),f857(f857(f101(x64291),x64292),x64293)),x64294),f857(f857(f101(x64291),x64292),f857(f857(f101(x64291),x64293),x64294)))
% 15.02/14.80 [6430]~P71(x64301)+E(f857(f857(f79(x64301),f857(f857(f79(x64301),x64302),x64303)),x64304),f857(f857(f79(x64301),x64302),f857(f857(f79(x64301),x64303),x64304)))
% 15.02/14.80 [6431]~P113(x64311)+E(f857(f857(f79(x64311),f857(f857(f79(x64311),x64312),x64313)),x64314),f857(f857(f79(x64311),x64312),f857(f857(f79(x64311),x64313),x64314)))
% 15.02/14.80 [6433]~P109(x64331)+E(f857(f857(f188(x64331),f857(f857(f188(x64331),x64332),x64333)),x64334),f857(f857(f188(x64331),x64332),f857(f857(f188(x64331),x64333),x64334)))
% 15.02/14.80 [6435]~P109(x64351)+E(f857(f857(f233(x64351),f857(f857(f233(x64351),x64352),x64353)),x64354),f857(f857(f233(x64351),x64352),f857(f857(f233(x64351),x64353),x64354)))
% 15.02/14.80 [6444]~P62(x64441)+E(f44(x64441,f857(f857(f79(x64441),x64442),f857(f857(f80(x64441),x64443),x64444)),x64444),f44(x64441,x64442,x64444))
% 15.02/14.80 [6445]~P62(x64451)+E(f44(x64451,f857(f857(f79(x64451),x64452),f857(f857(f80(x64451),x64453),x64454)),x64453),f44(x64451,x64452,x64453))
% 15.02/14.80 [6585]E(f857(f857(f164(x65851),f857(f857(f175(x65851),x65852),x65853)),x65854),f857(f857(f164(x65851),x65853),x65854))+~P106(f857(f857(f235(a919),x65854),x65852))
% 15.02/14.80 [6760]~E(x67602,x67604)+P106(f857(f857(f172(x67601),f857(f857(f151(x67601),x67602),x67603)),x67604))
% 15.02/14.80 [6762]~P113(x67621)+E(f857(f857(f80(x67621),f857(f857(f80(x67621),x67622),x67623)),x67624),f857(f857(f80(x67621),f857(f857(f80(x67621),x67622),x67624)),x67623))
% 15.02/14.80 [6763]~P113(x67631)+E(f857(f857(f79(x67631),f857(f857(f79(x67631),x67632),x67633)),x67634),f857(f857(f79(x67631),f857(f857(f79(x67631),x67632),x67634)),x67633))
% 15.02/14.80 [6823]~P146(x68232)+E(f857(f857(f8(x68231,x68232),f857(f18(x68232,x68231),x68233)),x68234),f857(f857(f80(x68232),f857(f100(x68232),f857(f34(x68231),x68234))),x68233))
% 15.02/14.80 [6994]E(f857(f857(f101(f927(x69941,a915)),f857(f857(f308(x69941),x69942),x69943)),x69944),f857(f857(f101(f927(x69941,a915)),x69943),x69944))+P106(f857(f857(f328(x69941),x69942),x69944))
% 15.02/14.80 [7063]~P99(x70631)+E(f857(f857(f101(x70631),f857(f857(f110(x70631),x70632),x70633)),f857(f857(f110(x70631),x70634),x70633)),f857(f857(f110(x70631),f857(f857(f101(x70631),x70632),x70634)),x70633))
% 15.02/14.80 [7064]~P80(x70641)+E(f857(f857(f188(x70641),f857(f857(f3(x70641),x70642),x70643)),f857(f857(f3(x70641),x70644),x70643)),f857(f857(f3(x70641),f857(f857(f188(x70641),x70642),x70644)),x70643))
% 15.02/14.80 [7065]~P80(x70651)+E(f857(f857(f233(x70651),f857(f857(f3(x70651),x70652),x70653)),f857(f857(f3(x70651),x70654),x70653)),f857(f857(f3(x70651),f857(f857(f233(x70651),x70652),x70654)),x70653))
% 15.02/14.80 [7067]~P114(x70671)+E(f857(f857(f79(x70671),f857(f857(f80(x70671),x70672),x70673)),f857(f857(f80(x70671),x70674),x70673)),f857(f857(f80(x70671),f857(f857(f79(x70671),x70672),x70674)),x70673))
% 15.02/14.80 [7068]~P99(x70681)+E(f857(f857(f110(x70681),f857(f857(f101(x70681),x70682),x70683)),f857(f857(f101(x70681),x70684),x70683)),f857(f857(f101(x70681),f857(f857(f110(x70681),x70682),x70684)),x70683))
% 15.02/14.80 [7069]~P85(x70691)+E(f857(f857(f188(x70691),f857(f857(f79(x70691),x70692),x70693)),f857(f857(f79(x70691),x70694),x70693)),f857(f857(f79(x70691),f857(f857(f188(x70691),x70692),x70694)),x70693))
% 15.02/14.80 [7070]~P85(x70701)+E(f857(f857(f233(x70701),f857(f857(f79(x70701),x70702),x70703)),f857(f857(f79(x70701),x70704),x70703)),f857(f857(f79(x70701),f857(f857(f233(x70701),x70702),x70704)),x70703))
% 15.02/14.80 [7071]~P109(x70711)+E(f857(f857(f233(x70711),f857(f857(f188(x70711),x70712),x70713)),f857(f857(f188(x70711),x70714),x70713)),f857(f857(f188(x70711),f857(f857(f233(x70711),x70712),x70714)),x70713))
% 15.02/14.80 [7072]~P124(x70721)+E(f857(f857(f3(x70721),f857(f857(f290(x70721),x70722),x70723)),f857(f857(f290(x70721),x70724),x70723)),f857(f857(f290(x70721),f857(f857(f3(x70721),x70722),x70724)),x70723))
% 15.02/14.80 [7073]~P124(x70731)+E(f857(f857(f79(x70731),f857(f857(f290(x70731),x70732),x70733)),f857(f857(f290(x70731),x70734),x70733)),f857(f857(f290(x70731),f857(f857(f79(x70731),x70732),x70734)),x70733))
% 15.02/14.80 [7074]~P113(x70741)+E(f857(f857(f80(x70741),f857(f857(f243(x70741),x70742),x70743)),f857(f857(f243(x70741),x70744),x70743)),f857(f857(f243(x70741),f857(f857(f80(x70741),x70742),x70744)),x70743))
% 15.02/14.80 [7075]~P77(x70751)+E(f857(f857(f80(x70751),f857(f857(f243(x70751),x70752),x70753)),f857(f857(f243(x70751),x70754),x70753)),f857(f857(f243(x70751),f857(f857(f80(x70751),x70752),x70754)),x70753))
% 15.02/14.80 [7076]~P65(x70761)+E(f857(f857(f290(x70761),f857(f857(f243(x70761),x70762),x70763)),f857(f857(f243(x70761),x70764),x70763)),f857(f857(f243(x70761),f857(f857(f290(x70761),x70762),x70764)),x70763))
% 15.02/14.80 [7077]~P109(x70771)+E(f857(f857(f188(x70771),f857(f857(f233(x70771),x70772),x70773)),f857(f857(f233(x70771),x70774),x70773)),f857(f857(f233(x70771),f857(f857(f188(x70771),x70772),x70774)),x70773))
% 15.02/14.80 [7078]~P113(x70781)+E(f857(f857(f79(x70781),f857(f857(f80(x70781),x70782),x70783)),f857(f857(f80(x70781),x70784),x70783)),f857(f857(f80(x70781),f857(f857(f79(x70781),x70782),x70784)),x70783))
% 15.02/14.80 [7110]E(f857(f857(f159(x71101,x71102),x71103),x71104),x71102)+~P106(f857(f857(f234(a919),f857(f190(f920(x71101)),x71102)),x71103))
% 15.02/14.80 [7137]~P106(f857(x71373,x71374))+P106(f857(f857(f857(f110(f927(x71371,a915)),x71372),x71373),x71374))
% 15.02/14.80 [7139]~P106(f857(x71392,x71394))+P106(f857(f857(f857(f110(f927(x71391,a915)),x71392),x71393),x71394))
% 15.02/14.80 [7158]E(f857(f857(f164(x71581),f857(f857(f134(x71581),x71582),x71583)),x71584),f857(f857(f164(x71581),x71582),x71584))+~P106(f857(f857(f235(a919),x71584),f857(f190(f920(x71581)),x71582)))
% 15.02/14.80 [7169]E(f857(f857(f3(f927(x71691,a915)),f857(f857(f308(x71691),x71692),x71693)),x71694),f857(f857(f3(f927(x71691,a915)),x71693),x71694))+~P106(f857(f857(f328(x71691),x71692),x71694))
% 15.02/14.80 [7209]~E(f139(a919,f857(f301(a919,x72091),x72092)),f857(f857(f151(a919),x72094),x72093))+E(f139(a919,f857(f301(a919,f857(f857(f79(a919),x72091),f77(a919))),x72092)),x72093)
% 15.02/14.80 [7231]~P106(f857(f857(f172(x72311),x72313),x72314))+P106(f857(f857(f172(x72311),f857(f857(f151(x72311),x72312),x72313)),x72314))
% 15.02/14.80 [7282]E(x72821,f2(a919))+E(f857(f857(f151(x72822),x72823),f857(f857(f175(x72822),f857(f857(f3(a919),x72821),f77(a919))),x72824)),f857(f857(f175(x72822),x72821),f857(f857(f151(x72822),x72823),x72824)))
% 15.02/14.80 [7384]E(f857(f857(f164(x73841),x73842),f857(f857(f3(a919),x73843),f857(f190(f920(x73841)),x73844))),f857(f857(f164(x73841),f857(f857(f134(x73841),x73844),x73842)),x73843))+P106(f857(f857(f235(a919),x73843),f857(f190(f920(x73841)),x73844)))
% 15.02/14.80 [7414]E(f857(f857(f101(f927(x74141,a915)),x74142),f857(f857(f308(x74141),x74143),x74144)),f857(f857(f308(x74141),x74143),f857(f857(f101(f927(x74141,a915)),x74142),x74144)))+~P106(f857(f857(f328(x74141),x74143),x74142))
% 15.02/14.80 [7452]E(f857(f857(f164(x74521),f857(f857(f159(x74521,x74522),x74523),x74524)),x74523),x74524)+~P106(f857(f857(f235(a919),x74523),f857(f190(f920(x74521)),x74522)))
% 15.02/14.80 [7474]E(x74741,f189(f927(x74742,a915)))+E(f857(f309(f926(x74743,x74742),x74743,f250(x74743,x74742)),f857(f857(f253(x74743,x74742),x74744),f857(f18(f927(x74742,a915),x74743),x74741))),x74744)
% 15.02/14.80 [7475]E(x74751,f189(f927(x74752,a915)))+E(f857(f309(f926(x74752,x74753),x74753,f255(x74752,x74753)),f857(f857(f253(x74752,x74753),x74751),f857(f18(f927(x74753,a915),x74752),x74754))),x74754)
% 15.02/14.80 [7547]E(f857(f857(f3(f927(x75471,a915)),f857(f857(f308(x75471),x75472),x75473)),x75474),f857(f857(f308(x75471),x75472),f857(f857(f3(f927(x75471,a915)),x75473),x75474)))+P106(f857(f857(f328(x75471),x75472),x75474))
% 15.02/14.80 [7583]~E(x75834,f189(f927(x75832,a915)))+E(f857(f309(f926(x75831,x75832),x75831,f250(x75831,x75832)),f857(f857(f253(x75831,x75832),x75833),f857(f18(f927(x75832,a915),x75831),x75834))),f189(f927(x75831,a915)))
% 15.02/14.80 [7584]~E(x75843,f189(f927(x75841,a915)))+E(f857(f309(f926(x75841,x75842),x75842,f255(x75841,x75842)),f857(f857(f253(x75841,x75842),x75843),f857(f18(f927(x75842,a915),x75841),x75844))),f189(f927(x75842,a915)))
% 15.02/14.80 [7636]~P106(f857(f857(f328(x76361),x76362),x76364))+P106(f857(f857(f328(x76361),x76362),f857(f857(f110(f927(x76361,a915)),x76363),x76364)))
% 15.02/14.80 [7639]~P106(f857(f857(f328(x76391),x76392),x76393))+P106(f857(f857(f328(x76391),x76392),f857(f857(f110(f927(x76391,a915)),x76393),x76394)))
% 15.02/14.80 [7657]E(f857(f857(f101(f927(x76571,a915)),f857(f857(f308(x76571),x76572),x76573)),x76574),f857(f857(f308(x76571),x76572),f857(f857(f101(f927(x76571,a915)),x76573),x76574)))+~P106(f857(f857(f328(x76571),x76572),x76574))
% 15.02/14.80 [7931]P106(f857(x79311,x79312))+~P106(f857(f857(f857(f101(f927(x79313,a915)),x79314),x79311),x79312))
% 15.02/14.80 [7932]P106(f857(x79321,x79322))+~P106(f857(f857(f857(f101(f927(x79323,a915)),x79321),x79324),x79322))
% 15.02/14.80 [7933]E(f857(f857(f8(x79331,a919),x79332),f857(f857(f3(f927(x79331,a915)),x79333),f857(f857(f308(x79331),x79334),f189(f927(x79331,a915))))),f857(f857(f8(x79331,a919),x79332),x79333))+P106(f857(f857(f328(x79331),x79334),x79333))
% 15.02/14.80 [7938]~P72(x79381)+E(f857(f165(x79381),f857(f857(f154(a919,x79381),x79382),f139(a919,f857(f301(a919,x79383),x79384)))),f857(f857(f8(a919,x79381),x79382),f857(f172(a919),f139(a919,f857(f301(a919,x79383),x79384)))))
% 15.02/14.80 [7939]~P72(x79391)+E(f857(f857(f8(a919,x79391),x79392),f857(f172(a919),f139(a919,f857(f301(a919,x79393),x79394)))),f857(f165(x79391),f857(f857(f154(a919,x79391),x79392),f139(a919,f857(f301(a919,x79393),x79394)))))
% 15.02/14.80 [8051]~E(x80513,x80514)+P106(f857(f61(x80511,x80512,f857(f857(f308(x80511),x80513),f189(f927(x80511,a915)))),x80514))
% 15.02/14.80 [8148]P106(f857(f857(f328(x81481),x81482),f857(f172(x81481),x81483)))+~P106(f857(f857(f328(x81481),x81482),f857(f172(x81481),f857(f857(f175(x81481),x81484),x81483))))
% 15.02/14.80 [8149]P106(f857(f857(f328(x81491),x81492),f857(f172(x81491),x81493)))+~P106(f857(f857(f328(x81491),x81492),f857(f172(x81491),f857(f857(f138(x81491),x81494),x81493))))
% 15.02/14.80 [8220]P106(f857(f857(f328(x82201),x82202),x82203))+~P106(f857(f857(f328(x82201),x82202),f857(f857(f3(f927(x82201,a915)),x82203),x82204)))
% 15.02/14.80 [8222]P106(f857(f857(f328(x82221),x82222),x82223))+~P106(f857(f857(f328(x82221),x82222),f857(f857(f101(f927(x82221,a915)),x82224),x82223)))
% 15.02/14.80 [8225]P106(f857(f857(f328(x82251),x82252),x82253))+~P106(f857(f857(f328(x82251),x82252),f857(f857(f101(f927(x82251,a915)),x82253),x82254)))
% 15.02/14.80 [8240]E(f857(f857(f134(x82401),f857(f857(f175(x82401),x82402),x82403)),f857(f857(f151(x82401),x82404),f857(f857(f138(x82401),f857(a112,x82402)),x82403))),f857(f857(f159(x82401,x82403),x82402),x82404))+~P106(f857(f857(f235(a919),x82402),f857(f190(f920(x82401)),x82403)))
% 15.02/14.80 [8263]P106(f857(f857(f328(x82631),x82632),x82633))+~P106(f857(f857(f234(f927(x82631,a915)),f857(f857(f308(x82631),x82632),x82634)),x82633))
% 15.02/14.80 [8299]~P106(f857(f857(f328(x82991),x82992),x82993))+~P106(f857(f857(f328(x82991),x82992),f857(f857(f3(f927(x82991,a915)),x82994),x82993)))
% 15.02/14.80 [8332]~P106(f857(f857(f235(a919),x83324),f857(f190(f920(x83321)),x83323)))+P106(f857(f857(f328(x83321),x83322),f857(f172(x83321),f857(f857(f159(x83321,x83323),x83324),x83322))))
% 15.02/14.80 [8385]E(f857(f857(f164(x83851),f857(f857(f138(x83851),x83852),x83853)),x83854),f857(f857(f164(x83851),x83853),f857(f857(f79(a919),x83852),x83854)))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x83852),x83854)),f857(f190(f920(x83851)),x83853)))
% 15.02/14.80 [8394]~P146(x83942)+E(f857(f857(f8(x83941,x83942),f857(f857(f10(a919,x83942,x83941),f100(x83942)),x83943)),x83944),f857(f100(x83942),f857(f857(f8(x83941,a919),x83943),x83944)))
% 15.02/14.80 [8395]~P143(x83952)+E(f857(f857(f8(x83951,x83952),f857(f857(f10(a1,x83952,x83951),f102(x83952)),x83953)),x83954),f857(f102(x83952),f857(f857(f8(x83951,a1),x83953),x83954)))
% 15.02/14.80 [8445]~P68(x84452)+E(f857(f857(f11(x84451,x84452),f857(f857(f10(x84452,x84452,x84451),f75(x84452)),x84453)),x84454),f857(f75(x84452),f857(f857(f11(x84451,x84452),x84453),x84454)))
% 15.02/14.80 [8446]~P69(x84462)+E(f857(f857(f8(x84461,x84462),f857(f857(f10(x84462,x84462,x84461),f78(x84462)),x84463)),x84464),f857(f78(x84462),f857(f857(f8(x84461,x84462),x84463),x84464)))
% 15.02/14.80 [8448]E(f857(f857(f8(x84481,a919),x84482),f857(f857(f3(f927(x84481,a915)),x84483),f857(f857(f308(x84481),x84484),f189(f927(x84481,a915))))),f857(f857(f3(a919),f857(f857(f8(x84481,a919),x84482),x84483)),f857(x84482,x84484)))+~P106(f857(f857(f328(x84481),x84484),x84483))
% 15.02/14.80 [8467]P106(f857(f857(f234(f927(x84671,a915)),x84672),x84673))+~P106(f857(f857(f234(f927(x84671,a915)),f857(f857(f308(x84671),x84674),x84672)),x84673))
% 15.02/14.80 [8590]~E(f857(f309(x85902,x85903,x85901),f241(f927(x85902,a915))),f241(f927(x85903,a915)))+E(f857(x85901,f857(f91(x85902,x85903,f241(f927(x85902,a915)),x85901),x85904)),x85904)
% 15.02/14.80 [8672]P39(x86721,x86722)+~P39(x86721,f857(f857(f308(f926(x86721,x86721)),f857(f857(f251(x86721,x86721),x86723),x86724)),x86722))
% 15.02/14.80 [8673]P59(x86731,x86732)+~P59(x86731,f857(f857(f308(f926(x86731,x86731)),f857(f857(f251(x86731,x86731),x86733),x86734)),x86732))
% 15.02/14.80 [8678]~P109(x86781)+E(f857(f857(f148(x86781,x86781,f7(x86781)),x86782),f857(f857(f148(x86781,x86781,f7(x86781)),x86783),x86784)),f857(f857(f148(x86781,x86781,f7(x86781)),x86783),f857(f857(f148(x86781,x86781,f7(x86781)),x86782),x86784)))
% 15.02/14.80 [8693]E(x86931,x86932)+~P106(f857(f61(x86933,x86934,f857(f857(f308(x86933),x86931),f189(f927(x86933,a915)))),x86932))
% 15.02/14.80 [8702]E(f857(f857(f134(x87021),f857(f857(f175(x87021),x87022),x87023)),f857(f857(f175(x87021),x87024),f857(f857(f138(x87021),x87022),x87023))),f857(f857(f175(x87021),f857(f857(f79(a919),x87022),x87024)),x87023))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x87022),x87024)),f857(f190(f920(x87021)),x87023)))
% 15.02/14.80 [8742]P106(f857(f60(x87421),x87422))+~E(x87422,f857(f309(a919,x87421,x87423),f857(f261(a919),f857(f857(f9(a919,a919,a915),f235(a919)),x87424))))
% 15.02/14.80 [8762]~P92(x87621)+E(f857(f142(x87621,x87621,f79(x87621),f857(f857(f79(x87621),x87622),x87623)),x87624),f857(f857(f79(x87621),x87622),f857(f142(x87621,x87621,f79(x87621),x87623),x87624)))
% 15.02/14.80 [8798]P106(f857(f857(f234(f927(x87981,a915)),f857(f263(x87981,x87982),x87983)),f857(f263(x87981,x87982),x87984)))+~P106(f857(f857(f234(f927(f926(x87981,x87982),a915)),x87983),x87984))
% 15.02/14.80 [8810]~P106(f857(f857(f234(a919),x88102),x88104))+P106(f857(f857(f234(f927(x88101,a915)),f857(f172(x88101),f857(f857(f175(x88101),x88102),x88103))),f857(f172(x88101),f857(f857(f175(x88101),x88104),x88103))))
% 15.02/14.80 [8811]~P106(f857(f857(f234(a919),x88114),x88112))+P106(f857(f857(f234(f927(x88111,a915)),f857(f172(x88111),f857(f857(f138(x88111),x88112),x88113))),f857(f172(x88111),f857(f857(f138(x88111),x88114),x88113))))
% 15.02/14.80 [8868]~P106(f857(f60(x88681),f857(f857(f3(f927(x88681,a915)),x88682),x88684)))+P106(f857(f60(x88681),f857(f857(f3(f927(x88681,a915)),x88682),f857(f857(f308(x88681),x88683),x88684))))
% 15.02/14.80 [8910]P106(f857(f857(f328(f926(x89101,x89101)),x89102),f306(x89101,x89103)))+~P106(f857(f857(f328(f926(x89101,x89101)),x89102),f857(f857(f183(f926(x89101,x89101),a915),x89104),x89103)))
% 15.02/14.80 [8996]~P106(f857(f60(x89961),f857(f857(f3(f927(x89961,a915)),x89962),f857(f857(f308(x89961),x89964),x89963))))+P106(f857(f60(x89961),f857(f857(f3(f927(x89961,a915)),x89962),x89963)))
% 15.02/14.80 [9207]~P2(x92071)+P106(f857(f857(f234(x92071),f857(f857(f110(x92071),x92072),f857(f857(f101(x92071),x92073),x92074))),f857(f857(f101(x92071),f857(f857(f110(x92071),x92072),x92073)),f857(f857(f110(x92071),x92072),x92074))))
% 15.02/14.80 [9208]~P109(x92081)+P106(f857(f857(f234(x92081),f857(f857(f233(x92081),x92082),f857(f857(f188(x92081),x92083),x92084))),f857(f857(f188(x92081),f857(f857(f233(x92081),x92082),x92083)),f857(f857(f233(x92081),x92082),x92084))))
% 15.02/14.80 [9355]E(x93551,x93552)+~P106(f857(f857(f328(f926(x93553,x93553)),f857(f857(f251(x93553,x93553),x93551),x93552)),f857(f172(f926(x93553,x93553)),f857(f857(f181(x93553,x93553),x93554),x93554))))
% 15.02/14.80 [9385]~P106(f857(f857(f328(f926(x93851,x93851)),f857(f857(f251(x93851,x93851),x93853),x93852)),f306(x93851,x93854)))+~P39(x93851,f857(f857(f308(f926(x93851,x93851)),f857(f857(f251(x93851,x93851),x93852),x93853)),x93854))
% 15.02/14.80 [9386]~P106(f857(f857(f328(f926(x93861,x93861)),f857(f857(f251(x93861,x93861),x93863),x93862)),f306(x93861,x93864)))+~P59(x93861,f857(f857(f308(f926(x93861,x93861)),f857(f857(f251(x93861,x93861),x93862),x93863)),x93864))
% 15.02/14.80 [9390]E(x93901,x93902)+E(f857(f136(x93903,f857(f857(f10(a915,a915,x93903),a321),f857(a324,x93901))),f857(f857(f151(x93903),x93902),x93904)),f857(f857(f151(x93903),x93902),f857(f136(x93903,f857(f857(f10(a915,a915,x93903),a321),f857(a324,x93901))),x93904)))
% 15.02/14.80 [9421]~P27(x94212,x94211,x94213,f241(f927(x94212,a915)),f241(f927(x94211,a915)))+E(f857(f309(x94211,x94212,f91(x94212,x94211,f241(f927(x94212,a915)),x94213)),x94214),f857(f310(x94212,x94211,x94213),x94214))
% 15.02/14.80 [9436]~P2(x94361)+P106(f857(f857(f234(x94361),f857(f857(f110(x94361),f857(f857(f101(x94361),x94362),x94363)),f857(f857(f101(x94361),x94362),x94364))),f857(f857(f101(x94361),x94362),f857(f857(f110(x94361),x94363),x94364))))
% 15.02/14.80 [9437]~P109(x94371)+P106(f857(f857(f234(x94371),f857(f857(f233(x94371),f857(f857(f188(x94371),x94372),x94373)),f857(f857(f188(x94371),x94372),x94374))),f857(f857(f188(x94371),x94372),f857(f857(f233(x94371),x94373),x94374))))
% 15.02/14.80 [9500]~P27(x95002,x95001,x95004,f241(f927(x95002,a915)),f241(f927(x95001,a915)))+E(f857(f261(x95001),f857(f857(f10(x95002,a915,x95001),x95003),f91(x95002,x95001,f241(f927(x95002,a915)),x95004))),f857(f309(x95002,x95001,x95004),f857(f261(x95002),x95003)))
% 15.02/14.80 [9514]~E(f857(f309(x95142,x95141,x95143),f241(f927(x95142,a915))),f241(f927(x95141,a915)))+P106(f857(f857(f234(f927(x95141,a915)),f857(f78(f927(x95141,a915)),f857(f309(x95142,x95141,x95143),x95144))),f857(f309(x95142,x95141,x95143),f857(f78(f927(x95142,a915)),x95144))))
% 15.02/14.80 [9847]P106(f857(f857(f328(f926(x98471,x98471)),f857(f857(f251(x98471,x98471),x98472),x98473)),f857(f285(x98471,x98471),f857(f857(f288(x98471,x98471,x98471),x98474),f306(x98471,x98474)))))+~P106(f857(f857(f328(f926(x98471,x98471)),f857(f857(f251(x98471,x98471),x98472),x98473)),f857(f857(f288(x98471,x98471,x98471),f857(f285(x98471,x98471),x98474)),f306(x98471,f857(f285(x98471,x98471),x98474)))))
% 15.02/14.80 [9848]~P106(f857(f857(f328(f926(x98481,x98481)),f857(f857(f251(x98481,x98481),x98482),x98483)),f857(f285(x98481,x98481),f857(f857(f288(x98481,x98481,x98481),x98484),f306(x98481,x98484)))))+P106(f857(f857(f328(f926(x98481,x98481)),f857(f857(f251(x98481,x98481),x98482),x98483)),f857(f857(f288(x98481,x98481,x98481),f857(f285(x98481,x98481),x98484)),f306(x98481,f857(f285(x98481,x98481),x98484)))))
% 15.02/14.80 [9869]~P106(f857(f857(f328(x98692),x98694),f857(f283(x98691,x98692),x98693)))+P106(f857(f857(f328(f926(x98691,x98692)),f857(f857(f251(x98691,x98692),f562(x98693,x98691,x98694,x98692)),x98694)),x98693))
% 15.02/14.80 [9870]~P106(f857(f857(f328(x98702),x98704),f857(f283(x98701,x98702),x98703)))+P106(f857(f857(f328(f926(x98701,x98702)),f857(f857(f251(x98701,x98702),f563(x98703,x98701,x98704,x98702)),x98704)),x98703))
% 15.02/14.80 [9895]~P106(f857(f857(f328(x98951),x98954),f857(f857(f110(f927(x98951,a915)),x98952),x98953)))+P106(f857(f857(f857(f110(f927(x98951,a915)),f857(f857(f9(x98951,f927(x98951,a915),a915),f328(x98951)),x98952)),f857(f857(f9(x98951,f927(x98951,a915),a915),f328(x98951)),x98953)),x98954))
% 15.02/14.80 [9896]~P106(f857(f857(f328(x98961),x98964),f857(f857(f101(f927(x98961,a915)),x98962),x98963)))+P106(f857(f857(f857(f101(f927(x98961,a915)),f857(f857(f9(x98961,f927(x98961,a915),a915),f328(x98961)),x98962)),f857(f857(f9(x98961,f927(x98961,a915),a915),f328(x98961)),x98963)),x98964))
% 15.02/14.80 [9976]~P106(f857(f857(f328(f926(x99761,x99761)),f857(f857(f251(x99761,x99761),x99764),x99763)),f857(f857(f288(x99761,x99761,x99761),x99762),f306(x99761,x99762))))+P106(f857(f857(f328(f926(x99761,x99761)),f857(f857(f251(x99761,x99761),f637(x99762,x99763,x99764,x99761)),x99763)),x99762))
% 15.02/14.80 [10011]P106(f857(f857(f328(x100111),x100112),f857(f857(f110(f927(x100111,a915)),x100113),x100114)))+~P106(f857(f857(f857(f110(f927(x100111,a915)),f857(f857(f9(x100111,f927(x100111,a915),a915),f328(x100111)),x100113)),f857(f857(f9(x100111,f927(x100111,a915),a915),f328(x100111)),x100114)),x100112))
% 15.02/14.80 [10012]P106(f857(f857(f328(x100121),x100122),f857(f857(f101(f927(x100121,a915)),x100123),x100124)))+~P106(f857(f857(f857(f101(f927(x100121,a915)),f857(f857(f9(x100121,f927(x100121,a915),a915),f328(x100121)),x100123)),f857(f857(f9(x100121,f927(x100121,a915),a915),f328(x100121)),x100124)),x100122))
% 15.02/14.80 [10298]P34(x102981,f857(f857(f9(x102981,f927(f926(x102981,x102981),a915),f927(x102981,a915)),f857(f857(f10(f927(x102981,f927(f927(f926(x102981,x102981),a915),a915)),f927(f927(f926(x102981,x102981),a915),f927(x102981,a915)),x102981),f9(x102981,f927(f926(x102981,x102981),a915),a915)),f857(f857(f10(f927(x102981,f926(x102981,x102981)),f927(x102981,f927(f927(f926(x102981,x102981),a915),a915)),x102981),f857(f10(f926(x102981,x102981),f927(f927(f926(x102981,x102981),a915),a915),x102981),f328(f926(x102981,x102981)))),f251(x102981,x102981)))),x102982),x102983,x102984)+~P106(f857(f857(f328(f926(f920(x102981),f920(x102981))),f857(f857(f251(f920(x102981),f920(x102981)),x102983),x102984)),f158(x102981,x102982)))
% 15.02/14.80 [10302]P60(x103021,f857(f857(f9(x103021,f927(f926(x103021,x103021),a915),f927(x103021,a915)),f857(f857(f10(f927(x103021,f927(f927(f926(x103021,x103021),a915),a915)),f927(f927(f926(x103021,x103021),a915),f927(x103021,a915)),x103021),f9(x103021,f927(f926(x103021,x103021),a915),a915)),f857(f857(f10(f927(x103021,f926(x103021,x103021)),f927(x103021,f927(f927(f926(x103021,x103021),a915),a915)),x103021),f857(f10(f926(x103021,x103021),f927(f927(f926(x103021,x103021),a915),a915),x103021),f328(f926(x103021,x103021)))),f251(x103021,x103021)))),x103022),x103023,x103024)+~P106(f857(f857(f328(f926(f927(x103021,a915),f927(x103021,a915))),f857(f857(f251(f927(x103021,a915),f927(x103021,a915)),x103023),x103024)),f317(x103021,x103022)))
% 15.02/14.80 [10338]E(x103381,x103382)+~E(f857(f857(f9(x103383,f927(f926(x103383,x103384),a915),f927(x103384,a915)),f857(f857(f10(f927(x103384,f927(f927(f926(x103383,x103384),a915),a915)),f927(f927(f926(x103383,x103384),a915),f927(x103384,a915)),x103383),f9(x103384,f927(f926(x103383,x103384),a915),a915)),f857(f857(f10(f927(x103384,f926(x103383,x103384)),f927(x103384,f927(f927(f926(x103383,x103384),a915),a915)),x103383),f857(f10(f926(x103383,x103384),f927(f927(f926(x103383,x103384),a915),a915),x103384),f328(f926(x103383,x103384)))),f251(x103383,x103384)))),x103381),f857(f857(f9(x103383,f927(f926(x103383,x103384),a915),f927(x103384,a915)),f857(f857(f10(f927(x103384,f927(f927(f926(x103383,x103384),a915),a915)),f927(f927(f926(x103383,x103384),a915),f927(x103384,a915)),x103383),f9(x103384,f927(f926(x103383,x103384),a915),a915)),f857(f857(f10(f927(x103384,f926(x103383,x103384)),f927(x103384,f927(f927(f926(x103383,x103384),a915),a915)),x103383),f857(f10(f926(x103383,x103384),f927(f927(f926(x103383,x103384),a915),a915),x103384),f328(f926(x103383,x103384)))),f251(x103383,x103384)))),x103382))
% 15.02/14.80 [10341]~P34(x103411,f857(f857(f9(x103411,f927(f926(x103411,x103411),a915),f927(x103411,a915)),f857(f857(f10(f927(x103411,f927(f927(f926(x103411,x103411),a915),a915)),f927(f927(f926(x103411,x103411),a915),f927(x103411,a915)),x103411),f9(x103411,f927(f926(x103411,x103411),a915),a915)),f857(f857(f10(f927(x103411,f926(x103411,x103411)),f927(x103411,f927(f927(f926(x103411,x103411),a915),a915)),x103411),f857(f10(f926(x103411,x103411),f927(f927(f926(x103411,x103411),a915),a915),x103411),f328(f926(x103411,x103411)))),f251(x103411,x103411)))),x103414),x103412,x103413)+P106(f857(f857(f328(f926(f920(x103411),f920(x103411))),f857(f857(f251(f920(x103411),f920(x103411)),x103412),x103413)),f158(x103411,x103414)))
% 15.02/14.80 [10342]~P60(x103421,f857(f857(f9(x103421,f927(f926(x103421,x103421),a915),f927(x103421,a915)),f857(f857(f10(f927(x103421,f927(f927(f926(x103421,x103421),a915),a915)),f927(f927(f926(x103421,x103421),a915),f927(x103421,a915)),x103421),f9(x103421,f927(f926(x103421,x103421),a915),a915)),f857(f857(f10(f927(x103421,f926(x103421,x103421)),f927(x103421,f927(f927(f926(x103421,x103421),a915),a915)),x103421),f857(f10(f926(x103421,x103421),f927(f927(f926(x103421,x103421),a915),a915),x103421),f328(f926(x103421,x103421)))),f251(x103421,x103421)))),x103424),x103422,x103423)+P106(f857(f857(f328(f926(f927(x103421,a915),f927(x103421,a915))),f857(f857(f251(f927(x103421,a915),f927(x103421,a915)),x103422),x103423)),f317(x103421,x103424)))
% 15.02/14.80 [7706]~P94(x77061)+E(f857(f857(f80(x77061),f857(f103(x77061),x77062)),f857(f857(f80(x77061),f857(f103(x77061),x77063)),x77064)),f857(f857(f80(x77061),f857(f103(x77061),f857(f857(f80(a1),x77062),x77063))),x77064))
% 15.02/14.80 [7707]~P94(x77071)+E(f857(f857(f79(x77071),f857(f103(x77071),x77072)),f857(f857(f3(x77071),f857(f103(x77071),x77073)),x77074)),f857(f857(f3(x77071),f857(f103(x77071),f857(f857(f79(a1),x77072),x77073))),x77074))
% 15.02/14.80 [7708]~P94(x77081)+E(f857(f857(f79(x77081),f857(f103(x77081),x77082)),f857(f857(f79(x77081),f857(f103(x77081),x77083)),x77084)),f857(f857(f79(x77081),f857(f103(x77081),f857(f857(f79(a1),x77082),x77083))),x77084))
% 15.02/14.80 [7749]~P146(x77491)+E(f857(f165(x77491),f857(f857(f154(x77492,x77491),f857(f18(x77491,x77492),x77493)),x77494)),f857(f857(f80(x77491),f857(f100(x77491),f857(f190(f920(x77492)),x77494))),x77493))
% 15.02/14.80 [7987]E(f857(f267(x79871,f857(f857(f151(f926(a99,x79871)),x79872),x79873)),x79874),f857(f255(a99,x79871),x79872))+~P106(f857(f857(f235(a99),x79874),f857(f250(a99,x79871),x79872)))
% 15.02/14.80 [8027]~P94(x80271)+E(f857(f857(f79(x80271),f857(f103(x80271),x80272)),f857(f857(f3(x80271),x80273),f857(f103(x80271),x80274))),f857(f857(f79(x80271),f857(f103(x80271),f857(f857(f79(a1),x80272),f857(f78(a1),x80274)))),x80273))
% 15.02/14.80 [8161]E(f857(f267(x81611,x81612),f857(f857(f3(a99),x81613),f857(f250(a99,x81611),x81614))),f857(f267(x81611,f857(f857(f151(f926(a99,x81611)),x81614),x81612)),x81613))+P106(f857(f857(f235(a99),x81613),f857(f250(a99,x81611),x81614)))
% 15.02/14.80 [8596]~P106(f857(f857(f328(x85961),x85962),f857(f172(x85961),f114(x85961,x85964))))+P106(f857(f857(f328(x85961),x85962),f857(f172(x85961),f114(x85961,f857(f857(f134(x85961),x85963),x85964)))))
% 15.02/14.80 [8597]~P106(f857(f857(f328(x85971),x85972),f857(f172(x85971),f114(x85971,x85973))))+P106(f857(f857(f328(x85971),x85972),f857(f172(x85971),f114(x85971,f857(f857(f134(x85971),x85973),x85974)))))
% 15.02/14.80 [8615]E(f857(f857(f110(f927(x86151,a915)),f857(f857(f101(f927(x86151,a915)),x86152),x86153)),x86154),f857(f857(f101(f927(x86151,a915)),x86152),f857(f857(f110(f927(x86151,a915)),x86153),x86154)))+~P106(f857(f857(f234(f927(x86151,a915)),x86154),x86152))
% 15.02/14.80 [8924]~E(f857(f857(f110(f927(x89241,a915)),f857(f857(f101(f927(x89241,a915)),x89243),x89244)),x89242),f857(f857(f101(f927(x89241,a915)),x89243),f857(f857(f110(f927(x89241,a915)),x89244),x89242)))+P106(f857(f857(f234(f927(x89241,a915)),x89242),x89243))
% 15.02/14.80 [9212]~P106(f857(f857(f234(f927(x92121,a915)),x92122),f857(f857(f110(f927(x92121,a915)),x92123),x92124)))+P106(f857(f857(f234(f927(x92121,a915)),f857(f857(f3(f927(x92121,a915)),x92122),x92123)),x92124))
% 15.02/14.80 [9327]~E(f857(f309(x93271,x93272,x93273),f241(f927(x93271,a915))),f241(f927(x93272,a915)))+E(f857(f309(x93271,x93272,x93273),f857(f309(x93272,x93271,f91(x93271,x93272,f241(f927(x93271,a915)),x93273)),x93274)),x93274)
% 15.02/14.80 [9332]P106(f857(f857(f234(f927(x93321,a915)),x93322),f857(f857(f110(f927(x93321,a915)),x93323),x93324)))+~P106(f857(f857(f234(f927(x93321,a915)),f857(f857(f3(f927(x93321,a915)),x93322),x93323)),x93324))
% 15.02/14.80 [9416]~P87(x94161)+E(f857(f75(x94161),f857(f857(f8(x94162,x94161),f857(f857(f10(x94161,x94161,x94162),f75(x94161)),x94163)),x94164)),f857(f857(f8(x94162,x94161),f857(f857(f10(x94161,x94161,x94162),f75(x94161)),x94163)),x94164))
% 15.02/14.80 [9590]~P87(x95901)+P106(f857(f857(f234(x95901),f2(x95901)),f857(f857(f8(x95902,x95901),f857(f857(f10(x95901,x95901,x95902),f75(x95901)),x95903)),x95904)))
% 15.02/14.80 [9594]~P69(x95941)+E(f857(f165(x95941),f857(f857(f154(x95942,x95941),f857(f72(x95941,x95941,x95942,f78(x95941)),x95943)),x95944)),f857(f78(x95941),f857(f165(x95941),f857(f857(f154(x95942,x95941),x95943),x95944))))
% 15.02/14.80 [9743]~P87(x97431)+P106(f857(f857(f234(x97431),f857(f75(x97431),f857(f857(f8(x97432,x97431),x97433),x97434))),f857(f857(f8(x97432,x97431),f857(f857(f10(x97431,x97431,x97432),f75(x97431)),x97433)),x97434)))
% 15.02/14.80 [9772]~E(f857(f857(f79(a919),x97721),x97724),f857(f857(f79(a919),x97723),x97722))+P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),f857(f857(f251(a919,a919),x97721),x97722)),f857(f857(f251(a919,a919),x97723),x97724))),a108))
% 15.02/14.80 [9773]~P106(f857(f857(f235(a919),x97731),x97733))+P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),f857(f857(f251(a919,a919),x97731),x97732)),f857(f857(f251(a919,a919),x97733),x97734))),a32))
% 15.02/14.80 [9774]~P106(f857(f857(f235(a919),x97741),x97743))+P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),f857(f857(f251(a919,a919),x97741),x97742)),f857(f857(f251(a919,a919),x97743),x97744))),a70))
% 15.02/14.80 [9920]E(f857(f857(f79(a919),x99201),x99202),f857(f857(f79(a919),x99203),x99204))+~P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),f857(f857(f251(a919,a919),x99201),x99204)),f857(f857(f251(a919,a919),x99203),x99202))),a108))
% 15.02/14.80 [9951]E(f857(f857(f164(x99511),f857(f857(f138(x99511),f857(f190(f920(x99511)),f177(x99511,x99512,x99513))),x99513)),x99514),f857(f857(f164(x99511),x99513),f857(f857(f79(a919),x99514),f857(f190(f920(x99511)),f177(x99511,x99512,x99513)))))+~P106(f857(f857(f235(a919),x99514),f857(f190(f920(x99511)),f857(f857(f138(x99511),f857(f190(f920(x99511)),f177(x99511,x99512,x99513))),x99513))))
% 15.02/14.80 [9967]~P106(f857(f857(f328(x99672),x99674),f857(f857(f38(x99671,f927(x99672,a915)),f241(f927(x99671,a915))),x99673)))+P106(f857(f857(f857(f38(x99671,f927(x99672,a915)),f241(f927(x99671,a915))),f857(f857(f10(f927(x99672,a915),f927(x99672,a915),x99671),f857(f9(x99672,f927(x99672,a915),a915),f328(x99672))),x99673)),x99674))
% 15.02/14.80 [9968]~P106(f857(f857(f328(x99682),x99684),f857(f857(f39(x99681,f927(x99682,a915)),f241(f927(x99681,a915))),x99683)))+P106(f857(f857(f857(f39(x99681,f927(x99682,a915)),f241(f927(x99681,a915))),f857(f857(f10(f927(x99682,a915),f927(x99682,a915),x99681),f857(f9(x99682,f927(x99682,a915),a915),f328(x99682))),x99683)),x99684))
% 15.02/14.80 [10038]~P106(f857(f48(x100381,x100382),f857(f857(f251(a1,a1),x100384),x100383)))+P106(f857(f48(f857(f78(a1),x100381),x100382),f857(f857(f251(a1,a1),f857(f857(f857(f96(a1),f857(f857(a324,x100383),f2(a1))),f857(f78(a1),x100384)),f857(f857(f3(a1),f857(f78(a1),x100384)),f77(a1)))),f857(f857(f857(f96(a1),f857(f857(a324,x100383),f2(a1))),f2(a1)),f857(f857(f3(a1),x100382),x100383)))))
% 15.02/14.80 [10050]P106(f857(f857(f328(x100501),x100502),f857(f857(f38(x100503,f927(x100501,a915)),f241(f927(x100503,a915))),x100504)))+~P106(f857(f857(f857(f38(x100503,f927(x100501,a915)),f241(f927(x100503,a915))),f857(f857(f10(f927(x100501,a915),f927(x100501,a915),x100503),f857(f9(x100501,f927(x100501,a915),a915),f328(x100501))),x100504)),x100502))
% 15.02/14.80 [10051]P106(f857(f857(f328(x100511),x100512),f857(f857(f39(x100513,f927(x100511,a915)),f241(f927(x100513,a915))),x100514)))+~P106(f857(f857(f857(f39(x100513,f927(x100511,a915)),f241(f927(x100513,a915))),f857(f857(f10(f927(x100511,a915),f927(x100511,a915),x100513),f857(f9(x100511,f927(x100511,a915),a915),f328(x100511))),x100514)),x100512))
% 15.02/14.80 [10063]E(f857(f857(f39(a919,f927(x100631,a915)),f241(f927(a919,a915))),x100632),f857(f857(f39(a919,f927(x100631,a915)),f241(f927(a919,a915))),x100633))+~E(f857(f857(f39(a919,f927(x100631,a915)),f857(f301(a919,f2(a919)),f496(x100632,x100634,x100633,x100631))),x100633),f857(f857(f39(a919,f927(x100631,a915)),f857(f301(a919,f2(a919)),f857(f857(f79(a919),f496(x100632,x100634,x100633,x100631)),x100634))),x100632))
% 15.02/14.80 [10418]~P106(f857(f857(f234(f927(f926(x104181,x104182),a915)),x104183),x104184))+P106(f857(f857(f234(f927(x104181,f927(x104182,a915))),f857(f857(f9(x104181,f927(f926(x104181,x104182),a915),f927(x104182,a915)),f857(f857(f10(f927(x104182,f927(f927(f926(x104181,x104182),a915),a915)),f927(f927(f926(x104181,x104182),a915),f927(x104182,a915)),x104181),f9(x104182,f927(f926(x104181,x104182),a915),a915)),f857(f857(f10(f927(x104182,f926(x104181,x104182)),f927(x104182,f927(f927(f926(x104181,x104182),a915),a915)),x104181),f857(f10(f926(x104181,x104182),f927(f927(f926(x104181,x104182),a915),a915),x104182),f328(f926(x104181,x104182)))),f251(x104181,x104182)))),x104183)),f857(f857(f9(x104181,f927(f926(x104181,x104182),a915),f927(x104182,a915)),f857(f857(f10(f927(x104182,f927(f927(f926(x104181,x104182),a915),a915)),f927(f927(f926(x104181,x104182),a915),f927(x104182,a915)),x104181),f9(x104182,f927(f926(x104181,x104182),a915),a915)),f857(f857(f10(f927(x104182,f926(x104181,x104182)),f927(x104182,f927(f927(f926(x104181,x104182),a915),a915)),x104181),f857(f10(f926(x104181,x104182),f927(f927(f926(x104181,x104182),a915),a915),x104182),f328(f926(x104181,x104182)))),f251(x104181,x104182)))),x104184)))
% 15.02/14.80 [10435]P106(f857(f857(f234(f927(f926(x104351,x104352),a915)),x104353),x104354))+~P106(f857(f857(f234(f927(x104351,f927(x104352,a915))),f857(f857(f9(x104351,f927(f926(x104351,x104352),a915),f927(x104352,a915)),f857(f857(f10(f927(x104352,f927(f927(f926(x104351,x104352),a915),a915)),f927(f927(f926(x104351,x104352),a915),f927(x104352,a915)),x104351),f9(x104352,f927(f926(x104351,x104352),a915),a915)),f857(f857(f10(f927(x104352,f926(x104351,x104352)),f927(x104352,f927(f927(f926(x104351,x104352),a915),a915)),x104351),f857(f10(f926(x104351,x104352),f927(f927(f926(x104351,x104352),a915),a915),x104352),f328(f926(x104351,x104352)))),f251(x104351,x104352)))),x104353)),f857(f857(f9(x104351,f927(f926(x104351,x104352),a915),f927(x104352,a915)),f857(f857(f10(f927(x104352,f927(f927(f926(x104351,x104352),a915),a915)),f927(f927(f926(x104351,x104352),a915),f927(x104352,a915)),x104351),f9(x104352,f927(f926(x104351,x104352),a915),a915)),f857(f857(f10(f927(x104352,f926(x104351,x104352)),f927(x104352,f927(f927(f926(x104351,x104352),a915),a915)),x104351),f857(f10(f926(x104351,x104352),f927(f927(f926(x104351,x104352),a915),a915),x104352),f328(f926(x104351,x104352)))),f251(x104351,x104352)))),x104354)))
% 15.02/14.80 [9463]~P106(f857(f857(f328(f926(x94631,x94631)),x94632),f306(x94631,x94634)))+P106(f857(f857(f328(f926(x94631,x94631)),x94632),f306(x94631,f857(f857(f110(f927(f926(x94631,x94631),a915)),x94633),x94634))))
% 15.02/14.80 [9464]~P106(f857(f857(f328(f926(x94641,x94641)),x94642),f306(x94641,x94643)))+P106(f857(f857(f328(f926(x94641,x94641)),x94642),f306(x94641,f857(f857(f110(f927(f926(x94641,x94641),a915)),x94643),x94644))))
% 15.02/14.80 [10151]~P106(f857(f857(f234(a919),f857(f857(f79(a919),x101511),x101514)),f857(f857(f79(a919),x101513),x101512)))+P106(f857(f857(f234(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x101511),x101512)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x101513),x101514)),f189(f927(f926(a919,a919),a915)))))))
% 15.02/14.80 [10152]~P106(f857(f857(f235(a919),f857(f857(f79(a919),x101521),x101524)),f857(f857(f79(a919),x101523),x101522)))+P106(f857(f857(f235(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x101521),x101522)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x101523),x101524)),f189(f927(f926(a919,a919),a915)))))))
% 15.02/14.80 [10239]P106(f857(f857(f234(a919),f857(f857(f79(a919),x102391),x102392)),f857(f857(f79(a919),x102393),x102394)))+~P106(f857(f857(f234(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x102391),x102394)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x102393),x102392)),f189(f927(f926(a919,a919),a915)))))))
% 15.02/14.80 [10240]P106(f857(f857(f235(a919),f857(f857(f79(a919),x102401),x102402)),f857(f857(f79(a919),x102403),x102404)))+~P106(f857(f857(f235(a1),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x102401),x102404)),f189(f927(f926(a919,a919),a915)))))),f857(a88,f857(f284(f926(a919,a919),f926(a919,a919),a108),f857(f857(f308(f926(a919,a919)),f857(f857(f251(a919,a919),x102403),x102402)),f189(f927(f926(a919,a919),a915)))))))
% 15.02/14.80 [10284]P106(f857(f857(f234(f927(x102841,a915)),f857(f857(f39(a919,f927(x102841,a915)),f241(f927(a919,a915))),x102842)),f857(f857(f39(a919,f927(x102841,a915)),f241(f927(a919,a915))),x102843)))+~P106(f857(f857(f234(f927(x102841,a915)),f857(f857(f39(a919,f927(x102841,a915)),f857(f301(a919,f2(a919)),f497(x102843,x102844,x102842,x102841))),x102842)),f857(f857(f39(a919,f927(x102841,a915)),f857(f301(a919,f2(a919)),f857(f857(f79(a919),f497(x102843,x102844,x102842,x102841)),x102844))),x102843)))
% 15.02/14.80 [10345]P106(f857(f857(f234(a99),x103454),f2(a99)))+E(f857(f857(f258(f926(a99,a99),f926(x103451,f927(a922,a322)),f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99))),f857(x103452,x103453)),f857(f857(f10(f927(f927(a99,f927(a915,f923(f921(x103451)))),f927(f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99)))),f927(f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99))),f926(x103451,f927(a922,a322))),f857(f258(f926(a99,a99),f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99))),f276(x103451,x103452,f857(f857(f3(a99),x103454),f77(a99)),x103453))),f857(f857(f10(f927(f927(a99,f927(a915,f923(f921(x103451)))),f927(a99,f927(a915,f923(f921(x103451))))),f927(f927(a99,f927(a915,f923(f921(x103451)))),f927(f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99)))),f926(x103451,f927(a922,a322))),f857(f10(f927(a99,f927(a915,f923(f921(x103451)))),f927(f926(a99,a99),f926(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99))),f927(a99,f927(a915,f923(f921(x103451))))),f251(f927(a99,f927(a915,f923(f921(x103451)))),f926(a99,a99)))),f857(f857(f10(f927(a99,f927(a915,f923(f921(x103451)))),f927(f927(a99,f927(a915,f923(f921(x103451)))),f927(a99,f927(a915,f923(f921(x103451))))),f926(x103451,f927(a922,a322))),f43(x103451)),f857(f857(f10(x103451,f927(a99,f927(a915,f923(f921(x103451)))),f926(x103451,f927(a922,a322))),f41(x103451)),f250(x103451,f927(a922,a322))))))),f276(x103451,x103452,x103454,x103453))
% 15.02/14.80 [10407]~P106(f857(f857(f328(x104072),x104074),f857(f283(x104071,x104072),x104073)))+P106(f857(f249(x104071,x104072,f857(f857(f9(x104071,f927(f926(x104071,x104072),a915),f927(x104072,a915)),f857(f857(f10(f927(x104072,f927(f927(f926(x104071,x104072),a915),a915)),f927(f927(f926(x104071,x104072),a915),f927(x104072,a915)),x104071),f9(x104072,f927(f926(x104071,x104072),a915),a915)),f857(f857(f10(f927(x104072,f926(x104071,x104072)),f927(x104072,f927(f927(f926(x104071,x104072),a915),a915)),x104071),f857(f10(f926(x104071,x104072),f927(f927(f926(x104071,x104072),a915),a915),x104072),f328(f926(x104071,x104072)))),f251(x104071,x104072)))),x104073)),x104074))
% 15.02/14.80 [10408]~P106(f857(f857(f328(x104081),x104084),f857(f263(x104081,x104082),x104083)))+P106(f857(f248(x104081,x104082,f857(f857(f9(x104081,f927(f926(x104081,x104082),a915),f927(x104082,a915)),f857(f857(f10(f927(x104082,f927(f927(f926(x104081,x104082),a915),a915)),f927(f927(f926(x104081,x104082),a915),f927(x104082,a915)),x104081),f9(x104082,f927(f926(x104081,x104082),a915),a915)),f857(f857(f10(f927(x104082,f926(x104081,x104082)),f927(x104082,f927(f927(f926(x104081,x104082),a915),a915)),x104081),f857(f10(f926(x104081,x104082),f927(f927(f926(x104081,x104082),a915),a915),x104082),f328(f926(x104081,x104082)))),f251(x104081,x104082)))),x104083)),x104084))
% 15.02/14.80 [10421]P106(f857(f857(f328(x104211),x104212),f857(f283(x104213,x104211),x104214)))+~P106(f857(f249(x104213,x104211,f857(f857(f9(x104213,f927(f926(x104213,x104211),a915),f927(x104211,a915)),f857(f857(f10(f927(x104211,f927(f927(f926(x104213,x104211),a915),a915)),f927(f927(f926(x104213,x104211),a915),f927(x104211,a915)),x104213),f9(x104211,f927(f926(x104213,x104211),a915),a915)),f857(f857(f10(f927(x104211,f926(x104213,x104211)),f927(x104211,f927(f927(f926(x104213,x104211),a915),a915)),x104213),f857(f10(f926(x104213,x104211),f927(f927(f926(x104213,x104211),a915),a915),x104211),f328(f926(x104213,x104211)))),f251(x104213,x104211)))),x104214)),x104212))
% 15.02/14.80 [10422]P106(f857(f857(f328(x104221),x104222),f857(f263(x104221,x104223),x104224)))+~P106(f857(f248(x104221,x104223,f857(f857(f9(x104221,f927(f926(x104221,x104223),a915),f927(x104223,a915)),f857(f857(f10(f927(x104223,f927(f927(f926(x104221,x104223),a915),a915)),f927(f927(f926(x104221,x104223),a915),f927(x104223,a915)),x104221),f9(x104223,f927(f926(x104221,x104223),a915),a915)),f857(f857(f10(f927(x104223,f926(x104221,x104223)),f927(x104223,f927(f927(f926(x104221,x104223),a915),a915)),x104221),f857(f10(f926(x104221,x104223),f927(f927(f926(x104221,x104223),a915),a915),x104223),f328(f926(x104221,x104223)))),f251(x104221,x104223)))),x104224)),x104222))
% 15.02/14.80 [10074]P106(f857(f160(x100741,x100742),x100743))+~P106(f857(f160(x100741,f857(f857(f20(x100741,a915,a915),f857(f857(f10(a915,f927(a915,a915),x100741),a325),x100744)),x100742)),x100743))
% 15.02/14.80 [10075]P106(f857(f160(x100751,x100752),x100753))+~P106(f857(f160(x100751,f857(f857(f20(x100751,a915,a915),f857(f857(f10(a915,f927(a915,a915),x100751),a325),x100752)),x100754)),x100753))
% 15.02/14.80 [10163]~P113(x101631)+E(f857(f857(f80(x101631),f857(f857(f79(x101631),f77(x101631)),f77(x101631))),f857(f857(f8(a919,x101631),f857(f857(f10(x101631,x101631,a919),f857(f79(x101631),x101632)),f857(f857(f9(a919,x101631,x101631),f857(f857(f10(x101631,f927(x101631,x101631),a919),f80(x101631)),f100(x101631))),x101633))),f857(f281(a919),x101634))),f857(f857(f80(x101631),f857(f100(x101631),x101634)),f857(f857(f79(x101631),x101632),f857(f857(f79(x101631),x101632),f857(f857(f80(x101631),f857(f100(x101631),f857(f857(f3(a919),x101634),f77(a919)))),x101633)))))
% 15.02/14.80 [10305]P106(f857(x103051,f572(x103052,x103053,x103054,x103051)))+P39(x103052,f857(f261(f926(x103052,x103052)),f857(f256(x103052,x103052,a915),f857(f857(f10(f927(x103052,a915),f927(x103052,a915),x103052),f857(f20(x103052,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103052),a325),x103051))),f857(f857(f9(x103052,f927(x103052,x103052),f927(x103052,a915)),f857(f857(f10(f927(x103052,a915),f927(f927(x103052,x103052),f927(x103052,a915)),x103052),f10(x103052,a915,x103052)),a324)),x103053)))))
% 15.02/14.80 [10322]~P106(f857(f857(f235(a919),f857(x103224,f857(x103223,f572(x103221,x103223,x103224,x103222)))),f857(x103224,f572(x103221,x103223,x103224,x103222))))+P39(x103221,f857(f261(f926(x103221,x103221)),f857(f256(x103221,x103221,a915),f857(f857(f10(f927(x103221,a915),f927(x103221,a915),x103221),f857(f20(x103221,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103221),a325),x103222))),f857(f857(f9(x103221,f927(x103221,x103221),f927(x103221,a915)),f857(f857(f10(f927(x103221,a915),f927(f927(x103221,x103221),f927(x103221,a915)),x103221),f10(x103221,a915,x103221)),a324)),x103223)))))
% 15.02/14.80 [10392]~P6(x103921)+E(f36(x103921,f857(f261(x103921),f857(f857(f10(f927(f927(x103922,x103921),a915),a915,x103921),f86(f927(x103922,x103921))),f857(f857(f10(f927(f927(x103922,x103921),a915),f927(f927(x103922,x103921),a915),x103921),f857(f20(f927(x103922,x103921),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x103922,x103921)),a325),f857(f857(f9(f927(x103922,x103921),f927(f927(x103922,x103921),a915),a915),f328(f927(x103922,x103921))),x103923)))),f857(f857(f9(x103921,f927(f927(x103922,x103921),x103921),f927(f927(x103922,x103921),a915)),f857(f857(f10(f927(x103921,a915),f927(f927(f927(x103922,x103921),x103921),f927(f927(x103922,x103921),a915)),x103921),f10(x103921,a915,f927(x103922,x103921))),a324)),f857(f857(f9(f927(x103922,x103921),x103922,x103921),f7(f927(x103922,x103921))),x103924)))))),f857(f36(f927(x103922,x103921),x103923),x103924))
% 15.02/14.80 [10393]~P6(x103931)+E(f36(x103931,f857(f261(x103931),f857(f857(f10(f927(f927(x103932,x103931),a915),a915,x103931),f86(f927(x103932,x103931))),f857(f857(f10(f927(f927(x103932,x103931),a915),f927(f927(x103932,x103931),a915),x103931),f857(f20(f927(x103932,x103931),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x103932,x103931)),a325),f857(f857(f9(f927(x103932,x103931),f927(f927(x103932,x103931),a915),a915),f328(f927(x103932,x103931))),x103933)))),f857(f857(f9(x103931,f927(f927(x103932,x103931),x103931),f927(f927(x103932,x103931),a915)),f857(f857(f10(f927(x103931,a915),f927(f927(f927(x103932,x103931),x103931),f927(f927(x103932,x103931),a915)),x103931),f10(x103931,a915,f927(x103932,x103931))),a324)),f857(f857(f9(f927(x103932,x103931),x103932,x103931),f7(f927(x103932,x103931))),x103934)))))),f857(f36(f927(x103932,x103931),x103933),x103934))
% 15.02/14.80 [10394]~P6(x103941)+E(f37(x103941,f857(f261(x103941),f857(f857(f10(f927(f927(x103942,x103941),a915),a915,x103941),f86(f927(x103942,x103941))),f857(f857(f10(f927(f927(x103942,x103941),a915),f927(f927(x103942,x103941),a915),x103941),f857(f20(f927(x103942,x103941),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x103942,x103941)),a325),f857(f857(f9(f927(x103942,x103941),f927(f927(x103942,x103941),a915),a915),f328(f927(x103942,x103941))),x103943)))),f857(f857(f9(x103941,f927(f927(x103942,x103941),x103941),f927(f927(x103942,x103941),a915)),f857(f857(f10(f927(x103941,a915),f927(f927(f927(x103942,x103941),x103941),f927(f927(x103942,x103941),a915)),x103941),f10(x103941,a915,f927(x103942,x103941))),a324)),f857(f857(f9(f927(x103942,x103941),x103942,x103941),f7(f927(x103942,x103941))),x103944)))))),f857(f37(f927(x103942,x103941),x103943),x103944))
% 15.02/14.80 [10395]~P6(x103951)+E(f37(x103951,f857(f261(x103951),f857(f857(f10(f927(f927(x103952,x103951),a915),a915,x103951),f86(f927(x103952,x103951))),f857(f857(f10(f927(f927(x103952,x103951),a915),f927(f927(x103952,x103951),a915),x103951),f857(f20(f927(x103952,x103951),a915,a915),f857(f857(f10(a915,f927(a915,a915),f927(x103952,x103951)),a325),f857(f857(f9(f927(x103952,x103951),f927(f927(x103952,x103951),a915),a915),f328(f927(x103952,x103951))),x103953)))),f857(f857(f9(x103951,f927(f927(x103952,x103951),x103951),f927(f927(x103952,x103951),a915)),f857(f857(f10(f927(x103951,a915),f927(f927(f927(x103952,x103951),x103951),f927(f927(x103952,x103951),a915)),x103951),f10(x103951,a915,f927(x103952,x103951))),a324)),f857(f857(f9(f927(x103952,x103951),x103952,x103951),f7(f927(x103952,x103951))),x103954)))))),f857(f37(f927(x103952,x103951),x103953),x103954))
% 15.02/14.80 [10448]~P106(f857(f857(f328(f926(x104481,x104481)),f857(f857(f251(x104481,x104481),x104483),x104484)),f857(f857(f110(f927(f926(x104481,x104481),a915)),x104482),f306(x104481,f189(f927(f926(x104481,x104481),a915))))))+P106(f857(f857(f857(f857(f110(f927(x104481,f927(x104481,a915))),f857(f857(f9(x104481,f927(f926(x104481,x104481),a915),f927(x104481,a915)),f857(f857(f10(f927(x104481,f927(f927(f926(x104481,x104481),a915),a915)),f927(f927(f926(x104481,x104481),a915),f927(x104481,a915)),x104481),f9(x104481,f927(f926(x104481,x104481),a915),a915)),f857(f857(f10(f927(x104481,f926(x104481,x104481)),f927(x104481,f927(f927(f926(x104481,x104481),a915),a915)),x104481),f857(f10(f926(x104481,x104481),f927(f927(f926(x104481,x104481),a915),a915),x104481),f328(f926(x104481,x104481)))),f251(x104481,x104481)))),x104482)),a324),x104483),x104484))
% 15.02/14.80 [10458]P106(f857(f857(f328(f926(x104581,x104581)),f857(f857(f251(x104581,x104581),x104582),x104583)),f857(f857(f110(f927(f926(x104581,x104581),a915)),x104584),f306(x104581,f189(f927(f926(x104581,x104581),a915))))))+~P106(f857(f857(f857(f857(f110(f927(x104581,f927(x104581,a915))),f857(f857(f9(x104581,f927(f926(x104581,x104581),a915),f927(x104581,a915)),f857(f857(f10(f927(x104581,f927(f927(f926(x104581,x104581),a915),a915)),f927(f927(f926(x104581,x104581),a915),f927(x104581,a915)),x104581),f9(x104581,f927(f926(x104581,x104581),a915),a915)),f857(f857(f10(f927(x104581,f926(x104581,x104581)),f927(x104581,f927(f927(f926(x104581,x104581),a915),a915)),x104581),f857(f10(f926(x104581,x104581),f927(f927(f926(x104581,x104581),a915),a915),x104581),f328(f926(x104581,x104581)))),f251(x104581,x104581)))),x104584)),a324),x104582),x104583))
% 15.02/14.80 [10403]E(f857(f857(f151(f920(x104031)),f857(f857(f151(x104031),x104032),f857(f142(f920(x104031),f920(x104031),f134(x104031),f113(x104031)),f857(f857(f154(f920(x104031),f920(x104031)),f156(f920(x104031),x104031,f113(x104031),f857(f857(f10(f920(x104031),f927(f920(x104031),f920(x104031)),x104031),f18(f920(x104031),f920(x104031))),f857(f857(f9(x104031,f920(x104031),f920(x104031)),f151(x104031)),f113(x104031))))),x104033)))),f179(x104031,f857(f857(f151(f920(x104031)),x104034),f857(f142(f920(f920(x104031)),f920(f920(x104031)),f134(f920(x104031)),f113(f920(x104031))),f857(f857(f154(f920(x104031),f920(f920(x104031))),f156(f920(f920(x104031)),x104031,f113(f920(x104031)),f857(f18(f927(f920(x104031),f920(f920(x104031))),x104031),f857(f857(f9(f920(x104031),f920(f920(x104031)),f920(f920(x104031))),f151(f920(x104031))),f113(f920(x104031)))))),x104033))))),f179(x104031,f857(f857(f151(f920(x104031)),f857(f857(f151(x104031),x104032),x104034)),x104033)))+~P106(f857(f314(f920(f920(x104031)),f180(x104031)),f857(f857(f151(f920(x104031)),f857(f857(f151(x104031),x104032),x104034)),x104033)))
% 15.02/14.80 [10447]~P106(f857(f60(x104472),f857(f261(x104472),x104474)))+P106(f857(f60(x104471),f857(f261(x104471),f857(f857(f10(f927(x104472,a915),a915,x104471),f86(x104472)),f857(f857(f9(x104471,f927(x104472,a915),f927(x104472,a915)),f857(f857(f10(f927(x104472,f927(a915,a915)),f927(f927(x104472,a915),f927(x104472,a915)),x104471),f20(x104472,a915,a915)),f857(f857(f10(f927(x104472,a915),f927(x104472,f927(a915,a915)),x104471),f857(f10(a915,f927(a915,a915),x104472),a325)),f857(f857(f9(x104471,f927(x104472,x104471),f927(x104472,a915)),f857(f857(f10(f927(x104471,a915),f927(f927(x104472,x104471),f927(x104472,a915)),x104471),f10(x104471,a915,x104472)),a324)),x104473)))),x104474)))))
% 15.02/14.80 [8962]P26(x89621,x89622,x89623,x89624)+~P27(x89621,x89622,x89623,x89624,x89625)
% 15.02/14.80 [5459]E(x54591,x54592)+~E(f169(x54593,x54591,x54594),f169(x54593,x54592,x54595))
% 15.02/14.80 [5460]E(x54601,x54602)+~E(f126(x54603,x54604,x54601),f126(x54603,x54605,x54602))
% 15.02/14.80 [5461]E(x54611,x54612)+~E(f126(x54613,x54611,x54614),f126(x54613,x54612,x54615))
% 15.02/14.80 [8293]~E(f857(x82933,x82934),x82935)+E(f74(x82931,x82932,x82933,x82934,x82935),x82933)
% 15.02/14.80 [8820]~E(f74(x88204,x88205,x88201,x88202,x88203),x88201)+E(f857(x88201,x88202),x88203)
% 15.02/14.80 [9434]~P27(x94342,x94341,x94344,x94343,x94345)+P27(x94341,x94342,f76(x94342,x94341,x94343,x94344),x94345,x94343)
% 15.02/14.80 [9435]~P27(x94352,x94351,x94354,x94353,x94355)+P27(x94351,x94352,f91(x94352,x94351,x94353,x94354),x94355,x94353)
% 15.02/14.80 [6271]P106(f857(f249(x62711,x62712,x62713),x62714))+~P106(f857(f857(x62713,x62715),x62714))
% 15.02/14.80 [6273]P106(f857(f248(x62731,x62732,x62733),x62734))+~P106(f857(f857(x62733,x62734),x62735))
% 15.02/14.80 [6751]~E(x67515,f2(a99))+E(f857(f197(x67511,x67512,x67513,x67514),x67515),f124(x67512))
% 15.02/14.80 [6752]~E(x67525,f2(a99))+E(f857(f199(x67521,x67522,x67523,x67524),x67525),f115(x67522))
% 15.02/14.80 [6889]~E(x68893,f2(a99))+E(f857(f272(x68891,x68892,x68893,x68894),x68895),f857(f251(x68891,x68892),x68895))
% 15.02/14.80 [7943]~P21(x79434,x79431,x79432,x79435)+E(f857(f72(x79431,x79431,x79431,f857(x79432,x79433)),f857(x79432,x79433)),f857(x79432,x79433))
% 15.02/14.80 [8333]~P17(x83335,x83331,x83332)+E(f857(f72(x83331,x83331,x83331,f857(x83332,x83333)),f857(x83332,x83334)),f857(f72(x83331,x83331,x83331,f857(x83332,x83334)),f857(x83332,x83333)))
% 15.02/14.80 [8655]P106(f857(f857(f328(f926(x86551,x86551)),f857(f857(f251(x86551,x86551),x86552),x86553)),f320(x86551,x86554,x86555)))+~P106(f857(f857(f235(a919),f857(x86554,x86552)),f857(x86554,x86553)))
% 15.02/14.80 [8748]~P106(f857(f857(f328(x87484),x87483),f298(x87484,x87481,x87482,x87485)))+P106(f857(f857(x87481,x87482),x87483))
% 15.02/14.80 [8749]~P106(f857(f857(f328(x87494),x87493),f289(x87494,x87491,x87492,x87495)))+P106(f857(f857(x87491,x87492),x87493))
% 15.02/14.80 [8750]~P106(f857(f857(f328(x87504),x87502),f298(x87504,x87501,x87505,x87503)))+P106(f857(f857(x87501,x87502),x87503))
% 15.02/14.80 [8751]~P106(f857(f857(f328(x87514),x87512),f289(x87514,x87511,x87515,x87513)))+P106(f857(f857(x87511,x87512),x87513))
% 15.02/14.80 [8832]~P27(x88321,x88323,x88325,x88322,x88324)+E(f857(f34(x88321),x88322),f857(f34(x88323),x88324))
% 15.02/14.80 [8880]~P27(x88801,x88802,x88803,x88804,x88805)+E(f857(f309(x88801,x88802,x88803),x88804),x88805)
% 15.02/14.80 [8900]~P58(x89002,x89001,x89005,x89003,x89004)+E(f857(f309(x89001,x89002,x89003),x89004),f241(f927(x89002,a915)))
% 15.02/14.80 [9344]~P36(x93441,x93442,x93443,x93444,x93445)+P36(x93441,x93442,x93443,f857(f168(x93441),x93444),f857(f168(x93442),x93445))
% 15.02/14.80 [9346]~P36(x93461,x93462,x93463,f857(f168(x93461),x93464),x93465)+P36(x93461,x93462,x93463,x93464,f857(f168(x93462),x93465))
% 15.02/14.80 [9347]~P36(x93471,x93472,x93473,x93474,f857(f168(x93472),x93475))+P36(x93471,x93472,x93473,f857(f168(x93471),x93474),x93475)
% 15.02/14.80 [9353]P36(x93531,x93532,x93533,x93534,x93535)+~P36(x93531,x93532,x93533,f857(f168(x93531),x93534),f857(f168(x93532),x93535))
% 15.02/14.80 [9762]P106(f857(f857(f328(f926(f920(x97621),f920(x97621))),f857(f857(f251(f920(x97621),f920(x97621)),f857(f857(f151(x97621),x97622),x97623)),f857(f857(f151(x97621),x97622),x97624))),f157(x97621,x97625)))+~P106(f857(f857(f328(f926(f920(x97621),f920(x97621))),f857(f857(f251(f920(x97621),f920(x97621)),x97623),x97624)),f157(x97621,x97625)))
% 15.02/14.80 [9763]P106(f857(f857(f328(f926(f920(x97631),f920(x97631))),f857(f857(f251(f920(x97631),f920(x97631)),f857(f857(f134(x97631),x97632),x97633)),f857(f857(f134(x97631),x97632),x97634))),f147(x97631,x97635)))+~P106(f857(f857(f328(f926(f920(x97631),f920(x97631))),f857(f857(f251(f920(x97631),f920(x97631)),x97633),x97634)),f147(x97631,x97635)))
% 15.02/14.80 [9958]E(f857(f857(f151(x99581),f653(x99582,x99583,x99584,x99585,x99581)),f654(x99582,x99583,x99584,x99585,x99581)),x99585)+~P106(f857(f857(f328(f926(f920(x99581),f920(x99581))),f857(f857(f251(f920(x99581),f920(x99581)),x99585),f857(f857(f151(x99581),x99584),x99583))),f158(x99581,x99582)))
% 15.02/14.80 [9979]E(f857(f857(f151(x99791),f655(x99792,x99793,x99794,x99795,x99791)),f656(x99792,x99793,x99794,x99795,x99791)),x99793)+~P106(f857(f857(f328(f926(f920(x99791),f920(x99791))),f857(f857(f251(f920(x99791),f920(x99791)),f857(f857(f151(x99791),x99795),x99794)),x99793)),f158(x99791,x99792)))
% 15.02/14.80 [10126]~P106(f857(f857(f328(f926(f920(x101261),f920(x101261))),f857(f857(f251(f920(x101261),f920(x101261)),f857(f857(f151(x101261),x101265),x101262)),x101264)),f158(x101261,x101263)))+P106(f857(f857(f328(f926(f920(x101261),f920(x101261))),f857(f857(f251(f920(x101261),f920(x101261)),x101262),f656(x101263,x101264,x101262,x101265,x101261))),f158(x101261,x101263)))
% 15.02/14.80 [10206]~P106(f857(f857(f328(f926(f920(x102061),f920(x102061))),f857(f857(f251(f920(x102061),f920(x102061)),x102065),f857(f857(f151(x102061),x102064),x102063))),f158(x102061,x102062)))+P106(f857(f857(f328(f926(f920(x102061),f920(x102061))),f857(f857(f251(f920(x102061),f920(x102061)),f654(x102062,x102063,x102064,x102065,x102061)),x102063)),f158(x102061,x102062)))
% 15.02/14.80 [10397]P106(f857(f857(f328(f926(x103971,x103971)),f857(f857(f251(x103971,x103971),f857(x103972,f857(f857(f79(a919),x103973),x103974))),f857(x103972,x103973))),f306(x103971,x103975)))+~P106(f857(f857(f328(f926(x103971,x103971)),f857(f857(f251(x103971,x103971),f857(x103972,f857(a112,f613(x103974,x103973,x103975,x103972,x103971)))),f857(x103972,f613(x103974,x103973,x103975,x103972,x103971)))),f306(x103971,x103975)))
% 15.02/14.80 [5427]E(x54271,x54272)+~E(f857(f857(f151(x54273),x54274),x54271),f857(f857(f151(x54273),x54275),x54272))
% 15.02/14.80 [5428]E(x54281,x54282)+~E(f857(f857(f151(x54283),x54281),x54284),f857(f857(f151(x54283),x54282),x54285))
% 15.02/14.80 [5476]P106(f857(x54761,x54762))+~E(f857(f136(x54763,x54761),x54764),f857(f857(f151(x54763),x54762),x54765))
% 15.02/14.80 [5477]P106(f857(x54771,x54772))+~E(f857(f857(f151(x54773),x54772),x54774),f857(f136(x54773,x54771),x54775))
% 15.02/14.80 [5636]~E(f857(f857(f138(x56361),x56363),x56362),f857(f857(f151(x56361),x56364),x56365))+E(f857(f857(f164(x56361),x56362),x56363),x56364)
% 15.02/14.80 [5777]~P15(x57774,x57775,x57771)+E(f857(f857(x57771,x57772),f857(f857(x57771,x57772),x57773)),f857(f857(x57771,x57772),x57773))
% 15.02/14.80 [6331]~E(x63314,f2(a99))+E(f857(f857(f117(x63311,x63312,x63313),x63314),x63315),f857(f857(f251(f920(x63312),x63311),f113(x63312)),x63315))
% 15.02/14.80 [6402]~P109(x64022)+~E(f857(f857(f148(x64021,x64022,x64023),x64024),x64025),f113(x64021))
% 15.02/14.80 [6791]E(x67911,x67912)+~E(f857(f857(f134(x67913),x67914),f857(f857(f151(x67913),x67911),f113(x67913))),f857(f857(f134(x67913),x67915),f857(f857(f151(x67913),x67912),f113(x67913))))
% 15.02/14.80 [6792]E(x67921,x67922)+~E(f857(f857(f134(x67923),x67921),f857(f857(f151(x67923),x67924),f113(x67923))),f857(f857(f134(x67923),x67922),f857(f857(f151(x67923),x67925),f113(x67923))))
% 15.02/14.80 [7108]E(f857(f857(f308(x71081),f857(x71082,x71083)),f857(f309(x71084,x71081,x71082),x71085)),f857(f309(x71084,x71081,x71082),x71085))+~P106(f857(f857(f328(x71084),x71083),x71085))
% 15.02/14.80 [7115]~P106(f857(x71154,f857(x71153,x71155)))+P106(f857(f857(f310(x71151,x71152,x71153),x71154),x71155))
% 15.02/14.80 [7118]~P106(f857(f857(x71183,x71185),x71184))+P106(f857(f857(f242(x71181,x71182,x71183),x71184),x71185))
% 15.02/14.80 [7213]~E(f857(f309(x72131,x72132,x72133),x72134),x72135)+E(f857(f309(f927(x72131,a915),f927(x72132,a915),f309(x72131,x72132,x72133)),f857(f307(x72131),x72134)),f857(f307(x72132),x72135))
% 15.02/14.80 [7242]E(f857(f270(x72421,x72422,x72423,x72424),x72425),f857(x72424,x72425))+~P106(f857(f857(f328(x72421),x72425),x72423))
% 15.02/14.80 [7555]P26(x75551,x75552,x75553,x75554)+~P26(x75551,x75552,x75553,f857(f857(f308(x75551),x75555),x75554))
% 15.02/14.80 [7620]P106(f857(x76201,x76202))+~P106(f857(f857(f92(x76203,x76204,x76201),x76205),x76202))
% 15.02/14.80 [7661]~P106(f857(f857(f328(x76614),x76613),x76615))+P106(f857(f857(f328(x76611),f857(x76612,x76613)),f857(f309(x76614,x76611,x76612),x76615)))
% 15.02/14.80 [7682]~P109(x76822)+E(f150(x76821,x76822,x76823,f857(f136(x76821,x76824),x76825)),f857(f136(x76821,x76824),f150(x76821,x76822,x76823,x76825)))
% 15.02/14.80 [7712]P106(f857(x77121,f857(x77122,x77123)))+~P106(f857(f857(f310(x77124,x77125,x77122),x77121),x77123))
% 15.02/14.80 [7715]P106(f857(f857(x77151,x77152),x77153))+~P106(f857(f857(f242(x77154,x77155,x77151),x77153),x77152))
% 15.02/14.80 [7716]P106(f857(f857(x77161,x77162),x77163))+~P106(f857(f857(f92(x77164,x77161,x77165),x77162),x77163))
% 15.02/14.80 [7779]~P106(f857(f857(f328(x77793),f857(x77794,x77792)),x77795))+P106(f857(f857(f328(x77791),x77792),f857(f310(x77791,x77793,x77794),x77795)))
% 15.02/14.80 [8175]~P106(f857(f857(f328(x81755),x81753),f857(f310(x81755,x81751,x81752),x81754)))+P106(f857(f857(f328(x81751),f857(x81752,x81753)),x81754))
% 15.02/14.80 [8472]~P17(x84722,x84721,x84723)+E(f857(f142(x84721,x84722,f857(f9(x84722,x84721,x84721),x84723),x84724),f152(x84722,x84725)),f857(f857(f63(x84722,x84721,x84723),x84724),f857(f172(x84722),x84725)))
% 15.02/14.80 [8494]E(f857(x84941,f499(x84942,x84941,x84943,x84944)),x84944)+~P106(f857(f857(f328(x84945),x84944),f857(f309(x84943,x84945,x84941),x84942)))
% 15.02/14.80 [8795]~E(x87952,f857(f857(f151(x87951),x87954),x87955))+P106(f857(f857(f328(f926(f920(x87951),f920(x87951))),f857(f857(f251(f920(x87951),f920(x87951)),f113(x87951)),x87952)),f147(x87951,x87953)))
% 15.02/14.80 [8841]E(f857(x88411,f857(f91(x88412,x88413,x88414,x88411),x88415)),x88415)+~P106(f857(f857(f328(x88413),x88415),f857(f309(x88412,x88413,x88411),x88414)))
% 15.02/14.80 [8844]P26(x88441,x88442,f91(x88442,x88441,x88443,x88444),x88445)+~P106(f857(f857(f234(f927(x88441,a915)),x88445),f857(f309(x88442,x88441,x88444),x88443)))
% 15.02/14.80 [8851]~P36(x88511,x88513,x88515,x88512,x88514)+E(f857(f190(f920(x88511)),x88512),f857(f190(f920(x88513)),x88514))
% 15.02/14.80 [8862]P106(f857(f857(f234(f927(x88621,a915)),f857(f857(f38(x88622,f927(x88621,a915)),x88623),x88624)),f857(x88624,x88625)))+~P106(f857(f857(f328(x88622),x88625),x88623))
% 15.02/14.80 [8916]~P58(x89161,x89162,x89163,x89165,x89164)+E(f857(f309(x89161,x89162,x89163),f241(f927(x89161,a915))),x89164)
% 15.02/14.80 [9141]E(f857(f136(x91411,x91412),f745(x91413,x91414,x91415,x91412,x91411)),x91413)+~E(f857(f136(x91411,x91412),x91415),f857(f857(f151(x91411),x91414),x91413))
% 15.02/14.80 [9142]E(f857(f136(x91421,x91422),f746(x91423,x91422,x91424,x91425,x91421)),x91424)+~E(f857(f857(f151(x91421),x91425),x91424),f857(f136(x91421,x91422),x91423))
% 15.02/14.80 [9233]E(f857(f190(f920(x92331)),x92332),x92333)+~P106(f857(f857(f328(f926(f920(x92331),f920(x92331))),f857(f857(f251(f920(x92331),f920(x92331)),x92334),x92332)),f857(f143(x92331,x92335),x92333)))
% 15.02/14.80 [9234]E(f857(f190(f920(x92341)),x92342),x92343)+~P106(f857(f857(f328(f926(f920(x92341),f920(x92341))),f857(f857(f251(f920(x92341),f920(x92341)),x92342),x92344)),f857(f143(x92341,x92345),x92343)))
% 15.02/14.80 [9303]P106(f857(f857(f328(x93031),f499(x93032,x93033,x93031,x93034)),x93032))+~P106(f857(f857(f328(x93035),x93034),f857(f309(x93031,x93035,x93033),x93032)))
% 15.02/14.80 [9461]E(f857(f309(x94611,x94612,x94613),f500(x94614,x94613,x94611,x94615,x94612)),x94615)+~P106(f857(f857(f234(f927(x94612,a915)),x94615),f857(f309(x94611,x94612,x94613),x94614)))
% 15.02/14.80 [9780]P106(f857(f857(f328(f926(f920(x97801),f920(x97801))),f857(f857(f251(f920(x97801),f920(x97801)),f857(f857(f151(x97801),x97802),x97803)),f857(f857(f151(x97801),x97802),x97804))),f306(f920(x97801),f157(x97801,x97805))))+~P106(f857(f857(f328(f926(f920(x97801),f920(x97801))),f857(f857(f251(f920(x97801),f920(x97801)),x97803),x97804)),f306(f920(x97801),f157(x97801,x97805))))
% 15.02/14.80 [9811]~E(f857(x98113,f694(x98115,x98114,x98113,x98112,x98111)),f857(x98115,f694(x98115,x98114,x98113,x98112,x98111)))+E(f857(f857(f154(x98111,x98112),x98113),x98114),f857(f857(f154(x98111,x98112),x98115),x98114))
% 15.02/14.80 [9886]~E(f857(f136(x98861,x98865),x98864),f857(f857(f151(x98861),x98863),x98862))+E(f857(f857(f134(x98861),f747(x98862,x98863,x98864,x98865,x98861)),f857(f857(f151(x98861),x98863),f745(x98862,x98863,x98864,x98865,x98861))),x98864)
% 15.02/14.80 [9887]~E(f857(f857(f151(x98871),x98875),x98874),f857(f136(x98871,x98873),x98872))+E(f857(f857(f134(x98871),f743(x98872,x98873,x98874,x98875,x98871)),f857(f857(f151(x98871),x98875),f746(x98872,x98873,x98874,x98875,x98871))),x98872)
% 15.02/14.80 [9891]E(f857(f857(f154(x98911,x98912),x98913),x98914),f857(f857(f154(x98911,x98912),x98915),x98914))+P106(f857(f857(f328(x98911),f694(x98913,x98914,x98915,x98912,x98911)),f857(f172(x98911),x98914)))
% 15.02/14.80 [9921]~P106(f857(f857(f328(x99215),x99214),f857(f284(x99211,x99215,x99213),x99212)))+P106(f857(f857(f328(x99211),f401(x99212,x99213,x99211,x99214,x99215)),x99212))
% 15.02/14.80 [9922]~P106(f857(f857(f328(x99225),x99224),f857(f284(x99221,x99225,x99223),x99222)))+P106(f857(f857(f328(x99221),f481(x99222,x99223,x99221,x99224,x99225)),x99222))
% 15.02/14.80 [9952]~P106(f857(f857(f234(f927(x99525,a915)),x99524),f857(f309(x99521,x99525,x99523),x99522)))+P106(f857(f857(f234(f927(x99521,a915)),f500(x99522,x99523,x99521,x99524,x99525)),x99522))
% 15.02/14.80 [10398]E(x103981,f2(a99))+E(f224(f926(f920(x103982),x103983),f926(x103982,x103983),f857(f857(f251(f920(x103982),x103983),f113(x103982)),x103984),f857(f256(x103982,x103983,f926(f920(x103982),x103983)),f857(f857(f9(x103982,f927(x103983,f926(f920(x103982),x103983)),f927(x103983,f926(f920(x103982),x103983))),f857(f857(f10(f927(f926(f920(x103982),x103983),f926(f920(x103982),x103983)),f927(f927(x103983,f926(f920(x103982),x103983)),f927(x103983,f926(f920(x103982),x103983))),x103982),f10(f926(f920(x103982),x103983),f926(f920(x103982),x103983),x103983)),f857(f857(f10(f927(f920(x103982),f927(x103983,f926(f920(x103982),x103983))),f927(f926(f920(x103982),x103983),f926(f920(x103982),x103983)),x103982),f256(f920(x103982),x103983,f926(f920(x103982),x103983))),f857(f857(f10(f927(f920(x103982),f920(x103982)),f927(f920(x103982),f927(x103983,f926(f920(x103982),x103983))),x103982),f857(f10(f920(x103982),f927(x103983,f926(f920(x103982),x103983)),f920(x103982)),f251(f920(x103982),x103983))),f151(x103982))))),f857(f117(x103983,x103982,x103985),f857(f857(f3(a99),x103981),f77(a99))))),f857(x103985,x103984)),f857(f857(f117(x103983,x103982,x103985),x103981),x103984))
% 15.02/14.80 [6205]E(x62051,x62052)+~E(f857(f255(x62053,x62054),f857(f857(f251(x62053,x62054),x62055),x62051)),x62052)
% 15.02/14.80 [6206]E(x62061,x62062)+~E(f857(f250(x62063,x62064),f857(f857(f251(x62063,x62064),x62061),x62065)),x62062)
% 15.02/14.80 [6476]~E(x64763,f857(f857(f134(x64761),x64764),f857(f857(f151(x64761),x64762),x64765)))+P106(f857(f857(f328(x64761),x64762),f857(f172(x64761),x64763)))
% 15.02/14.80 [6876]E(f857(f309(x68761,x68762,f857(f18(x68762,x68761),x68763)),x68764),f857(f857(f308(x68762),x68763),f189(f927(x68762,a915))))+~P106(f857(f857(f328(x68761),x68765),x68764))
% 15.02/14.80 [6949]E(f857(f857(f110(f927(x69491,a915)),f857(f172(x69491),x69492)),f857(f172(x69491),x69493)),f857(f172(x69491),x69494))+~E(f166(x69491,x69495,x69494),f857(f857(f251(f920(x69491),f920(x69491)),x69492),x69493))
% 15.02/14.80 [7048]~P109(x70482)+E(f857(f190(f920(x70481)),f857(f857(f148(x70481,x70482,x70483),x70484),x70485)),f857(a112,f857(f190(f920(x70481)),x70485)))
% 15.02/14.80 [7062]~P109(x70622)+E(f857(f172(x70621),f857(f857(f148(x70621,x70622,x70623),x70624),x70625)),f857(f857(f308(x70621),x70624),f857(f172(x70621),x70625)))
% 15.02/14.80 [7336]~P113(x73361)+E(f857(f857(f80(x73361),f857(f857(f80(x73361),x73362),x73363)),f857(f857(f80(x73361),x73364),x73365)),f857(f857(f80(x73361),f857(f857(f80(x73361),x73362),x73364)),f857(f857(f80(x73361),x73363),x73365)))
% 15.02/14.80 [7337]~P113(x73371)+E(f857(f857(f79(x73371),f857(f857(f79(x73371),x73372),x73373)),f857(f857(f79(x73371),x73374),x73375)),f857(f857(f79(x73371),f857(f857(f79(x73371),x73372),x73374)),f857(f857(f79(x73371),x73373),x73375)))
% 15.02/14.80 [7338]~P65(x73381)+E(f857(f857(f290(x73381),f857(f857(f80(x73381),x73382),x73383)),f857(f857(f80(x73381),x73384),x73385)),f857(f857(f80(x73381),f857(f857(f290(x73381),x73382),x73384)),f857(f857(f290(x73381),x73383),x73385)))
% 15.02/14.80 [7352]~P109(x73521)+E(f302(x73521,f857(f857(f233(x73521),x73522),x73523),f857(f857(f188(x73521),x73524),x73525)),f857(f857(f101(f927(x73521,a915)),f302(x73521,x73522,x73524)),f302(x73521,x73523,x73525)))
% 15.02/14.80 [7353]~P109(x73531)+E(f305(x73531,f857(f857(f233(x73531),x73532),x73533),f857(f857(f188(x73531),x73534),x73535)),f857(f857(f101(f927(x73531,a915)),f305(x73531,x73532,x73534)),f305(x73531,x73533,x73535)))
% 15.02/14.80 [7354]~P109(x73541)+E(f304(x73541,f857(f857(f233(x73541),x73542),x73543),f857(f857(f188(x73541),x73544),x73545)),f857(f857(f101(f927(x73541,a915)),f304(x73541,x73542,x73544)),f304(x73541,x73543,x73545)))
% 15.02/14.80 [7355]~P109(x73551)+E(f857(f857(f101(f927(x73551,a915)),f857(f301(x73551,x73552),x73553)),f857(f301(x73551,x73554),x73555)),f857(f301(x73551,f857(f857(f233(x73551),x73552),x73554)),f857(f857(f188(x73551),x73553),x73555)))
% 15.02/14.80 [7477]~P106(f857(x74771,f392(x74773,x74772,x74771)))+P106(f857(x74771,f857(f857(f251(x74772,x74773),x74774),x74775)))
% 15.02/14.80 [7586]~E(x75862,f857(x75864,x75865))+P106(f857(f857(f328(x75861),x75862),f857(f309(x75863,x75861,x75864),f241(f927(x75863,a915)))))
% 15.02/14.80 [7658]~P17(x76583,x76582,x76584)+P17(x76581,x76582,f857(f857(f10(x76583,f927(x76582,x76582),x76581),x76584),x76585))
% 15.02/14.80 [7659]~P15(x76593,x76592,x76594)+P15(x76591,x76592,f857(f857(f10(x76593,f927(x76592,x76592),x76591),x76594),x76595))
% 15.02/14.80 [7796]~P26(x77961,x77962,x77963,x77964)+P26(x77961,x77962,x77963,f857(f857(f3(f927(x77961,a915)),x77964),x77965))
% 15.02/14.80 [7952]~P106(f857(f857(x79523,x79524),x79525))+P106(f857(f857(f256(x79521,x79522,a915),x79523),f857(f857(f251(x79521,x79522),x79524),x79525)))
% 15.02/14.80 [8064]~P106(f857(x80642,x80644))+~E(f857(f857(f138(x80641),f857(f190(f920(x80641)),f177(x80641,x80642,x80643))),x80643),f857(f857(f151(x80641),x80644),x80645))
% 15.02/14.80 [8084]P26(x80841,x80842,x80843,x80844)+~P26(x80841,x80842,x80843,f857(f857(f110(f927(x80841,a915)),x80845),x80844))
% 15.02/14.80 [8085]P26(x80851,x80852,x80853,x80854)+~P26(x80851,x80852,x80853,f857(f857(f110(f927(x80851,a915)),x80854),x80855))
% 15.02/14.80 [8132]~P109(x81322)+E(f857(f857(f148(x81321,x81322,x81323),x81324),f150(x81321,x81322,x81323,x81325)),f150(x81321,x81322,x81323,f857(f857(f151(x81321),x81324),x81325)))
% 15.02/14.80 [8449]~P15(x84492,x84491,x84493)+E(f857(f142(x84491,x84492,f857(f9(x84492,x84491,x84491),x84493),x84494),x84495),f857(f857(f63(x84492,x84491,x84493),x84494),f857(f172(x84492),x84495)))
% 15.02/14.80 [8477]~E(f857(f857(f138(x84771),f857(f190(f920(x84771)),f177(x84771,x84772,x84773))),x84773),f857(f857(f151(x84771),x84774),x84775))+E(f857(f857(f134(x84771),f177(x84771,x84772,x84773)),f857(f857(f151(x84771),x84774),x84775)),x84773)
% 15.02/14.80 [8504]P106(f857(f857(x85041,x85042),x85043))+~P106(f857(f857(f256(x85044,x85045,a915),x85041),f857(f857(f251(x85044,x85045),x85042),x85043)))
% 15.02/14.80 [8979]P106(f857(f857(f234(f927(x89791,a915)),f857(f310(x89791,x89792,x89793),x89794)),f857(f310(x89791,x89792,x89793),x89795)))+~P106(f857(f857(f234(f927(x89792,a915)),x89794),x89795))
% 15.02/14.80 [8980]P106(f857(f857(f234(f927(x89801,a915)),f857(f309(x89802,x89801,x89803),x89804)),f857(f309(x89802,x89801,x89803),x89805)))+~P106(f857(f857(f234(f927(x89802,a915)),x89804),x89805))
% 15.02/14.80 [9059]E(x90591,f2(a99))+E(f857(f857(f258(x90592,x90593,x90592,f926(x90593,x90592)),f857(x90594,x90595)),f272(x90593,x90592,f857(f857(f3(a99),x90591),f77(a99)),x90594)),f857(f272(x90593,x90592,x90591,x90594),x90595))
% 15.02/14.80 [9166]P106(f857(f857(f254(x91661,x91662,a915,x91663),x91664),x91665))+~P106(f857(x91663,f857(f857(f251(x91661,x91662),x91664),x91665)))
% 15.02/14.80 [9440]~P106(f857(f857(f254(x94402,x94403,a915,x94401),x94404),x94405))+P106(f857(x94401,f857(f857(f251(x94402,x94403),x94404),x94405)))
% 15.02/14.80 [9624]~P106(f857(f857(f328(x96242),x96245),f857(f309(x96241,x96242,x96244),x96243)))+P106(f857(f857(f328(x96241),f857(f91(x96241,x96242,x96243,x96244),x96245)),x96243))
% 15.02/14.80 [9722]~P106(f857(f60(x97223),f857(f309(x97222,x97223,x97225),f241(f927(x97222,a915)))))+P106(f857(f60(x97221),f857(f309(x97222,x97221,f857(f857(f10(x97223,x97221,x97222),x97224),x97225)),f241(f927(x97222,a915)))))
% 15.02/14.80 [9747]P106(f857(f857(f234(f927(f927(x97471,a915),a915)),f857(f309(f927(x97472,a915),f927(x97471,a915),f309(x97472,x97471,x97473)),f857(f307(x97472),x97474))),f857(f307(x97471),x97475)))+~P106(f857(f857(f234(f927(x97471,a915)),f857(f309(x97472,x97471,x97473),x97474)),x97475))
% 15.02/14.80 [9819]E(x98191,x98192)+~P106(f857(f65(x98193,x98194,x98195,x98191,f189(f927(x98193,a915))),x98192))
% 15.02/14.80 [9835]E(f857(f857(f251(x98351,x98352),f544(x98353,x98354,x98355,x98352,x98351)),f545(x98353,x98354,x98355,x98352,x98351)),x98355)+~P106(f857(f857(f328(f926(x98351,x98352)),x98355),f857(f857(f253(x98351,x98352),x98354),x98353)))
% 15.02/14.80 [9927]P106(f857(f857(f328(x99271),f544(x99272,x99273,x99274,x99275,x99271)),x99273))+~P106(f857(f857(f328(f926(x99271,x99275)),x99274),f857(f857(f253(x99271,x99275),x99273),x99272)))
% 15.02/14.80 [10027]P25(x100275,x100274,f857(f857(f308(f918(x100275)),f857(f857(f857(f90(x100275),x100271),x100273),x100272)),f189(f927(f918(x100275),a915))))+P106(f857(f857(x100271,f529(x100272,x100273,x100274,x100275,x100271)),f530(x100272,x100273,x100274,x100275,x100271)))
% 15.02/14.80 [10083]P106(f857(f857(f328(x100831),f545(x100832,x100833,x100834,x100831,x100835)),f857(x100832,f544(x100832,x100833,x100834,x100831,x100835))))+~P106(f857(f857(f328(f926(x100835,x100831)),x100834),f857(f857(f253(x100835,x100831),x100833),x100832)))
% 15.02/14.80 [10103]P106(f857(f857(f328(f926(x101031,x101031)),f857(f857(f251(x101031,x101031),x101032),f633(x101033,x101034,x101035,x101032,x101031))),x101033))+~P106(f857(f857(f328(f926(x101031,x101031)),f857(f857(f251(x101031,x101031),x101032),x101035)),f857(f857(f183(f926(x101031,x101031),a915),f857(a112,x101034)),x101033)))
% 15.02/14.80 [10104]P106(f857(f857(f328(f926(x101041,x101041)),f857(f857(f251(x101041,x101041),x101042),f634(x101043,x101044,x101045,x101042,x101041))),x101043))+~P106(f857(f857(f328(f926(x101041,x101041)),f857(f857(f251(x101041,x101041),x101042),x101045)),f857(f857(f183(f926(x101041,x101041),a915),f857(a112,x101044)),x101043)))
% 15.02/14.80 [10121]~P106(f857(f857(f328(f926(f920(x101211),f920(x101211))),f857(f857(f251(f920(x101211),f920(x101211)),f857(f857(f151(x101211),x101212),x101215)),x101214)),f158(x101211,x101213)))+P106(f857(f857(f328(f926(x101211,x101211)),f857(f857(f251(x101211,x101211),x101212),f655(x101213,x101214,x101215,x101212,x101211))),x101213))
% 15.02/14.80 [10123]~P25(x101231,x101232,f857(f857(f308(f918(x101231)),f857(f857(f857(f90(x101231),f92(x101231,x101233,x101234)),x101235),x101233)),f189(f927(f918(x101231),a915))))+P25(x101231,x101232,f857(f857(f308(f918(x101231)),f857(f857(f857(f90(x101231),x101233),f29(x101234,x101235)),f92(x101231,x101233,f857(f72(a915,a915,a917,a321),x101234)))),f189(f927(f918(x101231),a915))))
% 15.02/14.80 [10124]~P30(x101241,x101242,f857(f857(f308(f918(x101241)),f857(f857(f857(f90(x101241),f92(x101241,x101243,x101244)),x101245),x101243)),f189(f927(f918(x101241),a915))))+P30(x101241,x101242,f857(f857(f308(f918(x101241)),f857(f857(f857(f90(x101241),x101243),f29(x101244,x101245)),f92(x101241,x101243,f857(f72(a915,a915,a917,a321),x101244)))),f189(f927(f918(x101241),a915))))
% 15.02/14.80 [10424]P25(x104241,x104242,f857(f857(f308(f918(x104241)),f857(f857(f857(f90(x104241),x104243),x104244),x104245)),f189(f927(f918(x104241),a915))))+~P25(x104241,x104242,f857(f857(f308(f918(x104241)),f857(f857(f857(f90(x104241),f857(f18(f927(a917,a915),x104241),f857(f857(f9(a917,a917,a915),a324),f530(x104245,x104244,x104242,x104241,x104243)))),x104244),f857(f18(f927(a917,a915),x104241),f857(x104245,f529(x104245,x104244,x104242,x104241,x104243))))),f189(f927(f918(x104241),a915))))
% 15.02/14.80 [6556]P106(f857(x65562,x65564))+E(f177(x65561,x65562,f857(f857(f134(x65561),x65563),f857(f857(f151(x65561),x65564),x65565))),f177(x65561,x65562,x65563))
% 15.02/14.80 [6605]~P2(x66052)+E(f857(f857(f857(f110(f927(x66051,x66052)),x66053),x66054),x66055),f857(f857(f110(x66052),f857(x66053,x66055)),f857(x66054,x66055)))
% 15.02/14.80 [6607]~P4(x66072)+E(f857(f857(f857(f3(f927(x66071,x66072)),x66073),x66074),x66075),f857(f857(f3(x66072),f857(x66073,x66075)),f857(x66074,x66075)))
% 15.02/14.80 [6609]~P2(x66092)+E(f857(f857(f857(f101(f927(x66091,x66092)),x66093),x66094),x66095),f857(f857(f101(x66092),f857(x66093,x66095)),f857(x66094,x66095)))
% 15.02/14.80 [6626]E(x66261,x66262)+E(f857(f857(f164(x66263),f857(f857(f159(x66263,x66264),x66261),x66265)),x66262),f857(f857(f164(x66263),x66264),x66262))
% 15.02/14.80 [6894]~E(x68944,f189(f927(x68943,a915)))+E(f857(f857(f110(f927(x68941,a915)),x68942),f857(f857(f39(x68943,f927(x68941,a915)),x68944),x68945)),x68942)
% 15.02/14.80 [6895]~E(x68954,f189(f927(x68953,a915)))+E(f857(f857(f3(f927(x68951,a915)),x68952),f857(f857(f39(x68953,f927(x68951,a915)),x68954),x68955)),x68952)
% 15.02/14.80 [6896]~E(x68964,f189(f927(x68963,a915)))+E(f857(f857(f101(f927(x68961,a915)),x68962),f857(f857(f38(x68963,f927(x68961,a915)),x68964),x68965)),x68962)
% 15.02/14.80 [6911]~E(x69114,f189(f927(x69113,a915)))+E(f857(f857(f308(x69111),x69112),f857(f857(f39(x69113,f927(x69111,a915)),x69114),x69115)),f857(f857(f308(x69111),x69112),f189(f927(x69111,a915))))
% 15.02/14.80 [7704]E(f857(f857(f164(x77041),f857(f857(f154(x77042,x77041),x77043),x77044)),x77045),f857(x77043,f857(f857(f164(x77042),x77044),x77045)))+~P106(f857(f857(f235(a919),x77045),f857(f190(f920(x77042)),x77044)))
% 15.02/14.80 [7767]E(f857(f857(f110(f927(x77671,a915)),f857(x77672,x77673)),f857(f857(f39(x77674,f927(x77671,a915)),x77675),x77672)),f857(f857(f39(x77674,f927(x77671,a915)),x77675),x77672))+~P106(f857(f857(f328(x77674),x77673),x77675))
% 15.02/14.80 [7768]E(f857(f857(f101(f927(x77681,a915)),f857(x77682,x77683)),f857(f857(f38(x77684,f927(x77681,a915)),x77685),x77682)),f857(f857(f38(x77684,f927(x77681,a915)),x77685),x77682))+~P106(f857(f857(f328(x77684),x77683),x77685))
% 15.02/14.80 [8372]~E(x83723,f189(f927(x83721,a915)))+E(f857(f857(f39(x83721,f927(x83722,a915)),x83723),f857(f857(f10(f927(x83722,a915),f927(x83722,a915),x83721),f857(f308(x83722),x83724)),x83725)),f189(f927(x83722,a915)))
% 15.02/14.80 [8377]~P106(f857(f857(f328(x83774),x83773),x83775))+P106(f857(f857(f234(f927(x83771,a915)),f857(x83772,x83773)),f857(f857(f39(x83774,f927(x83771,a915)),x83775),x83772)))
% 15.02/14.80 [8503]~E(f857(x85034,x85032),x85035)+P106(f857(f857(f328(x85031),x85032),f857(f310(x85031,x85033,x85034),f857(f857(f308(x85033),x85035),f189(f927(x85033,a915))))))
% 15.02/14.80 [8550]~P56(x85501,x85502,f857(f285(x85502,x85501),x85503))+E(f857(f857(f101(f927(x85501,a915)),f857(f284(x85502,x85501,x85503),x85504)),f857(f284(x85502,x85501,x85503),x85505)),f857(f284(x85502,x85501,x85503),f857(f857(f101(f927(x85502,a915)),x85504),x85505)))
% 15.02/14.80 [8624]E(x86241,f2(a99))+E(f857(f118(x86242,x86243,f857(x86244,f857(f857(f3(a99),x86241),f77(a99)))),f857(f857(f9(x86242,a99,f921(x86243)),x86245),x86241)),f857(f199(x86242,x86243,x86244,x86245),x86241))
% 15.02/14.80 [8662]E(x86621,f189(f927(x86622,a915)))+E(f857(f857(f39(x86622,f927(x86623,a915)),x86621),f857(f857(f10(f927(x86623,a915),f927(x86623,a915),x86622),f857(f308(x86623),x86624)),x86625)),f857(f857(f308(x86623),x86624),f857(f857(f39(x86622,f927(x86623,a915)),x86621),x86625)))
% 15.02/14.80 [8713]~P26(x87132,x87131,x87133,f241(f927(x87132,a915)))+E(f857(f857(f3(f927(x87131,a915)),f857(f309(x87132,x87131,x87133),x87134)),f857(f309(x87132,x87131,x87133),x87135)),f857(f309(x87132,x87131,x87133),f857(f857(f3(f927(x87132,a915)),x87134),x87135)))
% 15.02/14.80 [8714]~P26(x87142,x87141,x87143,f241(f927(x87142,a915)))+E(f857(f857(f101(f927(x87141,a915)),f857(f309(x87142,x87141,x87143),x87144)),f857(f309(x87142,x87141,x87143),x87145)),f857(f309(x87142,x87141,x87143),f857(f857(f101(f927(x87142,a915)),x87144),x87145)))
% 15.02/14.80 [8782]~P106(f857(f857(f66(x87821,x87822,x87825),x87823),x87824))+P106(f857(f857(f328(f926(x87821,x87822)),f857(f857(f251(x87821,x87822),x87823),x87824)),x87825))
% 15.02/14.80 [8814]P106(f857(f857(f328(x88141),x88142),f857(f283(x88143,x88141),x88144)))+~P106(f857(f857(f328(f926(x88143,x88141)),f857(f857(f251(x88143,x88141),x88145),x88142)),x88144))
% 15.02/14.80 [8816]P106(f857(f857(f328(x88161),x88162),f857(f263(x88161,x88163),x88164)))+~P106(f857(f857(f328(f926(x88161,x88163)),f857(f857(f251(x88161,x88163),x88162),x88165)),x88164))
% 15.02/14.80 [8963]P106(f857(f857(f66(x89631,x89632,x89633),x89634),x89635))+~P106(f857(f857(f328(f926(x89631,x89632)),f857(f857(f251(x89631,x89632),x89634),x89635)),x89633))
% 15.02/14.80 [9002]E(f857(x90021,x90022),x90023)+~P106(f857(f857(f328(x90024),x90022),f857(f310(x90024,x90025,x90021),f857(f857(f308(x90025),x90023),f189(f927(x90025,a915))))))
% 15.02/14.80 [9230]P106(f857(f857(f328(f926(x92301,x92302)),f857(f857(f251(x92301,x92302),x92303),x92304)),f857(f285(x92302,x92301),x92305)))+~P106(f857(f857(f328(f926(x92302,x92301)),f857(f857(f251(x92302,x92301),x92304),x92303)),x92305))
% 15.02/14.80 [9248]~P106(f857(f857(x92481,x92485),x92484))+P106(f857(f857(x92481,f857(f255(x92482,x92483),f857(f857(f251(x92482,x92483),x92484),x92485))),f857(f250(x92482,x92483),f857(f857(f251(x92482,x92483),x92484),x92485))))
% 15.02/14.80 [9278]~P106(f857(f857(f328(f926(x92782,x92781)),f857(f857(f251(x92782,x92781),x92784),x92783)),f857(f285(x92781,x92782),x92785)))+P106(f857(f857(f328(f926(x92781,x92782)),f857(f857(f251(x92781,x92782),x92783),x92784)),x92785))
% 15.02/14.80 [9310]~P106(f857(f857(f328(f926(x93103,x93101)),f857(f857(f251(x93103,x93101),x93105),x93102)),x93104))+P106(f857(f857(f328(x93101),x93102),f857(f284(x93103,x93101,x93104),f857(f857(f308(x93103),x93105),f189(f927(x93103,a915))))))
% 15.02/14.80 [9357]P106(f857(f857(f328(f926(x93571,x93572)),f857(f857(f251(x93571,x93572),x93573),x93574)),x93575))+~P106(f857(f857(f328(x93572),x93574),f857(f284(x93571,x93572,x93575),f857(f857(f308(x93571),x93573),f189(f927(x93571,a915))))))
% 15.02/14.80 [9447]~P72(x94471)+E(f857(f857(f8(a919,x94471),x94472),f302(a919,f857(f857(f79(a919),x94473),x94474),f857(f857(f79(a919),x94475),x94474))),f857(f857(f8(a919,x94471),f857(f857(f10(a919,x94471,a919),x94472),f857(f857(f9(a919,a919,a919),f79(a919)),x94474))),f302(a919,x94473,x94475)))
% 15.02/14.80 [9466]~P72(x94661)+E(f857(f857(f8(a919,x94661),x94662),f857(f301(a919,f857(f857(f79(a919),x94663),x94664)),f857(f857(f79(a919),x94665),x94664))),f857(f857(f8(a919,x94661),f857(f857(f10(a919,x94661,a919),x94662),f857(f857(f9(a919,a919,a919),f79(a919)),x94664))),f857(f301(a919,x94663),x94665)))
% 15.02/14.80 [9524]~P26(x95241,x95242,x95243,f241(f927(x95241,a915)))+E(f857(f857(f154(x95241,x95242),x95243),f857(f136(x95241,f857(f857(f10(a915,a915,x95241),a321),f857(a324,x95244))),x95245)),f857(f136(x95242,f857(f857(f10(a915,a915,x95242),a321),f857(a324,f857(x95243,x95244)))),f857(f857(f154(x95241,x95242),x95243),x95245)))
% 15.02/14.80 [9542]~P26(x95421,x95422,x95423,f857(f857(f308(x95421),x95424),f857(f172(x95421),x95425)))+E(f857(f857(f154(x95421,x95422),x95423),f857(f136(x95421,f857(f857(f10(a915,a915,x95421),a321),f857(a324,x95424))),x95425)),f857(f136(x95422,f857(f857(f10(a915,a915,x95422),a321),f857(a324,f857(x95423,x95424)))),f857(f857(f154(x95421,x95422),x95423),x95425)))
% 15.02/14.80 [9710]P106(f857(f857(f328(f926(f920(x97101),f920(x97101))),f857(f857(f251(f920(x97101),f920(x97101)),f857(f857(f151(x97101),x97102),x97103)),f857(f857(f151(x97101),x97104),x97103))),f157(x97101,x97105)))+~P106(f857(f857(f328(f926(x97101,x97101)),f857(f857(f251(x97101,x97101),x97102),x97104)),x97105))
% 15.02/14.80 [9830]E(f857(f857(f308(x98301),f550(x98302,x98303,x98304,x98305,x98301)),f564(x98302,x98303,x98304,x98305,x98301)),f857(f857(f308(x98301),x98304),x98303))+~P106(f857(f61(x98301,x98305,f857(f857(f308(x98301),x98304),x98303)),x98302))
% 15.02/14.80 [9831]E(f857(f857(f308(x98311),f577(x98312,x98313,x98314,x98315,x98311)),f587(x98312,x98313,x98314,x98315,x98311)),f857(f857(f308(x98311),x98314),x98313))+~P106(f857(f61(x98311,x98315,f857(f857(f308(x98311),x98314),x98313)),x98312))
% 15.02/14.80 [9912]P106(f857(f857(f328(x99121),f452(x99122,x99123,x99124,x99125,x99121)),x99124))+P106(f857(f857(f857(f38(x99121,f927(x99125,a915)),x99124),x99123),x99122))
% 15.02/14.80 [9917]P106(f857(f857(f328(x99171),f426(x99172,x99173,x99171,x99174,x99175)),x99173))+P106(f857(f857(f328(x99175),x99174),f857(f857(f38(x99171,f927(x99175,a915)),x99173),x99172)))
% 15.02/14.80 [9925]P106(f857(f857(f328(x99251),f428(x99252,x99253,x99251,x99254,x99255)),x99253))+P106(f857(f857(f234(f927(x99255,a915)),x99254),f857(f857(f38(x99251,f927(x99255,a915)),x99253),x99252)))
% 15.02/14.80 [9926]P106(f857(f857(f328(x99261),f834(x99262,x99263,x99264,x99265,x99261)),x99265))+P106(f857(f857(f234(f927(x99264,a915)),x99263),f857(f857(f38(x99261,f927(x99264,a915)),x99265),x99262)))
% 15.02/14.80 [9928]P106(f857(f857(x99281,f440(x99282,x99281,x99283,x99284,x99285)),x99282))+~P106(f857(f857(f857(f39(x99285,f927(x99284,a915)),x99283),x99281),x99282))
% 15.02/14.80 [9932]P106(f857(f857(f328(x99321),f440(x99322,x99323,x99324,x99325,x99321)),x99324))+~P106(f857(f857(f857(f39(x99321,f927(x99325,a915)),x99324),x99323),x99322))
% 15.02/14.80 [9933]P54(x99334,f857(f857(f38(x99331,f927(x99334,a915)),x99335),x99333),f857(f857(f38(x99331,f927(f926(x99334,x99334),a915)),x99335),x99332))+P106(f857(f857(f328(x99331),f774(x99332,x99333,x99334,x99335,x99331)),x99335))
% 15.02/14.80 [9934]P54(x99344,f857(f857(f39(x99341,f927(x99344,a915)),x99345),x99343),f857(f857(f39(x99341,f927(f926(x99344,x99344),a915)),x99345),x99342))+P106(f857(f857(f328(x99341),f826(x99342,x99343,x99344,x99345,x99341)),x99345))
% 15.02/14.80 [9944]P106(f857(f857(f328(x99441),f427(x99442,x99443,x99441,x99444,x99445)),x99443))+~P106(f857(f857(f328(x99445),x99444),f857(f857(f39(x99441,f927(x99445,a915)),x99443),x99442)))
% 15.02/14.80 [9950]P106(f857(f857(f328(x99501),x99502),f857(x99503,f427(x99503,x99504,x99505,x99502,x99501))))+~P106(f857(f857(f328(x99501),x99502),f857(f857(f39(x99505,f927(x99501,a915)),x99504),x99503)))
% 15.02/14.80 [10032]~P106(f857(f857(x100324,f452(x100325,x100324,x100323,x100322,x100321)),x100325))+P106(f857(f857(f857(f38(x100321,f927(x100322,a915)),x100323),x100324),x100325))
% 15.02/14.80 [10035]~P106(f857(f857(f328(x100351),x100352),f857(x100355,f426(x100355,x100354,x100353,x100352,x100351))))+P106(f857(f857(f328(x100351),x100352),f857(f857(f38(x100353,f927(x100351,a915)),x100354),x100355)))
% 15.02/14.80 [10039]~P54(x100391,f857(x100394,f774(x100395,x100394,x100391,x100393,x100392)),f857(x100395,f774(x100395,x100394,x100391,x100393,x100392)))+P54(x100391,f857(f857(f38(x100392,f927(x100391,a915)),x100393),x100394),f857(f857(f38(x100392,f927(f926(x100391,x100391),a915)),x100393),x100395))
% 15.02/14.80 [10040]~P54(x100401,f857(x100404,f826(x100405,x100404,x100401,x100403,x100402)),f857(x100405,f826(x100405,x100404,x100401,x100403,x100402)))+P54(x100401,f857(f857(f39(x100402,f927(x100401,a915)),x100403),x100404),f857(f857(f39(x100402,f927(f926(x100401,x100401),a915)),x100403),x100405))
% 15.02/14.80 [10041]~P106(f857(f857(f234(f927(x100411,a915)),x100412),f857(x100415,f428(x100415,x100414,x100413,x100412,x100411))))+P106(f857(f857(f234(f927(x100411,a915)),x100412),f857(f857(f38(x100413,f927(x100411,a915)),x100414),x100415)))
% 15.02/14.80 [10042]~P106(f857(f857(f234(f927(x100421,a915)),x100422),f857(x100425,f834(x100425,x100422,x100421,x100424,x100423))))+P106(f857(f857(f234(f927(x100421,a915)),x100422),f857(f857(f38(x100423,f927(x100421,a915)),x100424),x100425)))
% 15.02/14.80 [10107]~P106(f857(f857(f328(x101071),f550(x101075,x101074,x101073,x101072,x101071)),f564(x101075,x101074,x101073,x101072,x101071)))+~P106(f857(f61(x101071,x101072,f857(f857(f308(x101071),x101073),x101074)),x101075))
% 15.02/14.80 [10108]~P106(f857(f857(f328(x101081),f577(x101085,x101084,x101083,x101082,x101081)),f587(x101085,x101084,x101083,x101082,x101081)))+~P106(f857(f61(x101081,x101082,f857(f857(f308(x101081),x101083),x101084)),x101085))
% 15.02/14.80 [10109]~P106(f857(f857(f328(f926(x101091,x101091)),f857(f857(f251(x101091,x101091),x101092),x101095)),f857(f857(f183(f926(x101091,x101091),a915),f857(a112,x101094)),x101093)))+P106(f857(f857(f328(f926(x101091,x101091)),f857(f857(f251(x101091,x101091),x101092),f635(x101093,x101094,x101095,x101092,x101091))),f857(f857(f183(f926(x101091,x101091),a915),x101094),x101093)))
% 15.02/14.80 [10115]P106(f857(f65(x101151,x101151,x101152,f550(x101153,x101154,x101155,x101152,x101151),f564(x101153,x101154,x101155,x101152,x101151)),x101153))+~P106(f857(f61(x101151,x101152,f857(f857(f308(x101151),x101155),x101154)),x101153))
% 15.02/14.80 [10116]P106(f857(f65(x101161,x101161,x101162,f577(x101163,x101164,x101165,x101162,x101161),f587(x101163,x101164,x101165,x101162,x101161)),x101163))+~P106(f857(f61(x101161,x101162,f857(f857(f308(x101161),x101165),x101164)),x101163))
% 15.02/14.80 [10128]~P109(x101281)+P14(x101281,f857(f857(f154(x101282,x101281),x101283),f857(f136(x101282,f857(f857(f9(x101282,x101281,a915),f857(f857(f10(x101281,f927(x101281,a915),x101282),a324),x101283)),f857(x101284,x101285))),x101285)))
% 15.02/14.80 [10178]~P106(f857(f857(f328(x101782),x101785),f857(f284(x101781,x101782,x101784),x101783)))+P106(f857(f857(f328(f926(x101781,x101782)),f857(f857(f251(x101781,x101782),f401(x101783,x101784,x101781,x101785,x101782)),x101785)),x101784))
% 15.02/14.80 [10179]~P106(f857(f857(f328(x101792),x101795),f857(f284(x101791,x101792,x101794),x101793)))+P106(f857(f857(f328(f926(x101791,x101792)),f857(f857(f251(x101791,x101792),f481(x101793,x101794,x101791,x101795,x101792)),x101795)),x101794))
% 15.02/14.80 [10199]~P106(f857(f857(f328(f926(x101991,x101991)),f857(f857(f251(x101991,x101991),x101995),x101994)),f857(f857(f183(f926(x101991,x101991),a915),f857(a112,x101993)),x101992)))+P106(f857(f857(f328(f926(x101991,x101991)),f857(f857(f251(x101991,x101991),f635(x101992,x101993,x101994,x101995,x101991)),x101994)),x101992))
% 15.02/14.80 [10202]~P106(f857(f857(f328(f926(x102021,x102021)),f857(f857(f251(x102021,x102021),x102025),x102024)),f857(f857(f183(f926(x102021,x102021),a915),f857(a112,x102023)),x102022)))+P106(f857(f857(f328(f926(x102021,x102021)),f857(f857(f251(x102021,x102021),f633(x102022,x102023,x102024,x102025,x102021)),x102024)),f857(f857(f183(f926(x102021,x102021),a915),x102023),x102022)))
% 15.02/14.80 [10203]~P106(f857(f857(f328(f926(x102031,x102031)),f857(f857(f251(x102031,x102031),x102035),x102034)),f857(f857(f183(f926(x102031,x102031),a915),f857(a112,x102033)),x102032)))+P106(f857(f857(f328(f926(x102031,x102031)),f857(f857(f251(x102031,x102031),f634(x102032,x102033,x102034,x102035,x102031)),x102034)),f857(f857(f183(f926(x102031,x102031),a915),x102033),x102032)))
% 15.02/14.80 [10204]~P106(f857(f857(f328(f926(f920(x102041),f920(x102041))),f857(f857(f251(f920(x102041),f920(x102041)),x102045),f857(f857(f151(x102041),x102044),x102043))),f158(x102041,x102042)))+P106(f857(f857(f328(f926(x102041,x102041)),f857(f857(f251(x102041,x102041),f653(x102042,x102043,x102044,x102045,x102041)),x102044)),x102042))
% 15.02/14.80 [7788]~E(x77883,f189(f927(x77882,a915)))+E(f857(f857(f110(f927(x77881,a915)),f857(f857(f39(x77882,f927(x77881,a915)),x77883),x77884)),x77885),x77885)
% 15.02/14.80 [7789]~E(x77893,f189(f927(x77892,a915)))+E(f857(f857(f101(f927(x77891,a915)),f857(f857(f38(x77892,f927(x77891,a915)),x77893),x77894)),x77895),x77895)
% 15.02/14.80 [8214]~E(x82143,f189(f927(x82142,a915)))+E(f857(f857(f3(f927(x82141,a915)),f857(f857(f38(x82142,f927(x82141,a915)),x82143),x82144)),x82145),f857(f857(f3(f927(x82141,a915)),f241(f927(x82141,a915))),x82145))
% 15.02/14.80 [8346]E(f857(f857(f159(x83461,f857(f857(f134(x83461),x83462),x83463)),x83464),x83465),f857(f857(f134(x83461),f857(f857(f159(x83461,x83462),x83464),x83465)),x83463))+~P106(f857(f857(f235(a919),x83464),f857(f190(f920(x83461)),x83462)))
% 15.02/14.80 [8614]E(f857(f857(f164(x86141),f857(f857(f154(a919,x86141),x86142),f139(a919,f857(f301(a919,x86143),x86144)))),x86145),f857(x86142,f857(f857(f79(a919),x86143),x86145)))+~P106(f857(f857(f235(a919),x86145),f857(f857(f3(a919),x86144),x86143)))
% 15.02/14.80 [8628]E(x86281,f2(a99))+E(f122(x86282,x86283,f857(x86284,f857(f857(f3(a99),x86281),f77(a99))),f857(f857(f9(x86282,a99,f921(f923(x86283))),x86285),x86281)),f857(f197(x86282,x86283,x86284,x86285),x86281))
% 15.02/14.80 [8652]~E(x86523,f189(f927(x86521,a915)))+E(f857(f857(f38(x86521,f927(x86522,a915)),x86523),f857(f857(f10(f927(x86522,a915),f927(x86522,a915),x86521),f857(f3(f927(x86522,a915)),x86524)),x86525)),f241(f927(x86522,a915)))
% 15.02/14.80 [8653]~E(x86533,f189(f927(x86531,a915)))+E(f857(f857(f38(x86531,f927(x86532,a915)),x86533),f857(f857(f10(f927(x86532,a915),f927(x86532,a915),x86531),f857(f101(f927(x86532,a915)),x86534)),x86535)),f241(f927(x86532,a915)))
% 15.02/14.80 [8654]~E(x86543,f189(f927(x86541,a915)))+E(f857(f857(f39(x86541,f927(x86542,a915)),x86543),f857(f857(f10(f927(x86542,a915),f927(x86542,a915),x86541),f857(f110(f927(x86542,a915)),x86544)),x86545)),f189(f927(x86542,a915)))
% 15.02/14.80 [8656]~P147(x86562)+E(f857(f857(f8(x86561,x86562),f857(f857(f10(x86562,x86562,x86561),f857(f80(x86562),x86563)),x86564)),x86565),f857(f857(f80(x86562),x86563),f857(f857(f8(x86561,x86562),x86564),x86565)))
% 15.02/14.80 [8947]E(x89471,f189(f927(x89472,a915)))+E(f857(f857(f38(x89472,f927(x89473,a915)),x89471),f857(f857(f10(f927(x89473,a915),f927(x89473,a915),x89472),f857(f3(f927(x89473,a915)),x89474)),x89475)),f857(f857(f3(f927(x89473,a915)),x89474),f857(f857(f39(x89472,f927(x89473,a915)),x89471),x89475)))
% 15.02/14.80 [8948]E(x89481,f189(f927(x89482,a915)))+E(f857(f857(f38(x89482,f927(x89483,a915)),x89481),f857(f857(f10(f927(x89483,a915),f927(x89483,a915),x89482),f857(f101(f927(x89483,a915)),x89484)),x89485)),f857(f857(f101(f927(x89483,a915)),x89484),f857(f857(f38(x89482,f927(x89483,a915)),x89481),x89485)))
% 15.02/14.80 [8949]E(x89491,f189(f927(x89492,a915)))+E(f857(f857(f39(x89492,f927(x89493,a915)),x89491),f857(f857(f10(f927(x89493,a915),f927(x89493,a915),x89492),f857(f110(f927(x89493,a915)),x89494)),x89495)),f857(f857(f110(f927(x89493,a915)),x89494),f857(f857(f39(x89492,f927(x89493,a915)),x89491),x89495)))
% 15.02/14.80 [9148]~P106(f857(f857(f235(a919),f857(x91484,x91482)),f857(x91484,x91483)))+P106(f857(f857(f328(f926(x91481,x91481)),f857(f857(f251(x91481,x91481),x91482),x91483)),f153(x91481,f857(f857(f151(f927(x91481,a919)),x91484),x91485))))
% 15.02/14.80 [9412]~P26(x94122,x94121,x94123,f857(f857(f110(f927(x94122,a915)),x94124),x94125))+E(f857(f857(f101(f927(x94121,a915)),f857(f309(x94122,x94121,x94123),f857(f857(f3(f927(x94122,a915)),x94124),x94125))),f857(f309(x94122,x94121,x94123),f857(f857(f3(f927(x94122,a915)),x94125),x94124))),f189(f927(x94121,a915)))
% 15.02/14.80 [9671]~P26(x96713,x96711,x96715,f241(f927(x96713,a915)))+E(f857(f72(x96711,x96712,x96713,f857(f72(x96713,x96712,x96711,x96714),f91(x96713,x96711,f241(f927(x96713,a915)),x96715))),x96715),x96714)
% 15.02/14.80 [9706]~P106(f857(f857(f234(f927(x97063,a915)),f857(f284(x97061,x97063,x97064),x97062)),x97065))+P106(f857(f857(f234(f927(x97061,a915)),x97062),f857(f78(f927(x97061,a915)),f857(f284(x97063,x97061,f857(f285(x97061,x97063),x97064)),f857(f78(f927(x97063,a915)),x97065)))))
% 15.02/14.80 [9731]~P26(x97311,x97312,x97313,f857(f857(f308(x97311),x97314),x97315))+~P106(f857(f857(f328(x97312),f857(x97313,x97314)),f857(f309(x97311,x97312,x97313),f857(f857(f3(f927(x97311,a915)),x97315),f857(f857(f308(x97311),x97314),f189(f927(x97311,a915)))))))
% 15.02/14.80 [9784]P106(f857(f857(f234(f927(x97841,a915)),f857(f284(x97842,x97841,x97843),x97844)),x97845))+~P106(f857(f857(f234(f927(x97842,a915)),x97844),f857(f78(f927(x97842,a915)),f857(f284(x97841,x97842,f857(f285(x97842,x97841),x97843)),f857(f78(f927(x97841,a915)),x97845)))))
% 15.02/14.80 [9857]~P87(x98571)+P106(f857(f857(f234(x98571),f857(f75(x98571),f857(f857(f3(x98571),f857(f857(f79(x98571),x98572),x98573)),f857(f857(f79(x98571),x98574),x98575)))),f857(f857(f79(x98571),f857(f75(x98571),f857(f857(f3(x98571),x98572),x98574))),f857(f75(x98571),f857(f857(f3(x98571),x98573),x98575)))))
% 15.02/14.80 [9965]P106(f857(f857(f328(x99651),f429(x99652,x99653,x99654,x99651,x99655)),x99654))+P106(f857(f857(f234(f927(x99655,a915)),f857(f857(f39(x99651,f927(x99655,a915)),x99654),x99653)),x99652))
% 15.02/14.80 [10146]~P106(f857(f857(f234(f927(x101461,a915)),f857(x101464,f429(x101465,x101464,x101463,x101462,x101461))),x101465))+P106(f857(f857(f234(f927(x101461,a915)),f857(f857(f39(x101462,f927(x101461,a915)),x101463),x101464)),x101465))
% 15.02/14.80 [8761]E(f857(f857(f134(x87611),x87612),f857(f857(f159(x87611,x87613),f857(f857(f3(a919),x87614),f857(f190(f920(x87611)),x87612))),x87615)),f857(f857(f159(x87611,f857(f857(f134(x87611),x87612),x87613)),x87614),x87615))+P106(f857(f857(f235(a919),x87614),f857(f190(f920(x87611)),x87612)))
% 15.02/14.80 [8789]~P141(x87891)+E(f857(f857(f79(x87891),f857(f857(f80(x87891),x87892),x87893)),f857(f857(f79(x87891),f857(f857(f80(x87891),x87894),x87893)),x87895)),f857(f857(f79(x87891),f857(f857(f80(x87891),f857(f857(f79(x87891),x87892),x87894)),x87893)),x87895))
% 15.02/14.80 [9366]~P147(x93661)+E(f857(f165(x93661),f857(f857(f154(x93662,x93661),f857(f857(f10(x93661,x93661,x93662),f857(f80(x93661),x93663)),x93664)),x93665)),f857(f857(f80(x93661),x93663),f857(f165(x93661),f857(f857(f154(x93662,x93661),x93664),x93665))))
% 15.02/14.80 [9541]E(f857(f190(f920(x95411)),f857(f857(f175(x95411),f857(f857(f188(a919),f857(f190(f920(x95411)),x95412)),f857(f190(f920(x95413)),x95414))),x95412)),f857(f190(f920(x95413)),f857(f857(f175(x95413),f857(f857(f188(a919),f857(f190(f920(x95411)),x95412)),f857(f190(f920(x95413)),x95414))),x95414)))+P106(f857(x95415,f857(f857(f181(x95411,x95413),x95412),x95414)))
% 15.02/14.80 [9794]~P147(x97942)+E(f857(f857(f8(x97941,x97942),f857(f857(f9(x97941,x97942,x97942),f857(f857(f10(x97942,f927(x97942,x97942),x97941),f80(x97942)),x97943)),x97944)),x97945),f857(f857(f80(x97942),f857(f857(f8(x97941,x97942),x97943),x97945)),x97944))
% 15.02/14.80 [9795]~P66(x97952)+E(f857(f857(f8(x97951,x97952),f857(f857(f9(x97951,x97952,x97952),f857(f857(f10(x97952,f927(x97952,x97952),x97951),f290(x97952)),x97953)),x97954)),x97955),f857(f857(f290(x97952),f857(f857(f8(x97951,x97952),x97953),x97955)),x97954))
% 15.02/14.80 [9802]~P69(x98022)+E(f857(f857(f8(x98021,x98022),f857(f857(f20(x98021,x98022,x98022),f857(f857(f10(x98022,f927(x98022,x98022),x98021),f3(x98022)),x98023)),x98024)),x98025),f857(f857(f3(x98022),f857(f857(f8(x98021,x98022),x98023),x98025)),f857(f857(f8(x98021,x98022),x98024),x98025)))
% 15.02/14.80 [9803]~P72(x98032)+E(f857(f857(f8(x98031,x98032),f857(f857(f20(x98031,x98032,x98032),f857(f857(f10(x98032,f927(x98032,x98032),x98031),f79(x98032)),x98033)),x98034)),x98035),f857(f857(f79(x98032),f857(f857(f8(x98031,x98032),x98033),x98035)),f857(f857(f8(x98031,x98032),x98034),x98035)))
% 15.02/14.80 [9804]~P77(x98042)+E(f857(f857(f11(x98041,x98042),f857(f857(f20(x98041,x98042,x98042),f857(f857(f10(x98042,f927(x98042,x98042),x98041),f80(x98042)),x98043)),x98044)),x98045),f857(f857(f80(x98042),f857(f857(f11(x98041,x98042),x98043),x98045)),f857(f857(f11(x98041,x98042),x98044),x98045)))
% 15.02/14.80 [9842]~E(x98423,f189(f927(x98421,a915)))+E(f857(f857(f38(x98421,f927(x98422,a915)),x98423),f857(f857(f9(x98421,f927(x98422,a915),f927(x98422,a915)),f857(f857(f10(f927(x98422,a915),f927(f927(x98422,a915),f927(x98422,a915)),x98421),f3(f927(x98422,a915))),x98424)),x98425)),f241(f927(x98422,a915)))
% 15.02/14.80 [9843]~E(x98433,f189(f927(x98431,a915)))+E(f857(f857(f38(x98431,f927(x98432,a915)),x98433),f857(f857(f9(x98431,f927(x98432,a915),f927(x98432,a915)),f857(f857(f10(f927(x98432,a915),f927(f927(x98432,a915),f927(x98432,a915)),x98431),f101(f927(x98432,a915))),x98434)),x98435)),f241(f927(x98432,a915)))
% 15.02/14.80 [9844]~E(x98443,f189(f927(x98441,a915)))+E(f857(f857(f39(x98441,f927(x98442,a915)),x98443),f857(f857(f9(x98441,f927(x98442,a915),f927(x98442,a915)),f857(f857(f10(f927(x98442,a915),f927(f927(x98442,a915),f927(x98442,a915)),x98441),f110(f927(x98442,a915))),x98444)),x98445)),f189(f927(x98442,a915)))
% 15.02/14.80 [9865]E(x98651,f189(f927(x98652,a915)))+E(f857(f857(f38(x98652,f927(x98653,a915)),x98651),f857(f857(f9(x98652,f927(x98653,a915),f927(x98653,a915)),f857(f857(f10(f927(x98653,a915),f927(f927(x98653,a915),f927(x98653,a915)),x98652),f3(f927(x98653,a915))),x98654)),x98655)),f857(f857(f3(f927(x98653,a915)),f857(f857(f38(x98652,f927(x98653,a915)),x98651),x98654)),x98655))
% 15.02/14.80 [9866]E(x98661,f189(f927(x98662,a915)))+E(f857(f857(f38(x98662,f927(x98663,a915)),x98661),f857(f857(f9(x98662,f927(x98663,a915),f927(x98663,a915)),f857(f857(f10(f927(x98663,a915),f927(f927(x98663,a915),f927(x98663,a915)),x98662),f101(f927(x98663,a915))),x98664)),x98665)),f857(f857(f101(f927(x98663,a915)),f857(f857(f38(x98662,f927(x98663,a915)),x98661),x98664)),x98665))
% 15.02/14.80 [9867]E(x98671,f189(f927(x98672,a915)))+E(f857(f857(f39(x98672,f927(x98673,a915)),x98671),f857(f857(f9(x98672,f927(x98673,a915),f927(x98673,a915)),f857(f857(f10(f927(x98673,a915),f927(f927(x98673,a915),f927(x98673,a915)),x98672),f110(f927(x98673,a915))),x98674)),x98675)),f857(f857(f110(f927(x98673,a915)),f857(f857(f39(x98672,f927(x98673,a915)),x98671),x98674)),x98675))
% 15.02/14.80 [9417]~P106(f857(f857(f234(a919),x94171),x94174))+E(f857(f857(f3(a919),f857(f857(f79(a919),f857(f857(f80(a919),x94171),x94172)),x94173)),f857(f857(f79(a919),f857(f857(f80(a919),x94174),x94172)),x94175)),f857(f857(f3(a919),x94173),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x94174),x94171)),x94172)),x94175)))
% 15.02/14.80 [10014]~P147(x100141)+E(f857(f165(x100141),f857(f857(f154(x100142,x100141),f857(f857(f9(x100142,x100141,x100141),f857(f857(f10(x100141,f927(x100141,x100141),x100142),f80(x100141)),x100143)),x100144)),x100145)),f857(f857(f80(x100141),f857(f165(x100141),f857(f857(f154(x100142,x100141),x100143),x100145))),x100144))
% 15.02/14.80 [10020]~P69(x100201)+E(f857(f165(x100201),f857(f857(f154(x100202,x100201),f857(f857(f20(x100202,x100201,x100201),f857(f857(f10(x100201,f927(x100201,x100201),x100202),f3(x100201)),x100203)),x100204)),x100205)),f857(f857(f3(x100201),f857(f165(x100201),f857(f857(f154(x100202,x100201),x100203),x100205))),f857(f165(x100201),f857(f857(f154(x100202,x100201),x100204),x100205))))
% 15.02/14.80 [10021]~P72(x100211)+E(f857(f165(x100211),f857(f857(f154(x100212,x100211),f857(f857(f20(x100212,x100211,x100211),f857(f857(f10(x100211,f927(x100211,x100211),x100212),f79(x100211)),x100213)),x100214)),x100215)),f857(f857(f79(x100211),f857(f165(x100211),f857(f857(f154(x100212,x100211),x100213),x100215))),f857(f165(x100211),f857(f857(f154(x100212,x100211),x100214),x100215))))
% 15.02/14.80 [10170]P106(f857(x101701,f857(f857(f181(x101702,x101703),x101704),x101705)))+~P106(f857(x101701,f857(f857(f181(x101702,x101703),f857(f857(f175(x101702),f857(f857(f188(a919),f857(f190(f920(x101702)),x101704)),f857(f190(f920(x101703)),x101705))),x101704)),f857(f857(f175(x101703),f857(f857(f188(a919),f857(f190(f920(x101702)),x101704)),f857(f190(f920(x101703)),x101705))),x101705))))
% 15.02/14.80 [10434]~P106(f857(f857(f328(f926(x104342,x104341)),f857(f857(f251(x104342,x104341),x104344),x104345)),f857(f285(x104341,x104342),x104343)))+P106(f857(f857(f242(x104341,x104342,f857(f857(f9(x104341,f927(f926(x104341,x104342),a915),f927(x104342,a915)),f857(f857(f10(f927(x104342,f927(f927(f926(x104341,x104342),a915),a915)),f927(f927(f926(x104341,x104342),a915),f927(x104342,a915)),x104341),f9(x104342,f927(f926(x104341,x104342),a915),a915)),f857(f857(f10(f927(x104342,f926(x104341,x104342)),f927(x104342,f927(f927(f926(x104341,x104342),a915),a915)),x104341),f857(f10(f926(x104341,x104342),f927(f927(f926(x104341,x104342),a915),a915),x104342),f328(f926(x104341,x104342)))),f251(x104341,x104342)))),x104343)),x104344),x104345))
% 15.02/14.80 [10444]P106(f857(f857(f328(f926(x104441,x104442)),f857(f857(f251(x104441,x104442),x104443),x104444)),f857(f285(x104442,x104441),x104445)))+~P106(f857(f857(f242(x104442,x104441,f857(f857(f9(x104442,f927(f926(x104442,x104441),a915),f927(x104441,a915)),f857(f857(f10(f927(x104441,f927(f927(f926(x104442,x104441),a915),a915)),f927(f927(f926(x104442,x104441),a915),f927(x104441,a915)),x104442),f9(x104441,f927(f926(x104442,x104441),a915),a915)),f857(f857(f10(f927(x104441,f926(x104442,x104441)),f927(x104441,f927(f927(f926(x104442,x104441),a915),a915)),x104442),f857(f10(f926(x104442,x104441),f927(f927(f926(x104442,x104441),a915),a915),x104441),f328(f926(x104442,x104441)))),f251(x104442,x104441)))),x104445)),x104443),x104444))
% 15.02/14.80 [9670]~P106(f857(f857(f234(a919),x96704),x96701))+E(f857(f857(f3(a919),f857(f857(f79(a919),f857(f857(f80(a919),x96701),x96702)),x96703)),f857(f857(f79(a919),f857(f857(f80(a919),x96704),x96702)),x96705)),f857(f857(f3(a919),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x96701),x96704)),x96702)),x96703)),x96705))
% 15.02/14.80 [5453]E(x54531,x54532)+~E(f27(x54533,x54534,x54531),f27(x54535,x54536,x54532))
% 15.02/14.80 [5454]E(x54541,x54542)+~E(f27(x54543,x54541,x54544),f27(x54545,x54542,x54546))
% 15.02/14.80 [5455]E(x54551,x54552)+~E(f27(x54551,x54553,x54554),f27(x54552,x54555,x54556))
% 15.02/14.80 [5456]E(x54561,x54562)+~E(f26(x54563,x54564,x54561),f26(x54565,x54566,x54562))
% 15.02/14.80 [5457]E(x54571,x54572)+~E(f26(x54573,x54571,x54574),f26(x54575,x54572,x54576))
% 15.02/14.80 [5458]E(x54581,x54582)+~E(f26(x54581,x54583,x54584),f26(x54582,x54585,x54586))
% 15.02/14.80 [7485]E(x74851,x74852)+~E(f221(x74853,x74854,x74855,x74851),f221(x74853,x74854,x74856,x74852))
% 15.02/14.80 [7486]E(x74861,x74862)+~E(f221(x74863,x74864,x74861,x74865),f221(x74863,x74864,x74862,x74866))
% 15.02/14.80 [8599]~P20(x85995,x85991,x85992,x85996)+E(f857(f72(x85991,x85991,x85991,f857(x85992,x85993)),f857(x85992,x85994)),f857(f72(x85991,x85991,x85991,f857(x85992,x85994)),f857(x85992,x85993)))
% 15.02/14.80 [8833]~P58(x88334,x88335,x88332,x88331,x88336)+E(f857(x88331,f857(x88332,x88333)),x88333)
% 15.02/14.80 [9000]P26(x90001,x90002,x90003,x90004)+~P26(x90001,x90005,f857(f72(x90002,x90005,x90001,x90006),x90003),x90004)
% 15.02/14.80 [9073]~E(x90736,x90734)+E(f857(f74(x90731,x90732,x90733,x90734,x90735),x90736),x90735)
% 15.02/14.80 [9079]E(x90791,x90792)+E(f857(f74(x90793,x90794,x90795,x90792,x90796),x90791),f857(x90795,x90791))
% 15.02/14.80 [9091]~P26(x90914,x90912,f857(f72(x90911,x90912,x90914,x90913),x90915),x90916)+P26(x90911,x90912,x90913,f857(f309(x90914,x90911,x90915),x90916))
% 15.02/14.80 [9805]P106(f857(f60(x98051),x98052))+~P106(f857(f65(x98051,x98053,x98054,x98055,x98052),x98056))
% 15.02/14.80 [9814]~P106(f857(f857(f328(x98144),x98143),f299(x98144,x98145,x98141,x98142,x98146)))+P106(f857(f857(x98141,x98142),x98143))
% 15.02/14.80 [9815]~P106(f857(f857(f328(x98154),x98153),f296(x98154,x98151,x98155,x98152,x98156)))+P106(f857(f857(x98151,x98152),x98153))
% 15.02/14.80 [9816]~P106(f857(f857(f328(x98164),x98162),f299(x98164,x98161,x98165,x98166,x98163)))+P106(f857(f857(x98161,x98162),x98163))
% 15.02/14.80 [9817]~P106(f857(f857(f328(x98174),x98172),f296(x98174,x98175,x98171,x98176,x98173)))+P106(f857(f857(x98171,x98172),x98173))
% 15.02/14.80 [10323]P13(x103231,x103232,x103233,x103234,x103235,x103236)+~E(f857(f857(x103236,f843(x103233,x103236,x103235,x103232,x103234,x103231)),f851(x103233,x103236,x103235,x103232,x103234,x103231)),f857(f857(x103236,f844(x103233,x103236,x103235,x103232,x103234,x103231)),f852(x103233,x103236,x103235,x103232,x103234,x103231)))
% 15.02/14.80 [5967]E(x59671,x59672)+~E(f857(f857(f251(x59673,x59674),x59675),x59671),f857(f857(f251(x59673,x59674),x59676),x59672))
% 15.02/14.80 [5969]E(x59691,x59692)+~E(f857(f857(f251(x59693,x59694),x59691),x59695),f857(f857(f251(x59693,x59694),x59692),x59696))
% 15.02/14.80 [6105]~P17(x61055,x61056,x61051)+E(f857(f857(x61051,x61052),f857(f857(x61051,x61053),x61054)),f857(f857(x61051,x61053),f857(f857(x61051,x61052),x61054)))
% 15.02/14.80 [7549]~P34(x75494,x75491,f857(f857(f151(x75494),x75492),x75495),f857(f857(f151(x75494),x75493),x75496))+P106(f857(f857(x75491,x75492),x75493))
% 15.02/14.80 [7905]P34(x79051,x79052,x79053,x79054)+~P34(x79051,x79052,f857(f857(f151(x79051),x79055),x79053),f857(f857(f151(x79051),x79056),x79054))
% 15.02/14.80 [8937]~P58(x89375,x89371,x89372,x89376,x89374)+P106(f857(f857(f328(x89371),f857(x89372,x89373)),x89374))
% 15.02/14.80 [9139]~E(x91393,f857(f857(f151(x91391),x91395),x91396))+P106(f857(f857(f328(f926(f920(x91391),f920(x91391))),f857(f857(f251(f920(x91391),f920(x91391)),x91392),f857(f857(f134(x91391),x91392),x91393))),f147(x91391,x91394)))
% 15.02/14.80 [9372]~P36(x93721,x93722,x93723,x93725,x93726)+P36(x93721,x93722,x93723,f857(f857(f175(x93721),x93724),x93725),f857(f857(f175(x93722),x93724),x93726))
% 15.02/14.80 [9373]~P36(x93731,x93732,x93733,x93735,x93736)+P36(x93731,x93732,x93733,f857(f857(f138(x93731),x93734),x93735),f857(f857(f138(x93732),x93734),x93736))
% 15.02/14.80 [9634]E(f857(f309(x96341,x96342,f74(x96341,x96342,x96343,x96344,x96345)),x96346),f857(f309(x96341,x96342,x96343),x96346))+P106(f857(f857(f328(x96341),x96344),x96346))
% 15.02/14.80 [9637]E(f857(f857(f154(x96371,x96372),f74(x96371,x96372,x96373,x96374,x96375)),x96376),f857(f857(f154(x96371,x96372),x96373),x96376))+P106(f857(f857(f328(x96371),x96374),f857(f172(x96371),x96376)))
% 15.02/14.80 [9877]~P24(x98774,x98772,x98775,x98773,x98776,x98771)+E(f857(x98771,f189(f927(x98772,a915))),x98773)
% 15.02/14.80 [10110]~E(f857(x101104,f857(f250(x101101,x101103),x101105)),f857(x101106,f857(f250(x101101,x101103),x101105)))+E(f857(f257(x101101,x101102,x101103,x101103,x101104,f31(x101103)),x101105),f857(f257(x101101,x101102,x101103,x101103,x101106,f31(x101103)),x101105))
% 15.02/14.80 [10111]~E(f857(x101114,f857(f255(x101111,x101112),x101115)),f857(x101116,f857(f255(x101111,x101112),x101115)))+E(f857(f257(x101111,x101111,x101112,x101113,f31(x101111),x101114),x101115),f857(f257(x101111,x101111,x101112,x101113,f31(x101111),x101116),x101115))
% 15.02/14.80 [10166]~E(f857(f257(x101662,x101666,x101663,x101663,x101661,f31(x101663)),x101664),f857(f257(x101662,x101666,x101663,x101663,x101665,f31(x101663)),x101664))+E(f857(x101661,f857(f250(x101662,x101663),x101664)),f857(x101665,f857(f250(x101662,x101663),x101664)))
% 15.02/14.80 [10167]~E(f857(f257(x101672,x101672,x101673,x101676,f31(x101672),x101671),x101674),f857(f257(x101672,x101672,x101673,x101676,f31(x101672),x101675),x101674))+E(f857(x101671,f857(f255(x101672,x101673),x101674)),f857(x101675,f857(f255(x101672,x101673),x101674)))
% 15.02/14.80 [9040]P106(f857(f857(f328(x90401),x90402),x90403))+~P106(f857(f857(f328(f926(x90401,x90404)),f857(f857(f251(x90401,x90404),x90402),x90405)),f857(f857(f253(x90401,x90404),x90403),x90406)))
% 15.02/14.80 [9056]P106(f857(f857(f328(x90561),x90562),f857(x90563,x90564)))+~P106(f857(f857(f328(f926(x90565,x90561)),f857(f857(f251(x90565,x90561),x90564),x90562)),f857(f857(f253(x90565,x90561),x90566),x90563)))
% 15.02/14.80 [9491]P106(f857(f857(f328(f926(x94911,x94911)),f857(f857(f251(x94911,x94911),f857(x94912,x94913)),f857(x94912,x94914))),x94915))+~P106(f857(f857(f328(f926(x94916,x94916)),f857(f857(f251(x94916,x94916),x94913),x94914)),f857(f857(f287(x94911,x94916),x94915),x94912)))
% 15.02/14.80 [9511]~P106(f857(f857(f328(f926(x95114,x95114)),f857(f857(f251(x95114,x95114),f857(x95116,x95112)),f857(x95116,x95113))),x95115))+P106(f857(f857(f328(f926(x95111,x95111)),f857(f857(f251(x95111,x95111),x95112),x95113)),f857(f857(f287(x95114,x95111),x95115),x95116)))
% 15.02/14.80 [10169]E(f857(f857(f251(x101691,x101692),f646(x101693,x101694,x101695,x101696,x101692,x101691)),f647(x101693,x101694,x101695,x101696,x101692,x101691)),x101696)+~P106(f857(f857(f328(f926(x101691,x101692)),x101696),f857(f857(f288(x101691,x101695,x101692),x101694),x101693)))
% 15.02/14.80 [10388]~P106(f857(f857(f328(f926(x103881,x103886)),x103885),f857(f857(f288(x103881,x103882,x103886),x103884),x103883)))+P106(f857(f857(f328(f926(x103881,x103882)),f857(f857(f251(x103881,x103882),f646(x103883,x103884,x103882,x103885,x103886,x103881)),f648(x103883,x103884,x103882,x103885,x103886,x103881))),x103884))
% 15.02/14.80 [10389]~P106(f857(f857(f328(f926(x103896,x103892)),x103895),f857(f857(f288(x103896,x103891,x103892),x103894),x103893)))+P106(f857(f857(f328(f926(x103891,x103892)),f857(f857(f251(x103891,x103892),f648(x103893,x103894,x103891,x103895,x103892,x103896)),f647(x103893,x103894,x103891,x103895,x103892,x103896))),x103893))
% 15.02/14.80 [10390]P13(x103901,x103902,x103903,x103904,x103905,x103906)+P106(f857(f857(f328(f926(x103902,x103902)),f857(f857(f251(x103902,x103902),f852(x103903,x103906,x103905,x103902,x103904,x103901)),f851(x103903,x103906,x103905,x103902,x103904,x103901))),x103905))
% 15.02/14.80 [10391]P13(x103911,x103912,x103913,x103914,x103915,x103916)+P106(f857(f857(f328(f926(x103911,x103911)),f857(f857(f251(x103911,x103911),f844(x103913,x103916,x103915,x103912,x103914,x103911)),f843(x103913,x103916,x103915,x103912,x103914,x103911))),x103914))
% 15.02/14.80 [7975]~P6(x79752)+E(f857(f857(f38(x79751,x79752),x79753),f857(f857(f9(x79751,x79754,x79752),x79755),x79756)),f857(f857(f857(f38(x79751,f927(x79754,x79752)),x79753),x79755),x79756))
% 15.02/14.80 [7976]~P6(x79762)+E(f857(f857(f39(x79761,x79762),x79763),f857(f857(f9(x79761,x79764,x79762),x79765),x79766)),f857(f857(f857(f39(x79761,f927(x79764,x79762)),x79763),x79765),x79766))
% 15.02/14.80 [8744]E(f857(f857(f39(x87441,f927(x87442,a915)),x87443),f857(f857(f10(f927(x87442,a915),f927(x87442,a915),x87441),f857(f308(x87442),x87444)),x87445)),f857(f857(f308(x87442),x87444),f857(f857(f39(x87441,f927(x87442,a915)),x87443),x87445)))+~P106(f857(f857(f328(x87441),x87446),x87443))
% 15.02/14.80 [9192]~P6(x91922)+E(f857(f857(f38(x91921,x91922),x91923),f857(f857(f10(f927(x91924,x91922),x91922,x91921),f857(f38(x91924,x91922),x91925)),f857(f9(x91924,x91921,x91922),x91926))),f857(f857(f38(x91924,x91922),x91925),f857(f857(f10(f927(x91921,x91922),x91922,x91924),f857(f38(x91921,x91922),x91923)),x91926)))
% 15.02/14.80 [9193]~P6(x91932)+E(f857(f857(f39(x91931,x91932),x91933),f857(f857(f10(f927(x91934,x91932),x91932,x91931),f857(f39(x91934,x91932),x91935)),f857(f9(x91934,x91931,x91932),x91936))),f857(f857(f39(x91934,x91932),x91935),f857(f857(f10(f927(x91931,x91932),x91932,x91934),f857(f39(x91931,x91932),x91933)),x91936)))
% 15.02/14.80 [9397]P106(f857(f857(f328(x93971),x93972),f857(f172(x93971),x93973)))+~P106(f857(f857(f328(f926(x93974,x93971)),f857(f857(f251(x93974,x93971),x93975),x93972)),f857(f172(f926(x93974,x93971)),f857(f857(f181(x93974,x93971),x93976),x93973))))
% 15.02/14.80 [9398]P106(f857(f857(f328(x93981),x93982),f857(f172(x93981),x93983)))+~P106(f857(f857(f328(f926(x93981,x93984)),f857(f857(f251(x93981,x93984),x93982),x93985)),f857(f172(f926(x93981,x93984)),f857(f857(f181(x93981,x93984),x93983),x93986))))
% 15.02/14.80 [9507]P106(f857(f857(f234(f927(x95071,a915)),f857(f284(x95072,x95071,x95073),x95074)),x95075))+~P106(f857(f857(f234(f927(f926(x95072,x95071),a915)),x95073),f857(f857(f253(x95072,x95071),x95076),f857(f18(f927(x95071,a915),x95072),x95075))))
% 15.02/14.80 [9512]~P27(x95124,x95122,x95125,f241(f927(x95124,a915)),f241(f927(x95122,a915)))+E(f857(f857(f38(x95121,f927(x95122,a915)),x95123),f857(f857(f10(f927(x95124,a915),f927(x95122,a915),x95121),f309(x95124,x95122,x95125)),x95126)),f857(f309(x95124,x95122,x95125),f857(f857(f38(x95121,f927(x95124,a915)),x95123),x95126)))
% 15.02/14.80 [9709]P106(f857(f857(f328(f926(f920(x97091),f920(x97091))),f857(f857(f251(f920(x97091),f920(x97091)),f857(f857(f151(x97091),x97092),x97093)),f857(f857(f151(x97091),x97094),x97095))),f147(x97091,x97096)))+~P106(f857(f857(f328(f926(x97091,x97091)),f857(f857(f251(x97091,x97091),x97092),x97094)),x97096))
% 15.02/14.80 [10165]E(f857(f857(f251(x101651,x101652),f591(x101653,x101654,x101655,x101652,x101651,x101656)),f592(x101653,x101654,x101655,x101652,x101651,x101656)),x101656)+P106(f857(f857(f328(x101655),x101654),f857(f857(f256(x101651,x101652,f927(x101655,a915)),x101653),x101656)))
% 15.02/14.80 [10171]E(f857(f857(f251(x101711,x101712),f593(x101713,x101714,x101712,x101711,x101715,x101716)),f594(x101713,x101714,x101712,x101711,x101715,x101716)),x101713)+~P106(f857(f857(f328(x101716),x101715),f857(f857(f256(x101711,x101712,f927(x101716,a915)),x101714),x101713)))
% 15.02/14.80 [10336]P106(f857(f857(f328(x103361),x103362),f857(f857(x103363,f593(x103364,x103363,x103365,x103366,x103362,x103361)),f594(x103364,x103363,x103365,x103366,x103362,x103361))))+~P106(f857(f857(f328(x103361),x103362),f857(f857(f256(x103366,x103365,f927(x103361,a915)),x103363),x103364)))
% 15.02/14.80 [10361]~P106(f857(f857(f328(x103611),x103612),f857(f857(x103615,f591(x103615,x103612,x103611,x103614,x103613,x103616)),f592(x103615,x103612,x103611,x103614,x103613,x103616))))+P106(f857(f857(f328(x103611),x103612),f857(f857(f256(x103613,x103614,f927(x103611,a915)),x103615),x103616)))
% 15.02/14.80 [8644]E(x86441,x86442)+E(f857(f857(f159(x86443,f857(f857(f159(x86443,x86444),x86441),x86445)),x86442),x86446),f857(f857(f159(x86443,f857(f857(f159(x86443,x86444),x86442),x86446)),x86441),x86445))
% 15.02/14.80 [9769]~P106(f857(f857(f328(x97693),x97696),x97695))+E(f857(f857(f308(x97691),x97692),f857(f309(x97693,x97691,x97694),f857(f857(f3(f927(x97693,a915)),x97695),f857(f857(f308(x97693),x97696),f189(f927(x97693,a915)))))),f857(f309(x97693,x97691,f74(x97693,x97691,x97694,x97696,x97692)),x97695))
% 15.02/14.80 [9271]~P106(f857(f857(x92714,x92715),x92716))+P106(f857(f857(f857(f857(f110(f927(x92711,f927(x92712,a915))),x92713),x92714),x92715),x92716))
% 15.02/14.80 [9273]~P106(f857(f857(x92733,x92735),x92736))+P106(f857(f857(f857(f857(f110(f927(x92731,f927(x92732,a915))),x92733),x92734),x92735),x92736))
% 15.02/14.80 [9562]P106(f857(f857(x95621,x95622),x95623))+~P106(f857(f857(f857(f857(f101(f927(x95624,f927(x95625,a915))),x95626),x95621),x95622),x95623))
% 15.02/14.80 [9563]P106(f857(f857(x95631,x95632),x95633))+~P106(f857(f857(f857(f857(f101(f927(x95634,f927(x95635,a915))),x95631),x95636),x95632),x95633))
% 15.02/14.80 [10002]~P72(x100022)+E(f857(f857(f8(x100021,x100022),f857(f857(f9(x100021,f927(x100023,a915),x100022),f857(f857(f10(f927(x100023,x100022),f927(f927(x100023,a915),x100022),x100021),f8(x100023,x100022)),x100024)),x100025)),x100026),f857(f857(f8(f926(x100021,x100023),x100022),f857(f256(x100021,x100023,x100022),x100024)),f857(f857(f253(x100021,x100023),x100026),f857(f18(f927(x100023,a915),x100021),x100025))))
% 15.02/14.80 [10003]~P77(x100032)+E(f857(f857(f11(x100031,x100032),f857(f857(f9(x100031,f927(x100033,a915),x100032),f857(f857(f10(f927(x100033,x100032),f927(f927(x100033,a915),x100032),x100031),f11(x100033,x100032)),x100034)),x100035)),x100036),f857(f857(f11(f926(x100031,x100033),x100032),f857(f256(x100031,x100033,x100032),x100034)),f857(f857(f253(x100031,x100033),x100036),f857(f18(f927(x100033,a915),x100031),x100035))))
% 15.02/14.80 [10137]~P72(x101372)+E(f857(f857(f8(x101371,x101372),f857(f857(f9(x101371,f927(x101373,a915),x101372),f857(f857(f10(f927(x101373,x101372),f927(f927(x101373,a915),x101372),x101371),f8(x101373,x101372)),f857(f9(x101373,x101371,x101372),x101374))),x101375)),x101376),f857(f857(f8(x101373,x101372),f857(f857(f9(x101373,f927(x101371,a915),x101372),f857(f857(f10(f927(x101371,x101372),f927(f927(x101371,a915),x101372),x101373),f8(x101371,x101372)),x101374)),x101376)),x101375))
% 15.02/14.80 [10456]~P106(f857(f857(f328(f926(x104561,x104562)),f857(f857(f251(x104561,x104562),x104565),x104566)),f857(f857(f110(f927(f926(x104561,x104562),a915)),x104563),x104564)))+P106(f857(f857(f857(f857(f110(f927(x104561,f927(x104562,a915))),f857(f857(f9(x104561,f927(f926(x104561,x104562),a915),f927(x104562,a915)),f857(f857(f10(f927(x104562,f927(f927(f926(x104561,x104562),a915),a915)),f927(f927(f926(x104561,x104562),a915),f927(x104562,a915)),x104561),f9(x104562,f927(f926(x104561,x104562),a915),a915)),f857(f857(f10(f927(x104562,f926(x104561,x104562)),f927(x104562,f927(f927(f926(x104561,x104562),a915),a915)),x104561),f857(f10(f926(x104561,x104562),f927(f927(f926(x104561,x104562),a915),a915),x104562),f328(f926(x104561,x104562)))),f251(x104561,x104562)))),x104563)),f857(f857(f9(x104561,f927(f926(x104561,x104562),a915),f927(x104562,a915)),f857(f857(f10(f927(x104562,f927(f927(f926(x104561,x104562),a915),a915)),f927(f927(f926(x104561,x104562),a915),f927(x104562,a915)),x104561),f9(x104562,f927(f926(x104561,x104562),a915),a915)),f857(f857(f10(f927(x104562,f926(x104561,x104562)),f927(x104562,f927(f927(f926(x104561,x104562),a915),a915)),x104561),f857(f10(f926(x104561,x104562),f927(f927(f926(x104561,x104562),a915),a915),x104562),f328(f926(x104561,x104562)))),f251(x104561,x104562)))),x104564)),x104565),x104566))
% 15.02/14.80 [10457]~P106(f857(f857(f328(f926(x104571,x104572)),f857(f857(f251(x104571,x104572),x104575),x104576)),f857(f857(f101(f927(f926(x104571,x104572),a915)),x104573),x104574)))+P106(f857(f857(f857(f857(f101(f927(x104571,f927(x104572,a915))),f857(f857(f9(x104571,f927(f926(x104571,x104572),a915),f927(x104572,a915)),f857(f857(f10(f927(x104572,f927(f927(f926(x104571,x104572),a915),a915)),f927(f927(f926(x104571,x104572),a915),f927(x104572,a915)),x104571),f9(x104572,f927(f926(x104571,x104572),a915),a915)),f857(f857(f10(f927(x104572,f926(x104571,x104572)),f927(x104572,f927(f927(f926(x104571,x104572),a915),a915)),x104571),f857(f10(f926(x104571,x104572),f927(f927(f926(x104571,x104572),a915),a915),x104572),f328(f926(x104571,x104572)))),f251(x104571,x104572)))),x104573)),f857(f857(f9(x104571,f927(f926(x104571,x104572),a915),f927(x104572,a915)),f857(f857(f10(f927(x104572,f927(f927(f926(x104571,x104572),a915),a915)),f927(f927(f926(x104571,x104572),a915),f927(x104572,a915)),x104571),f9(x104572,f927(f926(x104571,x104572),a915),a915)),f857(f857(f10(f927(x104572,f926(x104571,x104572)),f927(x104572,f927(f927(f926(x104571,x104572),a915),a915)),x104571),f857(f10(f926(x104571,x104572),f927(f927(f926(x104571,x104572),a915),a915),x104572),f328(f926(x104571,x104572)))),f251(x104571,x104572)))),x104574)),x104575),x104576))
% 15.02/14.80 [10466]P106(f857(f857(f328(f926(x104661,x104662)),f857(f857(f251(x104661,x104662),x104663),x104664)),f857(f857(f110(f927(f926(x104661,x104662),a915)),x104665),x104666)))+~P106(f857(f857(f857(f857(f110(f927(x104661,f927(x104662,a915))),f857(f857(f9(x104661,f927(f926(x104661,x104662),a915),f927(x104662,a915)),f857(f857(f10(f927(x104662,f927(f927(f926(x104661,x104662),a915),a915)),f927(f927(f926(x104661,x104662),a915),f927(x104662,a915)),x104661),f9(x104662,f927(f926(x104661,x104662),a915),a915)),f857(f857(f10(f927(x104662,f926(x104661,x104662)),f927(x104662,f927(f927(f926(x104661,x104662),a915),a915)),x104661),f857(f10(f926(x104661,x104662),f927(f927(f926(x104661,x104662),a915),a915),x104662),f328(f926(x104661,x104662)))),f251(x104661,x104662)))),x104665)),f857(f857(f9(x104661,f927(f926(x104661,x104662),a915),f927(x104662,a915)),f857(f857(f10(f927(x104662,f927(f927(f926(x104661,x104662),a915),a915)),f927(f927(f926(x104661,x104662),a915),f927(x104662,a915)),x104661),f9(x104662,f927(f926(x104661,x104662),a915),a915)),f857(f857(f10(f927(x104662,f926(x104661,x104662)),f927(x104662,f927(f927(f926(x104661,x104662),a915),a915)),x104661),f857(f10(f926(x104661,x104662),f927(f927(f926(x104661,x104662),a915),a915),x104662),f328(f926(x104661,x104662)))),f251(x104661,x104662)))),x104666)),x104663),x104664))
% 15.02/14.80 [10467]P106(f857(f857(f328(f926(x104671,x104672)),f857(f857(f251(x104671,x104672),x104673),x104674)),f857(f857(f101(f927(f926(x104671,x104672),a915)),x104675),x104676)))+~P106(f857(f857(f857(f857(f101(f927(x104671,f927(x104672,a915))),f857(f857(f9(x104671,f927(f926(x104671,x104672),a915),f927(x104672,a915)),f857(f857(f10(f927(x104672,f927(f927(f926(x104671,x104672),a915),a915)),f927(f927(f926(x104671,x104672),a915),f927(x104672,a915)),x104671),f9(x104672,f927(f926(x104671,x104672),a915),a915)),f857(f857(f10(f927(x104672,f926(x104671,x104672)),f927(x104672,f927(f927(f926(x104671,x104672),a915),a915)),x104671),f857(f10(f926(x104671,x104672),f927(f927(f926(x104671,x104672),a915),a915),x104672),f328(f926(x104671,x104672)))),f251(x104671,x104672)))),x104675)),f857(f857(f9(x104671,f927(f926(x104671,x104672),a915),f927(x104672,a915)),f857(f857(f10(f927(x104672,f927(f927(f926(x104671,x104672),a915),a915)),f927(f927(f926(x104671,x104672),a915),f927(x104672,a915)),x104671),f9(x104672,f927(f926(x104671,x104672),a915),a915)),f857(f857(f10(f927(x104672,f926(x104671,x104672)),f927(x104672,f927(f927(f926(x104671,x104672),a915),a915)),x104671),f857(f10(f926(x104671,x104672),f927(f927(f926(x104671,x104672),a915),a915),x104672),f328(f926(x104671,x104672)))),f251(x104671,x104672)))),x104676)),x104673),x104674))
% 15.02/14.80 [10450]~P106(f857(f857(f328(f926(x104502,x104503)),f857(f857(f251(x104502,x104503),x104505),x104506)),f857(f857(f38(x104501,f927(f926(x104502,x104503),a915)),f241(f927(x104501,a915))),x104504)))+P106(f857(f857(f857(f857(f38(x104501,f927(x104502,f927(x104503,a915))),f241(f927(x104501,a915))),f857(f857(f10(f927(f926(x104502,x104503),a915),f927(x104502,f927(x104503,a915)),x104501),f857(f9(x104502,f927(f926(x104502,x104503),a915),f927(x104503,a915)),f857(f857(f10(f927(x104503,f927(f927(f926(x104502,x104503),a915),a915)),f927(f927(f926(x104502,x104503),a915),f927(x104503,a915)),x104502),f9(x104503,f927(f926(x104502,x104503),a915),a915)),f857(f857(f10(f927(x104503,f926(x104502,x104503)),f927(x104503,f927(f927(f926(x104502,x104503),a915),a915)),x104502),f857(f10(f926(x104502,x104503),f927(f927(f926(x104502,x104503),a915),a915),x104503),f328(f926(x104502,x104503)))),f251(x104502,x104503))))),x104504)),x104505),x104506))
% 15.02/14.80 [10451]~P106(f857(f857(f328(f926(x104512,x104513)),f857(f857(f251(x104512,x104513),x104515),x104516)),f857(f857(f39(x104511,f927(f926(x104512,x104513),a915)),f241(f927(x104511,a915))),x104514)))+P106(f857(f857(f857(f857(f39(x104511,f927(x104512,f927(x104513,a915))),f241(f927(x104511,a915))),f857(f857(f10(f927(f926(x104512,x104513),a915),f927(x104512,f927(x104513,a915)),x104511),f857(f9(x104512,f927(f926(x104512,x104513),a915),f927(x104513,a915)),f857(f857(f10(f927(x104513,f927(f927(f926(x104512,x104513),a915),a915)),f927(f927(f926(x104512,x104513),a915),f927(x104513,a915)),x104512),f9(x104513,f927(f926(x104512,x104513),a915),a915)),f857(f857(f10(f927(x104513,f926(x104512,x104513)),f927(x104513,f927(f927(f926(x104512,x104513),a915),a915)),x104512),f857(f10(f926(x104512,x104513),f927(f927(f926(x104512,x104513),a915),a915),x104513),f328(f926(x104512,x104513)))),f251(x104512,x104513))))),x104514)),x104515),x104516))
% 15.02/14.80 [10460]P106(f857(f857(f328(f926(x104601,x104602)),f857(f857(f251(x104601,x104602),x104603),x104604)),f857(f857(f38(x104605,f927(f926(x104601,x104602),a915)),f241(f927(x104605,a915))),x104606)))+~P106(f857(f857(f857(f857(f38(x104605,f927(x104601,f927(x104602,a915))),f241(f927(x104605,a915))),f857(f857(f10(f927(f926(x104601,x104602),a915),f927(x104601,f927(x104602,a915)),x104605),f857(f9(x104601,f927(f926(x104601,x104602),a915),f927(x104602,a915)),f857(f857(f10(f927(x104602,f927(f927(f926(x104601,x104602),a915),a915)),f927(f927(f926(x104601,x104602),a915),f927(x104602,a915)),x104601),f9(x104602,f927(f926(x104601,x104602),a915),a915)),f857(f857(f10(f927(x104602,f926(x104601,x104602)),f927(x104602,f927(f927(f926(x104601,x104602),a915),a915)),x104601),f857(f10(f926(x104601,x104602),f927(f927(f926(x104601,x104602),a915),a915),x104602),f328(f926(x104601,x104602)))),f251(x104601,x104602))))),x104606)),x104603),x104604))
% 15.02/14.80 [10461]P106(f857(f857(f328(f926(x104611,x104612)),f857(f857(f251(x104611,x104612),x104613),x104614)),f857(f857(f39(x104615,f927(f926(x104611,x104612),a915)),f241(f927(x104615,a915))),x104616)))+~P106(f857(f857(f857(f857(f39(x104615,f927(x104611,f927(x104612,a915))),f241(f927(x104615,a915))),f857(f857(f10(f927(f926(x104611,x104612),a915),f927(x104611,f927(x104612,a915)),x104615),f857(f9(x104611,f927(f926(x104611,x104612),a915),f927(x104612,a915)),f857(f857(f10(f927(x104612,f927(f927(f926(x104611,x104612),a915),a915)),f927(f927(f926(x104611,x104612),a915),f927(x104612,a915)),x104611),f9(x104612,f927(f926(x104611,x104612),a915),a915)),f857(f857(f10(f927(x104612,f926(x104611,x104612)),f927(x104612,f927(f927(f926(x104611,x104612),a915),a915)),x104611),f857(f10(f926(x104611,x104612),f927(f927(f926(x104611,x104612),a915),a915),x104612),f328(f926(x104611,x104612)))),f251(x104611,x104612))))),x104616)),x104613),x104614))
% 15.02/14.80 [7654]E(f857(x76541,f857(x76542,x76543)),f857(x76544,x76543))+~E(f857(f72(x76545,x76546,x76547,x76541),x76542),x76544)
% 15.02/14.80 [9785]E(x97851,x97852)+E(f74(x97853,x97854,f74(x97853,x97854,x97855,x97851,x97856),x97852,x97857),f74(x97853,x97854,f74(x97853,x97854,x97855,x97852,x97857),x97851,x97856))
% 15.02/14.80 [9876]~P23(x98763,x98764,x98761,x98765,x98766,x98767)+E(f857(f857(x98761,x98762),x98762),x98762)
% 15.02/14.80 [6207]~E(f857(f857(f154(x62071,x62075),x62076),x62072),f857(f857(f154(x62073,x62075),x62077),x62074))+E(f857(f190(f920(x62071)),x62072),f857(f190(f920(x62073)),x62074))
% 15.02/14.80 [8675]E(f857(x86751,f857(x86752,x86753)),f857(x86754,x86753))+~E(f857(f72(x86755,x86756,x86757,x86751),x86752),f857(f72(x86756,x86756,x86757,f31(x86756)),x86754))
% 15.02/14.80 [9029]~P36(x90294,x90295,x90291,f857(f857(f151(x90294),x90292),x90296),f857(f857(f151(x90295),x90293),x90297))+P106(f857(f857(x90291,x90292),x90293))
% 15.02/14.80 [9404]P36(x94041,x94042,x94043,x94044,x94045)+~P36(x94041,x94042,x94043,f857(f857(f151(x94041),x94046),x94044),f857(f857(f151(x94042),x94047),x94045))
% 15.02/14.80 [10036]P106(f857(f857(x100361,x100362),f565(x100363,x100362,x100364,x100361)))+~P106(f857(f857(f252(x100365,x100366,x100367,x100361,x100364),x100362),x100363))
% 15.02/14.80 [10060]P106(f857(f857(x100601,f565(x100602,x100603,x100601,x100604)),x100602))+~P106(f857(f857(f252(x100605,x100606,x100607,x100604,x100601),x100603),x100602))
% 15.02/14.80 [6257]E(x62571,x62572)+~E(f857(f857(f857(f90(x62573),x62574),x62575),x62571),f857(f857(f857(f90(x62573),x62576),x62577),x62572))
% 15.02/14.80 [6258]E(x62581,x62582)+~E(f857(f857(f857(f90(x62583),x62584),x62581),x62585),f857(f857(f857(f90(x62583),x62586),x62582),x62587))
% 15.02/14.80 [6259]E(x62591,x62592)+~E(f857(f857(f857(f90(x62593),x62591),x62594),x62595),f857(f857(f857(f90(x62593),x62592),x62596),x62597))
% 15.02/14.80 [9146]~P21(x91466,x91461,x91463,x91467)+E(f857(f72(x91461,x91461,x91462,f857(x91463,x91464)),f857(f72(x91461,x91461,x91462,f857(x91463,x91464)),x91465)),f857(f72(x91461,x91461,x91462,f857(x91463,x91464)),x91465))
% 15.02/14.80 [9515]~P36(x95153,x95152,x95154,f857(f857(f154(x95151,x95153),x95155),x95156),x95157)+P36(x95151,x95152,f857(f857(f10(x95153,f927(x95152,a915),x95151),x95154),x95155),x95156,x95157)
% 15.02/14.80 [9538]P36(x95381,x95382,x95383,f857(f857(f154(x95384,x95381),x95385),x95386),x95387)+~P36(x95384,x95382,f857(f857(f10(x95381,f927(x95382,a915),x95384),x95383),x95385),x95386,x95387)
% 15.02/14.80 [9145]~P106(f857(f857(f328(x91451),x91452),f857(f857(x91455,x91456),x91457)))+P106(f857(f857(f328(x91451),x91452),f857(f857(f256(x91453,x91454,f927(x91451,a915)),x91455),f857(f857(f251(x91453,x91454),x91456),x91457))))
% 15.02/14.80 [9430]P106(f857(f857(f857(x94301,x94302),x94303),x94304))+~P106(f857(f857(f857(f256(x94305,x94306,f927(x94307,a915)),x94301),f857(f857(f251(x94305,x94306),x94302),x94303)),x94304))
% 15.02/14.80 [9577]P106(f857(f857(f328(x95771),f857(f857(x95772,x95773),x95774)),f857(f309(f926(x95775,x95776),x95771,f857(f256(x95775,x95776,x95771),x95772)),x95777)))+~P106(f857(f857(f328(f926(x95775,x95776)),f857(f857(f251(x95775,x95776),x95773),x95774)),x95777))
% 15.02/14.80 [9923]P106(f857(f857(f328(f926(f920(x99231),f920(x99231))),f857(f857(f251(f920(x99231),f920(x99231)),f857(f857(f134(x99231),x99232),f857(f857(f151(x99231),x99233),x99234))),f857(f857(f134(x99231),x99232),f857(f857(f151(x99231),x99235),x99236)))),f147(x99231,x99237)))+~P106(f857(f857(f328(f926(x99231,x99231)),f857(f857(f251(x99231,x99231),x99233),x99235)),x99237))
% 15.02/14.80 [9987]~P36(x99871,x99873,x99874,x99876,f857(f857(f154(x99872,x99873),x99875),x99877))+P36(x99871,x99872,f857(f857(f9(x99871,f927(x99872,x99873),f927(x99872,a915)),f857(f857(f10(f927(x99873,a915),f927(f927(x99872,x99873),f927(x99872,a915)),x99871),f10(x99873,a915,x99872)),x99874)),x99875),x99876,x99877)
% 15.02/14.80 [10064]P36(x100641,x100642,x100643,x100644,f857(f857(f154(x100645,x100642),x100646),x100647))+~P36(x100641,x100645,f857(f857(f9(x100641,f927(x100645,x100642),f927(x100645,a915)),f857(f857(f10(f927(x100642,a915),f927(f927(x100645,x100642),f927(x100645,a915)),x100641),f10(x100642,a915,x100645)),x100643)),x100646),x100644,x100647)
% 15.02/14.80 [10375]P106(f857(f857(f328(x103751),f441(x103752,x103753,x103754,x103755,x103756,x103757,x103751)),x103755))+P106(f857(f857(f857(f857(f38(x103751,f927(x103757,f927(x103756,a915))),x103755),x103754),x103753),x103752))
% 15.02/14.80 [10376]P106(f857(f857(f328(x103761),f786(x103762,x103763,x103764,x103765,x103766,x103767,x103761)),x103767))+P106(f857(f857(f857(f857(f38(x103761,f927(x103763,f927(x103762,a915))),x103767),x103766),x103765),x103764))
% 15.02/14.80 [10377]P106(f857(f857(f328(x103771),f442(x103772,x103773,x103774,x103775,x103776,x103777,x103771)),x103775))+~P106(f857(f857(f857(f857(f39(x103771,f927(x103777,f927(x103776,a915))),x103775),x103774),x103773),x103772))
% 15.02/14.80 [10378]P106(f857(f857(f328(x103781),f787(x103782,x103783,x103784,x103785,x103786,x103787,x103781)),x103785))+~P106(f857(f857(f857(f857(f39(x103781,f927(x103787,f927(x103786,a915))),x103785),x103784),x103783),x103782))
% 15.02/14.80 [10413]P106(f857(f857(f857(x104131,f442(x104132,x104133,x104131,x104134,x104135,x104136,x104137)),x104133),x104132))+~P106(f857(f857(f857(f857(f39(x104137,f927(x104136,f927(x104135,a915))),x104134),x104131),x104133),x104132))
% 15.02/14.80 [10414]P106(f857(f857(f857(x104141,f787(x104142,x104143,x104141,x104144,x104145,x104146,x104147)),x104143),x104142))+~P106(f857(f857(f857(f857(f39(x104147,f927(x104146,f927(x104145,a915))),x104144),x104141),x104143),x104142))
% 15.02/14.80 [10431]~P106(f857(f857(f857(x104315,f441(x104317,x104316,x104315,x104314,x104313,x104312,x104311)),x104316),x104317))+P106(f857(f857(f857(f857(f38(x104311,f927(x104312,f927(x104313,a915))),x104314),x104315),x104316),x104317))
% 15.02/14.80 [10432]~P106(f857(f857(f857(x104325,f786(x104323,x104322,x104327,x104326,x104325,x104324,x104321)),x104326),x104327))+P106(f857(f857(f857(f857(f38(x104321,f927(x104322,f927(x104323,a915))),x104324),x104325),x104326),x104327))
% 15.02/14.80 [10449]~P106(f857(f857(f328(f926(x104491,x104493)),f857(f857(f251(x104491,x104493),x104496),x104497)),f857(f857(f288(x104491,x104492,x104493),x104494),x104495)))+P106(f857(f857(f252(x104491,x104492,x104493,f857(f857(f9(x104491,f927(f926(x104491,x104492),a915),f927(x104492,a915)),f857(f857(f10(f927(x104492,f927(f927(f926(x104491,x104492),a915),a915)),f927(f927(f926(x104491,x104492),a915),f927(x104492,a915)),x104491),f9(x104492,f927(f926(x104491,x104492),a915),a915)),f857(f857(f10(f927(x104492,f926(x104491,x104492)),f927(x104492,f927(f927(f926(x104491,x104492),a915),a915)),x104491),f857(f10(f926(x104491,x104492),f927(f927(f926(x104491,x104492),a915),a915),x104492),f328(f926(x104491,x104492)))),f251(x104491,x104492)))),x104494),f857(f857(f9(x104492,f927(f926(x104492,x104493),a915),f927(x104493,a915)),f857(f857(f10(f927(x104493,f927(f927(f926(x104492,x104493),a915),a915)),f927(f927(f926(x104492,x104493),a915),f927(x104493,a915)),x104492),f9(x104493,f927(f926(x104492,x104493),a915),a915)),f857(f857(f10(f927(x104493,f926(x104492,x104493)),f927(x104493,f927(f927(f926(x104492,x104493),a915),a915)),x104492),f857(f10(f926(x104492,x104493),f927(f927(f926(x104492,x104493),a915),a915),x104493),f328(f926(x104492,x104493)))),f251(x104492,x104493)))),x104495)),x104496),x104497))
% 15.02/14.80 [10459]P106(f857(f857(f328(f926(x104591,x104592)),f857(f857(f251(x104591,x104592),x104593),x104594)),f857(f857(f288(x104591,x104595,x104592),x104596),x104597)))+~P106(f857(f857(f252(x104591,x104595,x104592,f857(f857(f9(x104591,f927(f926(x104591,x104595),a915),f927(x104595,a915)),f857(f857(f10(f927(x104595,f927(f927(f926(x104591,x104595),a915),a915)),f927(f927(f926(x104591,x104595),a915),f927(x104595,a915)),x104591),f9(x104595,f927(f926(x104591,x104595),a915),a915)),f857(f857(f10(f927(x104595,f926(x104591,x104595)),f927(x104595,f927(f927(f926(x104591,x104595),a915),a915)),x104591),f857(f10(f926(x104591,x104595),f927(f927(f926(x104591,x104595),a915),a915),x104595),f328(f926(x104591,x104595)))),f251(x104591,x104595)))),x104596),f857(f857(f9(x104595,f927(f926(x104595,x104592),a915),f927(x104592,a915)),f857(f857(f10(f927(x104592,f927(f927(f926(x104595,x104592),a915),a915)),f927(f927(f926(x104595,x104592),a915),f927(x104592,a915)),x104595),f9(x104592,f927(f926(x104595,x104592),a915),a915)),f857(f857(f10(f927(x104592,f926(x104595,x104592)),f927(x104592,f927(f927(f926(x104595,x104592),a915),a915)),x104595),f857(f10(f926(x104595,x104592),f927(f927(f926(x104595,x104592),a915),a915),x104592),f328(f926(x104595,x104592)))),f251(x104595,x104592)))),x104597)),x104593),x104594))
% 15.02/14.80 [10387]~P147(x103872)+E(f857(f857(f8(x103871,x103872),f857(f857(f9(x103871,f927(x103873,a915),x103872),f857(f857(f10(f927(x103873,x103872),f927(f927(x103873,a915),x103872),x103871),f8(x103873,x103872)),f857(f857(f9(x103871,f927(x103873,x103872),f927(x103873,x103872)),f857(f857(f10(f927(x103872,x103872),f927(f927(x103873,x103872),f927(x103873,x103872)),x103871),f10(x103872,x103872,x103873)),f857(f857(f10(x103872,f927(x103872,x103872),x103871),f80(x103872)),x103874))),x103875))),x103876)),x103877),f857(f857(f80(x103872),f857(f857(f8(x103871,x103872),x103874),x103877)),f857(f857(f8(x103873,x103872),x103875),x103876)))
% 15.02/14.80 [9462]~P20(x94627,x94621,x94623,x94628)+E(f857(f72(x94621,x94621,x94622,f857(x94623,x94624)),f857(f72(x94621,x94621,x94622,f857(x94623,x94625)),x94626)),f857(f72(x94621,x94621,x94622,f857(x94623,x94625)),f857(f72(x94621,x94621,x94622,f857(x94623,x94624)),x94626)))
% 15.02/14.80 [10454]E(f857(f857(f251(x104541,x104542),f857(x104543,f546(x104544,x104545,x104543,x104546,x104547,x104548,x104542,x104541))),f857(x104545,f547(x104544,x104545,x104543,x104546,x104547,x104548,x104542,x104541))),x104548)+~P106(f857(f857(f328(f926(x104541,x104542)),x104548),f857(f309(f926(x104547,x104546),f926(x104541,x104542),f257(x104547,x104541,x104546,x104542,x104543,x104545)),x104544)))
% 15.02/14.80 [10472]~P106(f857(f857(f328(f926(x104728,x104727)),x104726),f857(f309(f926(x104721,x104722),f926(x104728,x104727),f257(x104721,x104728,x104722,x104727,x104725,x104724)),x104723)))+P106(f857(f857(f328(f926(x104721,x104722)),f857(f857(f251(x104721,x104722),f546(x104723,x104724,x104725,x104722,x104721,x104726,x104727,x104728)),f547(x104723,x104724,x104725,x104722,x104721,x104726,x104727,x104728))),x104723))
% 15.02/14.80 [9913]P106(f857(f857(f328(f926(f926(x99131,x99132),f926(x99131,x99132))),f857(f857(f251(f926(x99131,x99132),f926(x99131,x99132)),f857(f857(f251(x99131,x99132),x99133),x99134)),f857(f857(f251(x99131,x99132),x99135),x99136))),f318(x99131,x99132,x99137,x99138)))+~P106(f857(f857(f328(f926(x99131,x99131)),f857(f857(f251(x99131,x99131),x99133),x99135)),x99137))
% 15.02/14.80 [10443]E(f857(f142(x104431,x104432,f857(f9(x104432,x104431,x104431),x104433),f857(x104434,x104435)),x104436),f857(x104434,f857(f142(x104437,x104432,f857(f9(x104432,x104437,x104437),x104438),x104435),x104436)))+P106(f857(f857(f328(x104432),f734(x104435,x104438,x104434,x104433,x104437,x104431,x104436,x104432)),f857(f172(x104432),x104436)))
% 15.02/14.80 [10462]~E(f857(f72(x104621,x104621,x104627,f857(x104623,f734(x104625,x104628,x104624,x104623,x104627,x104621,x104626,x104622))),x104624),f857(f72(x104627,x104621,x104627,x104624),f857(x104628,f734(x104625,x104628,x104624,x104623,x104627,x104621,x104626,x104622))))+E(f857(f142(x104621,x104622,f857(f9(x104622,x104621,x104621),x104623),f857(x104624,x104625)),x104626),f857(x104624,f857(f142(x104627,x104622,f857(f9(x104622,x104627,x104627),x104628),x104625),x104626)))
% 15.02/14.80 [8680]E(f857(x86801,f857(x86802,x86803)),f857(x86804,f857(x86805,x86803)))+~E(f857(f72(x86806,x86807,x86808,x86801),x86802),f857(f72(x86809,x86807,x86808,x86804),x86805))
% 15.02/14.80 [10299]P106(f857(f857(f328(f926(x102991,x102992)),f857(f857(f251(x102991,x102992),f857(x102993,x102994)),f857(x102995,x102996))),f857(f309(f926(x102997,x102998),f926(x102991,x102992),f257(x102997,x102991,x102998,x102992,x102993,x102995)),x102999)))+~P106(f857(f857(f328(f926(x102997,x102998)),f857(f857(f251(x102997,x102998),x102994),x102996)),x102999))
% 15.02/14.80 [8975]~E(f857(x89754,f857(x89755,x89756)),f857(x89759,f857(x897510,x897511)))+E(f857(f857(f72(x89751,x89752,x89753,x89754),x89755),x89756),f857(f857(f72(x89757,x89752,x89758,x89759),x897510),x897511))
% 15.02/14.80 [4773]~P109(x47731)+~P102(x47731)+E(f101(x47731),f188(x47731))
% 15.02/14.80 [4774]~P109(x47741)+~P101(x47741)+E(f110(x47741),f233(x47741))
% 15.02/14.80 [5023]~P120(x50231)+~P94(x50231)+E(f857(f75(x50231),f857(f103(x50231),a97)),f77(x50231))
% 15.02/14.80 [5311]E(x53111,f2(a1))+E(f81(a1,x53111),f857(f78(a1),f77(a1)))+P106(f857(f857(f235(a1),f2(a1)),x53111))
% 15.02/14.80 [5520]E(x55201,f2(a1))+E(f81(a1,x55201),f77(a1))+~P106(f857(f857(f235(a1),f2(a1)),x55201))
% 15.02/14.80 [7553]~P42(x75531)+P106(f857(f60(a1),x75531))+~P106(f857(f60(a919),f857(f309(a1,a919,a104),x75531)))
% 15.02/14.80 [9875]E(x98751,f189(f927(f926(a919,a919),a915)))+~P106(f857(f60(f926(a919,a919)),x98751))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),f189(f927(f926(a919,a919),a915))),x98751)),a33))
% 15.02/14.80 [10037]E(x100371,f2(a919))+E(x100371,f857(a112,f2(a919)))+~P106(f857(f857(f235(a919),x100371),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.80 [10331]E(x103311,f2(a99))+E(f857(f857(f79(a1),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(a24,f857(f857(f35(a99),x103311),f857(f103(a99),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))),f77(a1)),f857(a24,x103311))+E(f44(a99,x103311,f857(f103(a99),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f2(a99))
% 15.02/14.80 [10175]E(x101751,f2(a99))+~E(f44(a99,x101751,f857(f103(a99),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f2(a99))+E(f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(a24,f857(f857(f35(a99),x101751),f857(f103(a99),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f857(a24,x101751))
% 15.02/14.80 [4854]~P59(x48541,x48542)+P46(x48541,x48542)+~P47(a915)
% 15.02/14.80 [4783]~P146(x47831)+P29(x47831,x47832)+~E(x47832,f2(x47831))
% 15.02/14.80 [4784]~P109(x47841)+P14(x47841,x47842)+~E(x47842,f113(x47841))
% 15.02/14.80 [4793]~P120(x47931)+~E(x47932,f2(x47931))+E(f81(x47931,x47932),f2(x47931))
% 15.02/14.80 [4794]~P91(x47941)+~E(x47942,f2(x47941))+E(f81(x47941,x47942),f2(x47941))
% 15.02/14.80 [4802]~P146(x48022)+~P29(x48022,x48021)+E(x48021,f2(x48022))
% 15.02/14.80 [4847]~P120(x48472)+~E(f81(x48472,x48471),f2(x48472))+E(x48471,f2(x48472))
% 15.02/14.80 [4861]~P5(x48612)+~P5(x48611)+P5(f927(x48611,x48612))
% 15.02/14.80 [4862]~P5(x48622)+~P5(x48621)+P5(f925(x48621,x48622))
% 15.02/14.80 [4863]~P5(x48632)+~P5(x48631)+P5(f926(x48631,x48632))
% 15.02/14.80 [4864]~P7(x48642)+~P7(x48641)+P7(f195(x48641,x48642))
% 15.02/14.80 [4865]~P64(x48652)+~P64(x48651)+P64(f927(x48651,x48652))
% 15.02/14.80 [4866]~P64(x48662)+~P64(x48661)+P64(f925(x48661,x48662))
% 15.02/14.80 [4867]~P64(x48672)+~P64(x48671)+P64(f926(x48671,x48672))
% 15.02/14.80 [4868]~P104(x48682)+~P104(x48681)+P104(f926(x48681,x48682))
% 15.02/14.80 [4995]~P109(x49951)+~P14(x49951,x49952)+P14(x49951,f152(x49951,x49952))
% 15.02/14.80 [5238]~P7(x52382)+~P7(x52381)+P7(f44(a1,x52381,x52382))
% 15.02/14.80 [4804]~P78(x48041)+~E(x48042,f2(x48041))+E(f857(f78(x48041),x48042),x48042)
% 15.02/14.80 [4819]~P143(x48191)+~E(x48192,f2(a1))+E(f857(f102(x48191),x48192),f2(x48191))
% 15.02/14.80 [4820]~P93(x48201)+~E(x48202,f2(a1))+E(f857(f102(x48201),x48202),f2(x48201))
% 15.02/14.80 [4844]~P76(x48441)+~E(f2(x48441),x48442)+E(f857(f78(x48441),x48442),f2(x48441))
% 15.02/14.80 [4845]~P87(x48451)+~E(x48452,f2(x48451))+E(f857(f75(x48451),x48452),f2(x48451))
% 15.02/14.80 [4846]~P76(x48461)+~E(x48462,f2(x48461))+E(f857(f78(x48461),x48462),f2(x48461))
% 15.02/14.80 [4870]~P78(x48702)+E(x48701,f2(x48702))+~E(f857(f78(x48702),x48701),x48701)
% 15.02/14.80 [4876]E(x48761,f857(a104,x48762))+~E(x48761,f2(a919))+~E(x48762,f857(f100(a1),x48761))
% 15.02/14.80 [4877]E(f857(a104,x48771),x48772)+~E(x48772,f2(a919))+~E(x48771,f857(f100(a1),x48772))
% 15.02/14.80 [4881]~P93(x48812)+E(x48811,f2(a1))+~E(f857(f102(x48812),x48811),f2(x48812))
% 15.02/14.80 [4885]~P87(x48852)+E(x48851,f2(x48852))+~E(f857(f75(x48852),x48851),f2(x48852))
% 15.02/14.80 [4886]~P76(x48862)+E(x48861,f2(x48862))+~E(f857(f78(x48862),x48861),f2(x48862))
% 15.02/14.80 [4887]~P76(x48871)+E(f2(x48871),x48872)+~E(f857(f78(x48871),x48872),f2(x48871))
% 15.02/14.80 [5070]~P109(x50701)+~P14(x50701,x50702)+P14(x50701,f857(f171(x50701),x50702))
% 15.02/14.80 [5097]~P106(x50972)+~P106(x50971)+P106(f857(f857(a325,x50971),x50972))
% 15.02/14.80 [5131]~E(f77(a919),f2(a919))+E(f857(f34(x51311),x51312),f2(a919))+~P106(f857(f60(x51311),x51312))
% 15.02/14.80 [5167]~P116(x51671)+~P147(x51671)+E(f857(f857(f243(x51671),f2(x51671)),f857(a112,x51672)),f2(x51671))
% 15.02/14.80 [5206]~P109(x52061)+P14(x52061,f139(x52061,x52062))+~P106(f857(f60(x52061),x52062))
% 15.02/14.80 [5207]~P109(x52071)+P14(x52071,f726(x52072,x52071))+~P106(f857(f60(x52071),x52072))
% 15.02/14.80 [5230]~P109(x52301)+E(f857(f172(x52301),f139(x52301,x52302)),x52302)+~P106(f857(f60(x52301),x52302))
% 15.02/14.80 [5231]~P109(x52311)+E(f857(f172(x52311),f726(x52312,x52311)),x52312)+~P106(f857(f60(x52311),x52312))
% 15.02/14.80 [5260]P106(x52601)+P106(x52602)+~P106(f857(f857(a326,x52602),x52601))
% 15.02/14.80 [5273]E(x52731,f189(f927(x52732,a915)))+~E(f857(f34(x52732),x52731),f2(a919))+~P106(f857(f60(x52732),x52731))
% 15.02/14.80 [5278]P106(x52781)+~P106(x52782)+~P106(f857(f857(a329,x52782),x52781))
% 15.02/14.80 [5329]~P75(x53291)+E(f857(f75(x53291),x53292),x53292)+P106(f857(f857(f235(x53291),x53292),f2(x53291)))
% 15.02/14.80 [5389]~P64(x53892)+~P106(f857(f55(x53892),x53891))+P106(f857(x53891,f727(x53891,x53892)))
% 15.02/14.80 [5390]~P64(x53902)+~P106(f857(f55(x53902),x53901))+P106(f857(x53901,f735(x53901,x53902)))
% 15.02/14.80 [5431]E(x54311,f113(x54312))+P106(f857(f137(x54312),f114(x54312,x54311)))+~P106(f857(f137(x54312),x54311))
% 15.02/14.80 [5436]~P109(x54361)+~P106(f857(f60(x54361),x54362))+P106(f857(f137(x54361),f139(x54361,x54362)))
% 15.02/14.80 [5437]~P109(x54371)+~P106(f857(f60(x54371),x54372))+P106(f857(f137(x54371),f726(x54372,x54371)))
% 15.02/14.80 [5442]~P143(x54421)+E(f857(f100(x54421),f857(a104,x54422)),f857(f102(x54421),x54422))+P106(f857(f857(f235(a1),x54422),f2(a1)))
% 15.02/14.80 [5469]P8(x54692,x54691)+E(f857(x54691,f443(x54691)),f857(x54691,f482(x54691)))+P106(f857(f857(x54691,f443(x54691)),f482(x54691)))
% 15.02/14.80 [5482]E(f857(f100(a1),f367(x54821,x54822)),x54821)+P106(f857(x54822,f857(a104,x54821)))+~P106(f857(x54822,f2(a919)))
% 15.02/14.80 [5494]~P64(x54941)+~P106(f857(x54942,f740(x54942,x54941)))+P106(f857(f56(x54941),x54942))
% 15.02/14.80 [5495]~P64(x54951)+~P106(f857(x54952,f750(x54952,x54951)))+P106(f857(f56(x54951),x54952))
% 15.02/14.80 [5530]~P120(x55301)+~E(f81(x55301,x55302),f857(f78(x55301),f77(x55301)))+P106(f857(f857(f235(x55301),x55302),f2(x55301)))
% 15.02/14.80 [5605]~E(x56052,f2(a1))+E(f216(x56051,x56052),f857(f857(f251(a1,a1),f2(a1)),f77(a1)))+P106(f857(f857(f235(a1),x56052),f2(a1)))
% 15.02/14.80 [5606]~E(x56061,f2(a1))+E(f216(x56061,x56062),f857(f857(f251(a1,a1),f2(a1)),f77(a1)))+P106(f857(f857(f235(a1),x56062),f2(a1)))
% 15.02/14.80 [5658]E(f857(f100(a1),f367(x56581,x56582)),x56581)+P106(f857(x56582,f857(a104,x56581)))+P106(f857(f857(f235(a1),x56581),f2(a1)))
% 15.02/14.80 [5727]~P120(x57271)+E(f81(x57271,x57272),f857(f78(x57271),f77(x57271)))+~P106(f857(f857(f235(x57271),x57272),f2(x57271)))
% 15.02/14.80 [5728]~P87(x57281)+E(f857(f75(x57281),x57282),f857(f78(x57281),x57282))+~P106(f857(f857(f234(x57281),x57282),f2(x57281)))
% 15.02/14.80 [5729]~P87(x57291)+E(f857(f75(x57291),x57292),f857(f78(x57291),x57292))+~P106(f857(f857(f235(x57291),x57292),f2(x57291)))
% 15.02/14.80 [5730]~P75(x57301)+E(f857(f75(x57301),x57302),f857(f78(x57301),x57302))+~P106(f857(f857(f235(x57301),x57302),f2(x57301)))
% 15.02/14.80 [5830]~P106(f857(x58301,f367(x58302,x58301)))+P106(f857(x58301,f857(a104,x58302)))+~P106(f857(x58301,f2(a919)))
% 15.02/14.80 [5837]E(x58371,f2(a919))+E(f857(a112,f860(x58372,x58371)),x58371)+~P106(f857(f857(f235(a919),x58371),f857(a112,x58372)))
% 15.02/14.80 [5841]P8(x58411,x58412)+~E(f857(x58412,f443(x58412)),f857(x58412,f482(x58412)))+~P106(f857(f857(x58412,f443(x58412)),f482(x58412)))
% 15.02/14.80 [5859]~P109(x58591)+P14(x58591,x58592)+P106(f857(f857(f234(a919),f709(x58592,x58591)),f710(x58592,x58591)))
% 15.02/14.80 [5860]~P109(x58601)+P14(x58601,x58602)+P106(f857(f857(f234(a919),f717(x58602,x58601)),f722(x58602,x58601)))
% 15.02/14.80 [5946]~P87(x59461)+~E(x59462,f2(x59461))+P106(f857(f857(f234(x59461),f857(f75(x59461),x59462)),f2(x59461)))
% 15.02/14.80 [6034]~P106(f857(x60341,f367(x60342,x60341)))+P106(f857(x60341,f857(a104,x60342)))+P106(f857(f857(f235(a1),x60342),f2(a1)))
% 15.02/14.80 [6059]~P106(f857(x60591,f857(a104,x60592)))+P106(f857(x60591,f2(a919)))+~P106(f857(f857(f235(a1),x60592),f2(a1)))
% 15.02/14.80 [6412]~P120(x64121)+~P106(f857(f857(f235(x64121),x64122),f2(x64121)))+P106(f857(f857(f235(x64121),f81(x64121,x64122)),f2(x64121)))
% 15.02/14.80 [6529]~P120(x65291)+P106(f857(f857(f234(x65291),f857(f102(x65291),x65292)),f2(x65291)))+~P106(f857(f857(f234(a1),x65292),f2(a1)))
% 15.02/14.80 [6530]~P120(x65301)+P106(f857(f857(f235(x65301),f857(f102(x65301),x65302)),f2(x65301)))+~P106(f857(f857(f235(a1),x65302),f2(a1)))
% 15.02/14.80 [6539]~P87(x65392)+E(x65391,f2(x65392))+~P106(f857(f857(f234(x65392),f857(f75(x65392),x65391)),f2(x65392)))
% 15.02/14.80 [6615]~P143(x66151)+~P106(f857(f857(f328(x66151),x66152),f109(x66151)))+P106(f857(f857(f328(x66151),f857(f78(x66151),x66152)),f109(x66151)))
% 15.02/14.80 [6647]~P120(x66471)+~P106(f857(f857(f235(x66471),f81(x66471,x66472)),f2(x66471)))+P106(f857(f857(f235(x66471),x66472),f2(x66471)))
% 15.02/14.80 [6821]~P120(x68212)+~P106(f857(f857(f234(x68212),f857(f102(x68212),x68211)),f2(x68212)))+P106(f857(f857(f234(a1),x68211),f2(a1)))
% 15.02/14.80 [6822]~P120(x68222)+~P106(f857(f857(f235(x68222),f857(f102(x68222),x68221)),f2(x68222)))+P106(f857(f857(f235(a1),x68221),f2(a1)))
% 15.02/14.80 [7328]~P78(x73281)+~P106(f857(f857(f234(x73281),x73282),f2(x73281)))+P106(f857(f857(f234(x73281),f857(f857(f79(x73281),x73282),x73282)),f2(x73281)))
% 15.02/14.80 [7330]~P120(x73301)+~P106(f857(f857(f235(x73301),x73302),f2(x73301)))+P106(f857(f857(f235(x73301),f857(f857(f79(x73301),x73302),x73302)),f2(x73301)))
% 15.02/14.80 [7331]~P78(x73311)+~P106(f857(f857(f235(x73311),x73312),f2(x73311)))+P106(f857(f857(f235(x73311),f857(f857(f79(x73311),x73312),x73312)),f2(x73311)))
% 15.02/14.80 [7899]~P78(x78991)+~P106(f857(f857(f234(x78991),f857(f857(f79(x78991),x78992),x78992)),f2(x78991)))+P106(f857(f857(f234(x78991),x78992),f2(x78991)))
% 15.02/14.80 [7900]~P120(x79001)+~P106(f857(f857(f235(x79001),f857(f857(f79(x79001),x79002),x79002)),f2(x79001)))+P106(f857(f857(f235(x79001),x79002),f2(x79001)))
% 15.02/14.80 [7901]~P78(x79011)+~P106(f857(f857(f235(x79011),f857(f857(f79(x79011),x79012),x79012)),f2(x79011)))+P106(f857(f857(f235(x79011),x79012),f2(x79011)))
% 15.02/14.80 [4922]~E(x49222,f77(a919))+~E(x49221,f77(a919))+E(f857(f857(f80(a919),x49221),x49222),f77(a919))
% 15.02/14.80 [4923]~E(x49232,f77(a1))+~E(x49231,f77(a1))+E(f857(f857(f80(a1),x49231),x49232),f77(a1))
% 15.02/14.80 [4924]~E(x49242,f2(a919))+~E(x49241,f2(a919))+E(f857(f857(f79(a919),x49241),x49242),f2(a919))
% 15.02/14.80 [4979]~P124(x49792)+E(x49791,f2(x49792))+E(f857(f857(f290(x49792),x49791),x49791),f77(x49792))
% 15.02/14.80 [4980]~P62(x49802)+E(x49801,f2(x49802))+E(f857(f857(f35(x49802),x49801),x49801),f77(x49802))
% 15.02/14.80 [4981]~P125(x49812)+E(x49811,f2(x49812))+E(f857(f857(f290(x49812),x49811),x49811),f77(x49812))
% 15.02/14.80 [5001]~P144(x50011)+~E(x50012,f77(x50011))+E(f857(f857(f80(x50011),x50012),x50012),f77(x50011))
% 15.02/14.80 [5002]~P78(x50021)+~E(x50022,f2(x50021))+E(f857(f857(f79(x50021),x50022),x50022),f2(x50021))
% 15.02/14.80 [5003]~P125(x50031)+~E(x50032,f2(x50031))+E(f857(f857(f290(x50031),x50032),x50032),f2(x50031))
% 15.02/14.80 [5048]~E(x50482,f2(a919))+~E(x50481,f2(a919))+E(f857(f78(a1),f857(f100(a1),x50481)),f857(f100(a1),x50482))
% 15.02/14.80 [5067]E(x50671,f77(a919))+E(x50672,f2(a919))+~E(f857(f857(f80(a919),x50672),x50671),x50672)
% 15.02/14.80 [5079]E(x50791,f2(a919))+E(x50792,f2(a919))+~E(f857(f857(f80(a919),x50792),x50791),f2(a919))
% 15.02/14.80 [5106]~E(x51062,f2(a919))+~E(x51061,f857(a112,f2(a919)))+E(f857(f857(f79(a919),x51061),x51062),f857(a112,f2(a919)))
% 15.02/14.80 [5107]~E(x51071,f2(a919))+~E(x51072,f857(a112,f2(a919)))+E(f857(f857(f79(a919),x51071),x51072),f857(a112,f2(a919)))
% 15.02/14.80 [5114]E(x51141,f77(a1))+E(x51142,f857(f103(a1),a97))+~E(f857(f857(f80(a1),x51141),x51142),f77(a1))
% 15.02/14.80 [5115]E(x51151,f77(a1))+E(x51152,f857(f103(a1),a97))+~E(f857(f857(f80(a1),x51152),x51151),f77(a1))
% 15.02/14.80 [5116]E(x51161,f77(a1))+E(x51161,f857(f103(a1),a97))+~E(f857(f857(f80(a1),x51162),x51161),f77(a1))
% 15.02/14.80 [5118]E(x51181,f77(a1))+E(x51181,f857(f103(a1),a97))+~E(f857(f857(f80(a1),x51181),x51182),f77(a1))
% 15.02/14.80 [5139]~P78(x51392)+E(x51391,f2(x51392))+~E(f857(f857(f79(x51392),x51391),x51391),f2(x51392))
% 15.02/14.80 [5145]~E(x51451,f857(f103(a1),a97))+~E(x51452,f857(f103(a1),a97))+E(f857(f857(f80(a1),x51451),x51452),f77(a1))
% 15.02/14.80 [5156]E(x51561,f2(a919))+E(x51562,f2(a919))+~E(f857(f857(f79(a919),x51562),x51561),f857(a112,f2(a919)))
% 15.02/14.80 [5166]~P65(x51661)+~P94(x51661)+E(f857(f857(f290(x51661),x51662),f857(f103(x51661),a82)),f2(x51661))
% 15.02/14.80 [5172]~P144(x51721)+~E(x51722,f857(f78(x51721),f77(x51721)))+E(f857(f857(f80(x51721),x51722),x51722),f77(x51721))
% 15.02/14.80 [5177]~P7(x51772)+~P7(x51771)+P7(f857(f857(f80(a1),x51771),x51772))
% 15.02/14.80 [5178]~P7(x51782)+~P7(x51781)+P7(f857(f857(f79(a1),x51781),x51782))
% 15.02/14.80 [5179]~P7(x51792)+~P7(x51791)+P7(f857(f857(f35(a1),x51791),x51792))
% 15.02/14.80 [5181]~E(x51812,f2(a1))+E(x51811,f2(a1))+E(f45(x51811,x51812),f857(f857(f251(a1,a1),f2(a1)),x51811))
% 15.02/14.80 [5204]~E(x52042,f857(a112,f2(a919)))+~E(x52041,f857(a112,f2(a919)))+E(f857(f857(f80(a919),x52041),x52042),f857(a112,f2(a919)))
% 15.02/14.80 [5221]E(x52211,f2(a919))+E(x52212,f857(a112,f2(a919)))+~E(f857(f857(f243(a919),x52212),x52211),f857(a112,f2(a919)))
% 15.02/14.80 [5222]E(x52221,f2(a919))+E(x52221,f857(a112,f2(a919)))+~E(f857(f857(f79(a919),x52222),x52221),f857(a112,f2(a919)))
% 15.02/14.80 [5223]E(x52231,f2(a919))+E(x52231,f857(a112,f2(a919)))+~E(f857(f857(f79(a919),x52231),x52232),f857(a112,f2(a919)))
% 15.02/14.80 [5232]~P65(x52321)+~P94(x52321)+E(f857(f857(f290(x52321),x52322),f857(f103(x52321),a97)),f857(f78(x52321),x52322))
% 15.02/14.80 [5252]E(x52521,f857(a104,x52522))+~E(x52521,f2(a919))+P106(f857(f857(f234(a1),f2(a1)),x52522))
% 15.02/14.80 [5253]E(f857(a104,x52531),x52532)+~E(x52532,f2(a919))+P106(f857(f857(f234(a1),f2(a1)),x52531))
% 15.02/14.80 [5269]E(x52691,f857(a112,f2(a919)))+E(x52692,f857(a112,f2(a919)))+~E(f857(f857(f79(a919),x52691),x52692),f857(a112,f2(a919)))
% 15.02/14.80 [5280]~E(x52801,f857(a104,x52802))+E(x52801,f2(a919))+P106(f857(f857(f234(a1),f2(a1)),x52802))
% 15.02/14.80 [5281]~E(f857(a104,x52812),x52811)+E(x52811,f2(a919))+P106(f857(f857(f234(a1),f2(a1)),x52812))
% 15.02/14.80 [5303]~P2(x53031)+E(f857(f62(x53031,f110(x53031)),x53032),f12(x53031,x53032))+~P106(f857(f60(x53031),x53032))
% 15.02/14.80 [5304]~P2(x53041)+E(f857(f62(x53041,f101(x53041)),x53042),f13(x53041,x53042))+~P106(f857(f60(x53041),x53042))
% 15.02/14.80 [5305]~P109(x53051)+E(f857(f62(x53051,f188(x53051)),x53052),f16(x53051,x53052))+~P106(f857(f60(x53051),x53052))
% 15.02/14.80 [5306]~P109(x53061)+E(f857(f62(x53061,f233(x53061)),x53062),f17(x53061,x53062))+~P106(f857(f60(x53061),x53062))
% 15.02/14.80 [5384]E(x53841,x53842)+~E(f857(f857(f3(a919),x53842),x53841),f2(a919))+~E(f857(f857(f3(a919),x53841),x53842),f2(a919))
% 15.02/14.80 [5402]P7(x54021)+~P42(x54022)+~P106(f857(f857(f328(a1),x54021),x54022))
% 15.02/14.80 [5432]~P120(x54321)+~E(f81(x54321,x54322),f77(x54321))+P106(f857(f857(f235(x54321),f2(x54321)),x54322))
% 15.02/14.80 [5443]~P94(x54431)+E(f857(f100(x54431),f857(f103(a919),x54432)),f857(f103(x54431),x54432))+P106(f857(a194,f857(f103(a1),x54432)))
% 15.02/14.80 [5448]~P46(x54481,x54482)+P47(a915)+P106(f857(f60(f926(x54481,x54481)),x54482))
% 15.02/14.80 [5522]~P109(x55221)+E(f857(f62(x55221,f188(x55221)),x55222),f14(x55221,f188(x55221),x55222))+~P106(f857(f60(x55221),x55222))
% 15.02/14.80 [5523]~P109(x55231)+E(f857(f62(x55231,f233(x55231)),x55232),f15(x55231,f233(x55231),x55232))+~P106(f857(f60(x55231),x55232))
% 15.02/14.80 [5537]E(x55371,x55372)+P106(f857(f857(f235(a919),x55372),x55371))+P106(f857(f857(f235(a919),x55371),x55372))
% 15.02/14.80 [5538]E(x55381,x55382)+P106(f857(f857(f235(a1),x55382),x55381))+P106(f857(f857(f235(a1),x55381),x55382))
% 15.02/14.80 [5592]~P94(x55921)+E(f857(f100(x55921),f857(f103(a919),x55922)),f2(x55921))+~P106(f857(a194,f857(f103(a1),x55922)))
% 15.02/14.80 [5595]~E(x55952,f857(a104,x55951))+E(x55951,f857(f100(a1),x55952))+~P106(f857(f857(f234(a1),f2(a1)),x55951))
% 15.02/14.80 [5596]~E(f857(a104,x55961),x55962)+E(x55961,f857(f100(a1),x55962))+~P106(f857(f857(f234(a1),f2(a1)),x55961))
% 15.02/14.80 [5597]~E(x55971,f857(a104,x55972))+E(f857(f100(a1),x55971),x55972)+~P106(f857(f857(f234(a1),f2(a1)),x55972))
% 15.02/14.80 [5607]E(x56071,f857(a104,x56072))+~E(x56072,f857(f100(a1),x56071))+~P106(f857(f857(f234(a1),f2(a1)),x56072))
% 15.02/14.80 [5608]E(f857(a104,x56081),x56082)+~E(x56081,f857(f100(a1),x56082))+~P106(f857(f857(f234(a1),f2(a1)),x56081))
% 15.02/14.80 [5649]~P87(x56492)+E(x56491,f2(x56492))+P106(f857(f857(f235(x56492),f2(x56492)),f857(f75(x56492),x56491)))
% 15.02/14.80 [5714]~P120(x57141)+E(f81(x57141,x57142),f77(x57141))+~P106(f857(f857(f235(x57141),f2(x57141)),x57142))
% 15.02/14.80 [5720]~P94(x57201)+E(f857(f100(x57201),f857(f103(a919),x57202)),f2(x57201))+P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x57202)))
% 15.02/14.80 [5731]~P87(x57311)+E(f857(f75(x57311),x57312),x57312)+~P106(f857(f857(f234(x57311),f2(x57311)),x57312))
% 15.02/14.80 [5732]~P87(x57321)+E(f857(f75(x57321),x57322),x57322)+~P106(f857(f857(f235(x57321),f2(x57321)),x57322))
% 15.02/14.80 [5741]E(x57411,f2(a919))+~E(f139(a919,f857(f301(a919,x57412),x57411)),f113(a919))+P106(f857(f857(f234(a919),x57411),x57412))
% 15.02/14.80 [5752]~P72(x57521)+E(f857(f857(f8(x57521,x57521),f7(x57521)),f857(f172(x57521),x57522)),f857(f165(x57521),x57522))+~P106(f857(f137(x57521),x57522))
% 15.02/14.80 [5755]~P143(x57551)+E(f857(f100(x57551),f857(a104,x57552)),f857(f102(x57551),x57552))+~P106(f857(f857(f234(a1),f2(a1)),x57552))
% 15.02/14.80 [5782]E(x57821,x57822)+P106(f857(f857(f235(a919),x57821),x57822))+~P106(f857(f857(f234(a919),x57821),x57822))
% 15.02/14.80 [5783]E(x57831,x57832)+P106(f857(f857(f235(a1),x57831),x57832))+~P106(f857(f857(f234(a1),x57831),x57832))
% 15.02/14.80 [5786]E(x57861,f77(a1))+~E(f857(f857(f80(a1),x57862),x57861),f77(a1))+~P106(f857(f857(f235(a1),f2(a1)),x57862))
% 15.02/14.80 [5787]E(x57871,f77(a1))+~E(f857(f857(f80(a1),x57871),x57872),f77(a1))+~P106(f857(f857(f235(a1),f2(a1)),x57871))
% 15.02/14.80 [5827]~P42(x58272)+P106(f857(f857(f234(a1),f2(a1)),x58271))+~P106(f857(f857(f328(a1),x58271),x58272))
% 15.02/14.80 [5846]~P59(x58461,x58462)+P39(x58461,x58462)+~P106(f857(f60(f926(x58461,x58461)),x58462))
% 15.02/14.80 [5848]~P59(x58481,x58482)+P46(x58481,x58482)+~P106(f857(f60(f926(x58481,x58481)),x58482))
% 15.02/14.80 [5890]E(x58901,f189(f927(x58902,a915)))+~P106(f857(f60(x58902),x58901))+P106(f857(f857(f235(a919),f2(a919)),f857(f34(x58902),x58901)))
% 15.02/14.80 [5917]~P106(f857(x59171,x59172))+P106(f857(x59171,f2(a919)))+P106(f857(f857(f235(a919),f905(x59172,x59171)),x59172))
% 15.02/14.80 [5940]E(x59401,f2(a919))+~E(f857(f165(a919),x59402),f2(a919))+~P106(f857(f857(f328(a919),x59401),f857(f172(a919),x59402)))
% 15.02/14.80 [6008]E(x60081,x60082)+~P106(f857(f857(f234(a919),x60082),x60081))+~P106(f857(f857(f234(a919),x60081),x60082))
% 15.02/14.80 [6009]E(x60091,x60092)+~P106(f857(f857(f234(a1),x60092),x60091))+~P106(f857(f857(f234(a1),x60091),x60092))
% 15.02/14.80 [6011]E(f857(f34(x60111),x60112),f2(a919))+~P106(f857(f60(x60111),x60112))+P106(f857(f857(f328(x60111),f906(x60112,x60111)),x60112))
% 15.02/14.80 [6020]E(f49(x60201,x60202),f45(x60201,x60202))+P106(f857(f857(f234(a1),f2(a1)),x60201))+~P106(f857(f857(f235(a1),f2(a1)),x60202))
% 15.02/14.80 [6046]~P106(f857(x60461,f363(x60461)))+P106(f857(x60461,f857(a104,x60462)))+~P106(f857(f857(f234(a1),f2(a1)),x60462))
% 15.02/14.80 [6049]P106(f857(f857(f234(a919),x60491),f413(x60492)))+~P106(f857(f60(a919),x60492))+~P106(f857(f857(f328(a919),x60491),x60492))
% 15.02/14.80 [6050]P106(f857(f857(f235(a919),x60501),f411(x60502)))+~P106(f857(f60(a919),x60502))+~P106(f857(f857(f328(a919),x60501),x60502))
% 15.02/14.80 [6081]E(x60811,x60812)+~P106(f857(f857(f235(a919),x60811),f857(a112,x60812)))+P106(f857(f857(f235(a919),x60811),x60812))
% 15.02/14.80 [6117]E(x61171,f857(a112,x61172))+~P106(f857(f857(f234(a919),x61171),f857(a112,x61172)))+P106(f857(f857(f234(a919),x61171),x61172))
% 15.02/14.80 [6133]P106(f857(x61331,f368(x61331)))+~P106(f857(x61331,f857(a104,x61332)))+~P106(f857(f857(f234(a1),f2(a1)),x61332))
% 15.02/14.80 [6149]~P106(f857(x61491,x61492))+~P106(f857(f857(f234(a1),f2(a1)),x61492))+P106(f857(x61491,f857(f100(a1),f338(x61491))))
% 15.02/14.80 [6160]~P87(x61602)+~E(x61601,f2(x61602))+~P106(f857(f857(f235(x61602),f2(x61602)),f857(f75(x61602),x61601)))
% 15.02/14.80 [6185]~P59(x61851,x61852)+P39(x61851,f857(f285(x61851,x61851),x61852))+~P106(f857(f60(f926(x61851,x61851)),x61852))
% 15.02/14.80 [6194]~P94(x61941)+E(f857(f100(x61941),f857(f103(a919),x61942)),f857(f103(x61941),x61942))+~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x61942)))
% 15.02/14.80 [6197]E(f857(a112,x61971),x61972)+~P106(f857(f857(f235(a919),x61971),x61972))+P106(f857(f857(f235(a919),f857(a112,x61971)),x61972))
% 15.02/14.80 [6213]E(f857(f857(f35(a1),x62131),x62132),f2(a1))+~P106(f857(f857(f234(a1),x62131),f2(a1)))+~P106(f857(f857(f235(a1),x62132),x62131))
% 15.02/14.80 [6225]E(f44(a1,x62251,x62252),x62251)+~P106(f857(f857(f234(a1),x62251),f2(a1)))+~P106(f857(f857(f235(a1),x62252),x62251))
% 15.02/14.80 [6239]E(f46(x62391,x62392),f45(x62391,x62392))+~P106(f857(f857(f234(a1),f2(a1)),x62391))+~P106(f857(f857(f234(a1),f2(a1)),x62392))
% 15.02/14.80 [6249]E(f857(f857(f35(a1),x62491),x62492),f2(a1))+~P106(f857(f857(f234(a1),f2(a1)),x62491))+~P106(f857(f857(f235(a1),x62491),x62492))
% 15.02/14.80 [6263]E(f44(a919,f857(f103(a919),x62631),f857(f103(a919),x62632)),f857(f103(a919),x62631))+P106(f857(a194,f857(f103(a1),x62631)))+~P106(f857(a194,f857(f103(a1),x62632)))
% 15.02/14.80 [6265]E(f44(a1,x62651,x62652),x62651)+~P106(f857(f857(f234(a1),f2(a1)),x62651))+~P106(f857(f857(f235(a1),x62651),x62652))
% 15.02/14.80 [6266]E(x62661,x62662)+~P106(f857(f857(f235(a919),x62661),f857(a112,x62662)))+~P106(f857(f857(f234(a919),x62662),x62661))
% 15.02/14.80 [6280]~P78(x62801)+~P106(f857(f857(f234(x62801),x62802),f2(x62801)))+P106(f857(f857(f234(x62801),x62802),f857(f78(x62801),x62802)))
% 15.02/14.80 [6281]~P120(x62811)+~P106(f857(f857(f235(x62811),x62812),f2(x62811)))+P106(f857(f857(f235(x62811),x62812),f857(f78(x62811),x62812)))
% 15.02/14.80 [6291]~P6(x62911)+E(f857(f857(f63(x62911,x62911,f110(x62911)),f189(x62911)),x62912),f36(x62911,x62912))+~P106(f857(f60(x62911),x62912))
% 15.02/14.80 [6292]~P6(x62921)+E(f857(f857(f63(x62921,x62921,f101(x62921)),f241(x62921)),x62922),f37(x62921,x62922))+~P106(f857(f60(x62921),x62922))
% 15.02/14.80 [6309]~P120(x63091)+~P106(f857(f857(f234(a1),f2(a1)),x63092))+P106(f857(f857(f234(x63091),f2(x63091)),f857(f102(x63091),x63092)))
% 15.02/14.80 [6310]~P127(x63101)+~P106(f857(f857(f235(a919),f2(a919)),x63102))+P106(f857(f857(f235(x63101),f2(x63101)),f857(f100(x63101),x63102)))
% 15.02/14.80 [6311]~P120(x63111)+~P106(f857(f857(f235(a1),f2(a1)),x63112))+P106(f857(f857(f235(x63111),f2(x63111)),f857(f102(x63111),x63112)))
% 15.02/14.80 [6314]~P7(x63142)+~P7(x63141)+E(f857(f309(a919,a1,f100(a1)),f302(a919,f857(a104,x63141),f857(a104,x63142))),f302(a1,x63141,x63142))
% 15.02/14.80 [6320]P106(f857(x63201,x63202))+~P106(f857(f857(f234(a1),f2(a1)),x63202))+~P106(f857(x63201,f857(f100(a1),f351(x63201))))
% 15.02/14.80 [6350]E(f857(f857(f79(a919),f857(f103(a919),x63501)),f857(f103(a919),x63502)),f857(f103(a919),x63501))+P106(f857(f857(f235(a1),x63501),a82))+~P106(f857(f857(f235(a1),x63502),a82))
% 15.02/14.80 [6354]~P120(x63541)+P106(f857(f857(f235(x63541),f2(x63541)),f81(x63541,x63542)))+~P106(f857(f857(f235(x63541),f2(x63541)),x63542))
% 15.02/14.80 [6368]~P80(x63681)+~P106(f857(f857(f234(x63681),x63682),f2(x63681)))+P106(f857(f857(f234(x63681),f2(x63681)),f857(f78(x63681),x63682)))
% 15.02/14.80 [6369]~P80(x63691)+~P106(f857(f857(f235(x63691),x63692),f2(x63691)))+P106(f857(f857(f235(x63691),f2(x63691)),f857(f78(x63691),x63692)))
% 15.02/14.80 [6372]E(x63721,f241(f927(x63722,a915)))+~E(f857(f34(x63722),x63721),f857(f34(x63722),f241(f927(x63722,a915))))+~P106(f857(f60(x63722),f241(f927(x63722,a915))))
% 15.02/14.80 [6404]~P78(x64041)+P106(f857(f857(f234(x64041),x64042),f2(x64041)))+~P106(f857(f857(f234(x64041),x64042),f857(f78(x64041),x64042)))
% 15.02/14.80 [6405]~P120(x64051)+P106(f857(f857(f235(x64051),x64052),f2(x64051)))+~P106(f857(f857(f235(x64051),x64052),f857(f78(x64051),x64052)))
% 15.02/14.80 [6414]~P94(x64141)+P106(f857(f857(f328(x64141),f857(f103(x64141),x64142)),f186(x64141)))+~P106(f857(f857(f234(a1),a82),x64142))
% 15.02/14.80 [6443]E(x64431,f2(a919))+~P106(f857(f857(f235(a919),x64431),f857(a112,x64432)))+P106(f857(f857(f235(a919),f860(x64432,x64431)),x64432))
% 15.02/14.80 [6466]~P120(x64661)+~P106(f857(f857(f235(x64661),f2(x64661)),f81(x64661,x64662)))+P106(f857(f857(f235(x64661),f2(x64661)),x64662))
% 15.02/14.80 [6468]~E(f857(f103(a919),x64682),f857(f103(a919),x64681))+P106(f857(f857(f234(a1),f857(f103(a1),x64681)),f2(a1)))+~P106(f857(a194,f857(f103(a1),x64682)))
% 15.02/14.80 [6497]E(f857(f250(a1,a1),f49(x64971,x64972)),f857(f857(f35(a1),x64971),x64972))+~P106(f857(f857(f235(a1),x64971),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x64972))
% 15.02/14.80 [6537]E(f857(f255(a1,a1),f49(x65371,x65372)),f44(a1,x65371,x65372))+~P106(f857(f857(f235(a1),x65371),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x65372))
% 15.02/14.80 [6540]~P120(x65402)+~P106(f857(f857(f234(x65402),f2(x65402)),f857(f102(x65402),x65401)))+P106(f857(f857(f234(a1),f2(a1)),x65401))
% 15.02/14.80 [6541]~P127(x65412)+~P106(f857(f857(f235(x65412),f2(x65412)),f857(f100(x65412),x65411)))+P106(f857(f857(f235(a919),f2(a919)),x65411))
% 15.02/14.80 [6542]~P120(x65422)+~P106(f857(f857(f235(x65422),f2(x65422)),f857(f102(x65422),x65421)))+P106(f857(f857(f235(a1),f2(a1)),x65421))
% 15.02/14.80 [6546]E(f857(f250(a1,a1),f46(x65461,x65462)),f857(f857(f35(a1),x65461),x65462))+~P106(f857(f857(f234(a1),f2(a1)),x65462))+~P106(f857(f857(f235(a1),f2(a1)),x65461))
% 15.02/14.80 [6560]E(f857(f255(a1,a1),f46(x65601,x65602)),f44(a1,x65601,x65602))+~P106(f857(f857(f234(a1),f2(a1)),x65602))+~P106(f857(f857(f235(a1),f2(a1)),x65601))
% 15.02/14.80 [6576]~P80(x65761)+P106(f857(f857(f234(x65761),x65762),f2(x65761)))+~P106(f857(f857(f234(x65761),f2(x65761)),f857(f78(x65761),x65762)))
% 15.02/14.80 [6577]~P80(x65771)+P106(f857(f857(f235(x65771),x65772),f2(x65771)))+~P106(f857(f857(f235(x65771),f2(x65771)),f857(f78(x65771),x65772)))
% 15.02/14.80 [6603]P106(f857(f48(x66031,x66032),f49(x66031,x66032)))+~P106(f857(f857(f235(a1),x66031),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x66032))
% 15.02/14.80 [6627]P106(f857(f48(x66271,x66272),f46(x66271,x66272)))+~P106(f857(f857(f234(a1),f2(a1)),x66271))+~P106(f857(f857(f235(a1),f2(a1)),x66272))
% 15.02/14.80 [6670]~P80(x66701)+P106(f857(f857(f234(x66701),f857(f78(x66701),x66702)),f2(x66701)))+~P106(f857(f857(f234(x66701),f2(x66701)),x66702))
% 15.02/14.80 [6671]~P80(x66711)+P106(f857(f857(f235(x66711),f857(f78(x66711),x66712)),f2(x66711)))+~P106(f857(f857(f235(x66711),f2(x66711)),x66712))
% 15.02/14.80 [6689]E(f857(f857(f3(a919),f857(a104,x66891)),f857(a104,x66892)),f857(a104,f195(x66891,x66892)))+~P106(f857(f857(f234(a1),f2(a1)),x66892))+~P106(f857(f857(f234(a1),f2(a1)),x66891))
% 15.02/14.80 [6707]P106(f857(f857(f234(a1),f2(a1)),f195(x67071,x67072)))+~P106(f857(f857(f234(a1),f2(a1)),x67072))+~P106(f857(f857(f234(a1),f2(a1)),x67071))
% 15.02/14.80 [6744]~P106(f857(x67441,x67442))+P106(f857(x67441,f2(a919)))+P106(f857(x67441,f857(f857(f79(a919),f905(x67442,x67441)),f77(a919))))
% 15.02/14.80 [6828]E(f857(f103(a919),x68281),f857(f103(a919),x68282))+~P106(f857(f857(f234(a1),f857(f103(a1),x68282)),f2(a1)))+~P106(f857(a194,f857(f103(a1),x68281)))
% 15.02/14.80 [6840]~E(x68401,f2(a919))+~E(f675(x68402,x68401),f2(a919))+E(f857(f142(a919,a919,f79(a919),x68401),x68402),f2(a919))
% 15.02/14.80 [6864]~P106(f857(f60(x68641),f875(x68642,x68641)))+~P106(f857(f60(f927(x68641,a915)),x68642))+P106(f857(f60(x68641),f36(f927(x68641,a915),x68642)))
% 15.02/14.80 [6870]E(x68701,x68702)+P106(f857(f857(f235(a1),x68701),x68702))+~P106(f857(f857(f235(a1),x68701),f857(f857(f79(a1),x68702),f77(a1))))
% 15.02/14.80 [6871]P106(f857(f857(f234(a919),f857(a104,x68711)),f857(a104,x68712)))+~P106(f857(f857(f234(a1),f2(a1)),x68712))+~P106(f857(f857(f234(a1),x68711),x68712))
% 15.02/14.80 [6872]P106(f857(f857(f234(a919),f857(a104,x68721)),f857(a104,x68722)))+~P106(f857(f857(f235(a1),f2(a1)),x68721))+~P106(f857(f857(f234(a1),x68721),x68722))
% 15.02/14.80 [6874]P106(f857(f857(f235(a919),f857(a104,x68741)),f857(a104,x68742)))+~P106(f857(f857(f234(a1),f2(a1)),x68741))+~P106(f857(f857(f235(a1),x68741),x68742))
% 15.02/14.80 [6875]P106(f857(f857(f235(a919),f857(a104,x68751)),f857(a104,x68752)))+~P106(f857(f857(f235(a1),f2(a1)),x68752))+~P106(f857(f857(f235(a1),x68751),x68752))
% 15.02/14.80 [6886]E(f44(a919,f857(a104,x68861),f857(a104,x68862)),f857(a104,f44(a1,x68861,x68862)))+~P106(f857(f857(f234(a1),f2(a1)),x68862))+~P106(f857(f857(f234(a1),f2(a1)),x68861))
% 15.02/14.80 [6909]~P80(x69091)+~P106(f857(f857(f234(x69091),f857(f78(x69091),x69092)),f2(x69091)))+P106(f857(f857(f234(x69091),f2(x69091)),x69092))
% 15.02/14.80 [6910]~P80(x69101)+~P106(f857(f857(f235(x69101),f857(f78(x69101),x69102)),f2(x69101)))+P106(f857(f857(f235(x69101),f2(x69101)),x69102))
% 15.02/14.80 [6925]~P106(f857(f857(f235(a1),a82),x69252))+~P106(f857(f857(f235(a1),x69251),x69252))+P106(f857(f857(f235(a919),f857(f103(a919),x69251)),f857(f103(a919),x69252)))
% 15.02/14.80 [7017]~P106(f857(f857(f234(a1),f2(a1)),x70171))+P106(f857(f857(f235(a919),f857(a104,x70171)),x70172))+~P106(f857(f857(f235(a1),x70171),f857(f100(a1),x70172)))
% 15.02/14.80 [7022]P106(f857(x70221,x70222))+~P106(f857(x70221,f857(a22,f810(x70221,x70222))))+~P106(f857(f857(f328(a919),x70222),f241(f927(a919,a915))))
% 15.02/14.80 [7033]E(x70331,f2(a1))+E(f44(a1,x70332,x70331),f2(a1))+E(f857(f857(f3(a1),f857(f78(a1),f857(f857(f35(a1),x70332),x70331))),f77(a1)),f857(f857(f35(a1),x70332),f857(f78(a1),x70331)))
% 15.02/14.80 [7047]~P106(f857(f857(f234(a1),f2(a1)),x70471))+~P106(f857(f857(f235(a919),f857(a104,x70471)),x70472))+P106(f857(f857(f235(a1),x70471),f857(f100(a1),x70472)))
% 15.02/14.80 [7083]~P106(f857(f857(f234(a919),f857(a104,x70831)),f857(a104,x70832)))+~P106(f857(f857(f234(a1),f2(a1)),x70832))+P106(f857(f857(f234(a1),x70831),x70832))
% 15.02/14.80 [7084]~P106(f857(f857(f234(a919),f857(a104,x70841)),f857(a104,x70842)))+~P106(f857(f857(f235(a1),f2(a1)),x70841))+P106(f857(f857(f234(a1),x70841),x70842))
% 15.02/14.80 [7114]P106(f857(f857(f234(a1),x71141),x71142))+~P106(f857(f857(f234(a919),f857(f103(a919),x71141)),f857(f103(a919),x71142)))+P106(f857(f857(f234(a1),x71141),a82))
% 15.02/14.80 [7140]P106(f857(f857(f234(a1),f2(a1)),f44(a1,x71401,x71402)))+~P106(f857(f857(f234(a1),f2(a1)),x71402))+~P106(f857(f857(f234(a1),f2(a1)),x71401))
% 15.02/14.80 [7237]P106(f857(f857(f235(a1),a82),x72371))+~P106(f857(f857(f235(a1),x72372),x72371))+~P106(f857(f857(f235(a919),f857(f103(a919),x72372)),f857(f103(a919),x72371)))
% 15.02/14.80 [7291]E(f857(f857(f251(a1,a1),f857(f857(f35(a1),x72911),x72912)),f44(a1,x72911,x72912)),f49(x72911,x72912))+~P106(f857(f857(f235(a1),x72911),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x72912))
% 15.02/14.80 [7311]E(f857(f857(f251(a1,a1),f857(f857(f35(a1),x73111),x73112)),f44(a1,x73111,x73112)),f46(x73111,x73112))+~P106(f857(f857(f234(a1),f2(a1)),x73112))+~P106(f857(f857(f234(a1),f2(a1)),x73111))
% 15.02/14.80 [7365]~P97(x73652)+E(x73651,f113(x73652))+E(f857(f142(x73652,x73652,f80(x73652),f857(f141(x73652),x73651)),f857(f171(x73652),x73651)),f857(f62(x73652,f80(x73652)),f857(f172(x73652),x73651)))
% 15.02/14.80 [7482]~E(x74821,f2(a919))+E(f857(f142(a919,a919,f79(a919),x74821),x74822),f2(a919))+P106(f857(f857(f328(a919),f675(x74822,x74821)),f857(f172(a919),x74822)))
% 15.02/14.80 [7533]~P106(f857(f857(f234(a1),x75331),f2(a1)))+P106(f857(f857(f234(a1),f857(f857(f35(a1),x75331),x75332)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x75332))
% 15.02/14.80 [7534]~P106(f857(f857(f235(a1),x75342),f2(a1)))+P106(f857(f857(f234(a1),f857(f857(f35(a1),x75341),x75342)),f2(a1)))+~P106(f857(f857(f234(a1),f2(a1)),x75341))
% 15.02/14.80 [7535]~P106(f857(f857(f235(a1),x75352),f2(a1)))+P106(f857(f857(f235(a1),f857(f857(f35(a1),x75351),x75352)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x75351))
% 15.02/14.80 [7537]~P106(f857(f857(f235(a1),x75371),f2(a1)))+P106(f857(f857(f235(a1),f857(f857(f35(a1),x75371),x75372)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x75372))
% 15.02/14.80 [7543]P106(f857(f857(f328(f927(x75431,a915)),f875(x75432,x75431)),x75432))+~P106(f857(f60(f927(x75431,a915)),x75432))+P106(f857(f60(x75431),f36(f927(x75431,a915),x75432)))
% 15.02/14.80 [7633]P26(x76331,x76331,x76332,f241(f927(x76331,a915)))+~E(f857(f309(x76331,x76331,x76332),f241(f927(x76331,a915))),f241(f927(x76331,a915)))+~P106(f857(f60(x76331),f241(f927(x76331,a915))))
% 15.02/14.80 [7753]~P26(x77531,x77531,x77532,f241(f927(x77531,a915)))+E(f857(f309(x77531,x77531,x77532),f241(f927(x77531,a915))),f241(f927(x77531,a915)))+~P106(f857(f60(x77531),f241(f927(x77531,a915))))
% 15.02/14.80 [7893]E(f857(f857(f35(a1),x78931),x78932),f857(f103(a1),a97))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x78931),x78932)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x78931))
% 15.02/14.80 [7949]~P106(f857(f857(f235(a1),x79492),f2(a1)))+~P106(f857(f857(f235(a1),f857(f857(f35(a1),x79491),x79492)),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x79491))
% 15.02/14.80 [7954]E(f857(f857(f79(a1),x79541),x79542),f44(a1,x79541,x79542))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),x79541),x79542)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x79541))
% 15.02/14.80 [7957]P106(f857(f857(f235(a1),x79571),f2(a1)))+~P106(f857(f857(f235(a1),f857(f857(f35(a1),x79571),x79572)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x79572))
% 15.02/14.80 [8649]~P109(x86491)+P14(x86491,x86492)+~P106(f857(f857(f234(x86491),f857(f857(f164(x86491),x86492),f709(x86492,x86491))),f857(f857(f164(x86491),x86492),f710(x86492,x86491))))
% 15.02/14.80 [8650]~P109(x86501)+P14(x86501,x86502)+~P106(f857(f857(f234(x86501),f857(f857(f164(x86501),x86502),f717(x86502,x86501))),f857(f857(f164(x86501),x86502),f722(x86502,x86501))))
% 15.02/14.80 [5883]E(x58831,f2(a1))+~E(f44(a1,x58832,x58831),f2(a1))+E(f857(f857(f35(a1),x58832),f857(f78(a1),x58831)),f857(f78(a1),f857(f857(f35(a1),x58832),x58831)))
% 15.02/14.80 [5901]~P42(x59012)+~P42(x59011)+P42(f857(f857(f110(f927(a1,a915)),x59011),x59012))
% 15.02/14.80 [5902]~P42(x59022)+~P42(x59021)+P42(f857(f857(f101(f927(a1,a915)),x59021),x59022))
% 15.02/14.80 [5920]~P65(x59201)+~P94(x59201)+E(f857(f78(x59201),f857(f857(f290(x59201),f77(x59201)),x59202)),f857(f857(f290(x59201),f857(f103(x59201),a97)),x59202))
% 15.02/14.80 [6038]E(x60381,f2(a1))+~E(f44(a1,x60382,x60381),f2(a1))+E(f857(f857(f35(a1),f857(f78(a1),x60382)),x60381),f857(f78(a1),f857(f857(f35(a1),x60382),x60381)))
% 15.02/14.80 [6179]~P109(x61791)+P14(x61791,x61792)+P106(f857(f857(f235(a919),f710(x61792,x61791)),f857(f190(f920(x61791)),x61792)))
% 15.02/14.80 [6180]~P109(x61801)+P14(x61801,x61802)+P106(f857(f857(f235(a919),f722(x61802,x61801)),f857(f190(f920(x61801)),x61802)))
% 15.02/14.80 [6344]~P94(x63441)+~E(f857(f103(x63441),x63442),f2(x63441))+P29(x63441,f857(f103(x63441),f857(f857(f79(a1),x63442),f857(f78(a1),a82))))
% 15.02/14.80 [6345]~P94(x63451)+~E(f857(f103(x63451),x63452),f2(x63451))+P29(x63451,f857(f103(x63451),f857(f857(f79(a1),a82),f857(f78(a1),x63452))))
% 15.02/14.80 [6347]E(f857(a50,f46(f857(f78(a1),x63471),f857(f78(a1),x63472))),f45(x63471,x63472))+P106(f857(f857(f234(a1),f2(a1)),x63471))+P106(f857(f857(f235(a1),f2(a1)),x63472))
% 15.02/14.80 [6474]~E(x64742,f2(a919))+~E(x64741,f2(a919))+P106(f857(f857(f234(a1),f857(f100(a1),x64741)),f857(f78(a1),f857(f100(a1),x64742))))
% 15.02/14.80 [6503]E(f857(f857(f79(a919),f857(f103(a919),x65031)),f857(f103(a919),x65032)),f857(f103(a919),f857(f857(f79(a1),x65031),x65032)))+P106(f857(f857(f235(a1),x65031),a82))+P106(f857(f857(f235(a1),x65032),a82))
% 15.02/14.80 [6636]~P78(x66361)+~P106(f857(f857(f234(x66361),f2(x66361)),x66362))+P106(f857(f857(f234(x66361),f857(f78(x66361),x66362)),x66362))
% 15.02/14.80 [6637]~P78(x66371)+~P106(f857(f857(f235(x66371),f2(x66371)),x66372))+P106(f857(f857(f235(x66371),f857(f78(x66371),x66372)),x66372))
% 15.02/14.80 [6814]E(f857(f857(f3(a919),f857(a104,x68141)),f857(a104,x68142)),f857(a104,f857(f857(f3(a1),x68141),x68142)))+~P106(f857(f857(f234(a1),f2(a1)),x68142))+~P106(f857(f857(f234(a1),x68142),x68141))
% 15.02/14.80 [6848]E(f857(a104,f44(a1,f857(f103(a1),x68481),f857(f103(a1),x68482))),f44(a919,f857(f103(a919),x68481),f857(f103(a919),x68482)))+P106(f857(a194,f857(f103(a1),x68481)))+P106(f857(a194,f857(f103(a1),x68482)))
% 15.02/14.80 [6865]~P78(x68651)+P106(f857(f857(f234(x68651),f2(x68651)),x68652))+~P106(f857(f857(f234(x68651),f857(f78(x68651),x68652)),x68652))
% 15.02/14.80 [6866]~P78(x68661)+P106(f857(f857(f235(x68661),f2(x68661)),x68662))+~P106(f857(f857(f235(x68661),f857(f78(x68661),x68662)),x68662))
% 15.02/14.80 [6878]~P78(x68781)+~P106(f857(f857(f234(x68781),f2(x68781)),x68782))+P106(f857(f857(f234(x68781),f2(x68781)),f857(f857(f79(x68781),x68782),x68782)))
% 15.02/14.80 [6880]~P78(x68801)+~P106(f857(f857(f235(x68801),f2(x68801)),x68802))+P106(f857(f857(f235(x68801),f2(x68801)),f857(f857(f79(x68801),x68802),x68802)))
% 15.02/14.80 [6892]E(f857(f857(f79(a919),f857(a104,x68921)),f857(a104,x68922)),f857(a104,f857(f857(f79(a1),x68921),x68922)))+~P106(f857(f857(f234(a1),f2(a1)),x68922))+~P106(f857(f857(f234(a1),f2(a1)),x68921))
% 15.02/14.80 [6903]E(x69031,f2(a919))+P106(f857(f857(f235(a919),f2(a919)),x69032))+~P106(f857(f857(f235(a919),f2(a919)),f857(f857(f243(a919),x69032),x69031)))
% 15.02/14.80 [6937]~P94(x69371)+E(f857(f103(x69371),x69372),f2(x69371))+~P29(x69371,f857(f103(x69371),f857(f857(f79(a1),a82),f857(f78(a1),x69372))))
% 15.02/14.80 [6938]~P94(x69381)+E(f857(f103(x69381),x69382),f2(x69381))+~P29(x69381,f857(f103(x69381),f857(f857(f79(a1),x69382),f857(f78(a1),a82))))
% 15.02/14.80 [6995]~P106(f857(f60(x69951),x69952))+~P106(f857(f60(x69951),f241(f927(x69951,a915))))+P106(f857(f60(x69951),f857(f78(f927(x69951,a915)),x69952)))
% 15.02/14.80 [7018]~P106(f857(f857(f235(a1),f2(a1)),x70182))+~P106(f857(f857(f234(a1),x70182),x70181))+P106(f857(f857(f235(a1),f2(a1)),f857(f857(f35(a1),x70181),x70182)))
% 15.02/14.80 [7019]~P106(f857(f857(f234(a1),x70191),f2(a1)))+~P106(f857(f857(f235(a1),x70192),f2(a1)))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f35(a1),x70191),x70192)))
% 15.02/14.80 [7057]~P106(f857(f857(f234(a1),f2(a1)),x70572))+~P106(f857(f857(f234(a1),f2(a1)),x70571))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f80(a1),x70571),x70572)))
% 15.02/14.80 [7058]~P106(f857(f857(f234(a1),f2(a1)),x70582))+~P106(f857(f857(f234(a1),f2(a1)),x70581))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),x70581),x70582)))
% 15.02/14.80 [7059]~P106(f857(f857(f234(a1),f2(a1)),x70592))+~P106(f857(f857(f234(a1),f2(a1)),x70591))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f35(a1),x70591),x70592)))
% 15.02/14.80 [7060]~P106(f857(f857(f234(a1),f2(a1)),x70601))+~P106(f857(f857(f235(a1),f2(a1)),x70602))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f35(a1),x70601),x70602)))
% 15.02/14.80 [7061]~P106(f857(f857(f235(a919),f2(a919)),x70612))+~P106(f857(f857(f235(a919),f2(a919)),x70611))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f80(a919),x70611),x70612)))
% 15.02/14.80 [7127]E(x71271,f2(a1))+E(f44(a1,x71272,x71271),f2(a1))+E(f857(f857(f3(a1),f857(f78(a1),f857(f857(f35(a1),x71272),x71271))),f77(a1)),f857(f857(f35(a1),f857(f78(a1),x71272)),x71271))
% 15.02/14.80 [7182]P106(f857(f857(f235(a919),f2(a919)),x71821))+P106(f857(f857(f235(a919),f2(a919)),x71822))+~P106(f857(f857(f235(a919),f2(a919)),f857(f857(f79(a919),x71822),x71821)))
% 15.02/14.80 [7186]~P78(x71861)+P106(f857(f857(f234(x71861),f2(x71861)),x71862))+~P106(f857(f857(f234(x71861),f2(x71861)),f857(f857(f79(x71861),x71862),x71862)))
% 15.02/14.80 [7187]~P78(x71871)+P106(f857(f857(f235(x71871),f2(x71871)),x71872))+~P106(f857(f857(f235(x71871),f2(x71871)),f857(f857(f79(x71871),x71872),x71872)))
% 15.02/14.80 [7238]~P106(f857(f60(x72381),x72382))+P106(f857(f60(x72381),f241(f927(x72381,a915))))+~P106(f857(f60(x72381),f857(f78(f927(x72381,a915)),x72382)))
% 15.02/14.80 [7303]P106(f857(f857(f234(a1),x73031),f2(a1)))+~P106(f857(f857(f235(a1),x73032),f2(a1)))+~P106(f857(f857(f234(a1),f2(a1)),f857(f857(f35(a1),x73031),x73032)))
% 15.02/14.80 [7309]~P106(f857(f857(f235(a1),f2(a1)),x73091))+P106(f857(f857(f234(a1),x73091),x73092))+~P106(f857(f857(f235(a1),f2(a1)),f857(f857(f35(a1),x73092),x73091)))
% 15.02/14.80 [7310]~P106(f857(f857(f234(a1),f2(a1)),x73102))+P106(f857(f857(f234(a1),x73101),x73102))+~P106(f857(f857(f235(a1),f2(a1)),f857(f857(f35(a1),x73102),x73101)))
% 15.02/14.80 [7340]P106(f857(f857(f234(a1),f2(a1)),x73401))+~P106(f857(f857(f235(a1),f2(a1)),x73402))+~P106(f857(f857(f234(a1),f2(a1)),f857(f857(f35(a1),x73401),x73402)))
% 15.02/14.80 [7341]P106(f857(f857(f235(a1),f2(a1)),x73411))+~P106(f857(f857(f234(a1),f2(a1)),x73412))+~P106(f857(f857(f235(a1),f2(a1)),f857(f857(f35(a1),x73412),x73411)))
% 15.02/14.80 [7784]~P106(f857(f60(x77842),f241(f927(x77842,a915))))+~P106(f857(f60(x77841),f241(f927(x77841,a915))))+P106(f857(f60(f925(x77841,x77842)),f241(f927(f925(x77841,x77842),a915))))
% 15.02/14.80 [7785]~P106(f857(f60(x77852),f241(f927(x77852,a915))))+~P106(f857(f60(x77851),f241(f927(x77851,a915))))+P106(f857(f60(f926(x77851,x77852)),f241(f927(f926(x77851,x77852),a915))))
% 15.02/14.80 [7857]~P106(f857(f857(f235(a919),f857(a112,f2(a919))),x78571))+~P106(f857(f857(f235(a919),f857(a112,f2(a919))),x78572))+P106(f857(f857(f235(a919),x78571),f857(f857(f80(a919),x78572),x78571)))
% 15.02/14.80 [7858]~P106(f857(f857(f235(a919),f857(a112,f2(a919))),x78581))+~P106(f857(f857(f235(a919),f857(a112,f2(a919))),x78582))+P106(f857(f857(f235(a919),x78581),f857(f857(f80(a919),x78581),x78582)))
% 15.02/14.80 [7892]E(f857(f34(x78921),f241(f927(x78921,a915))),f857(a112,f2(a919)))+P106(f857(f60(x78922),f241(f927(x78922,a915))))+~P106(f857(f60(f927(x78922,x78921)),f241(f927(f927(x78922,x78921),a915))))
% 15.02/14.80 [8017]~P106(f857(f857(f234(a919),f857(a112,f2(a919))),x80171))+~P106(f857(f857(f234(a919),f857(a112,f2(a919))),x80172))+P106(f857(f857(f234(a919),f857(a112,f2(a919))),f857(f857(f80(a919),x80171),x80172)))
% 15.02/14.80 [8018]~P106(f857(f857(f235(a919),f857(a112,f2(a919))),x80182))+~P106(f857(f857(f235(a919),f857(a112,f2(a919))),x80181))+P106(f857(f857(f235(a919),f857(a112,f2(a919))),f857(f857(f80(a919),x80181),x80182)))
% 15.02/14.80 [8696]E(x86961,f113(x86962))+~P106(f857(f137(x86962),x86961))+E(f177(x86962,f857(f857(f10(a915,a915,x86962),a321),f857(f857(f9(x86962,x86962,a915),a324),f144(x86962,x86961))),x86961),f114(x86962,x86961))
% 15.02/14.80 [8791]~P42(x87912)+~P42(x87911)+E(f857(f309(a919,a1,f100(a1)),f857(f857(f110(f927(a919,a915)),f857(f309(a1,a919,a104),x87911)),f857(f309(a1,a919,a104),x87912))),f857(f857(f110(f927(a1,a915)),x87911),x87912))
% 15.02/14.80 [8792]~P42(x87922)+~P42(x87921)+E(f857(f309(a919,a1,f100(a1)),f857(f857(f101(f927(a919,a915)),f857(f309(a1,a919,a104),x87921)),f857(f309(a1,a919,a104),x87922))),f857(f857(f101(f927(a1,a915)),x87921),x87922))
% 15.02/14.80 [9456]~P94(x94561)+~E(f857(f103(x94561),x94562),f77(x94561))+P29(x94561,f857(f103(x94561),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f78(a1),x94562))))
% 15.02/14.80 [9707]~P94(x97071)+E(f857(f103(x97071),x97072),f77(x97071))+~P29(x97071,f857(f103(x97071),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f78(a1),x97072))))
% 15.02/14.80 [10469]E(x104691,f2(a1))+E(x104692,f2(a1))+E(f857(f257(a1,a1,a1,a1,f31(a1),f857(f80(a1),f81(a1,x104692))),f857(f857(f857(f96(f926(a1,a1)),f857(f857(a324,f81(a1,x104691)),f81(a1,x104692))),f52(x104691,x104692)),f857(f857(f256(a1,a1,f926(a1,a1)),f857(f857(f20(a1,f927(a1,f926(a1,a1)),f927(a1,f926(a1,a1))),f857(f857(f10(f927(a1,f927(f926(a1,a1),f926(a1,a1))),f927(f927(a1,f926(a1,a1)),f927(a1,f926(a1,a1))),a1),f20(a1,f926(a1,a1),f926(a1,a1))),f857(f857(f10(f926(a1,a1),f927(a1,f927(f926(a1,a1),f926(a1,a1))),a1),f857(f9(a1,f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),f857(f857(f10(a915,f927(f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),a1),f96(f926(a1,a1))),f857(f857(f9(a1,a1,a915),a324),f2(a1))))),f857(f857(f9(a1,a1,f926(a1,a1)),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f78(a1))),f2(a1))))),f857(f857(f9(a1,f927(a1,a1),f927(a1,f926(a1,a1))),f857(f857(f10(f927(a1,f926(a1,a1)),f927(f927(a1,a1),f927(a1,f926(a1,a1))),a1),f10(a1,f926(a1,a1),a1)),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f857(f857(f9(a1,a1,a1),f857(f857(f10(a1,f927(a1,a1),a1),f3(a1)),f78(a1))),f77(a1))))),f857(f3(a1),f857(f75(a1),x104692))))),f52(x104691,x104692)))),f45(x104691,x104692))
% 15.02/14.80 [10470]E(x104701,f2(a1))+E(x104702,f2(a1))+E(f857(f257(a1,a1,a1,a1,f31(a1),f857(f80(a1),f81(a1,x104702))),f857(f857(f857(f96(f926(a1,a1)),f857(f857(a326,f857(f857(a325,f857(f857(f235(a1),f2(a1)),x104702)),f857(f857(f234(a1),f2(a1)),x104701))),f857(f857(a325,f857(f857(f235(a1),x104702),f2(a1))),f857(f857(f235(a1),x104701),f2(a1))))),f52(x104701,x104702)),f857(f857(f256(a1,a1,f926(a1,a1)),f857(f857(f20(a1,f927(a1,f926(a1,a1)),f927(a1,f926(a1,a1))),f857(f857(f10(f927(a1,f927(f926(a1,a1),f926(a1,a1))),f927(f927(a1,f926(a1,a1)),f927(a1,f926(a1,a1))),a1),f20(a1,f926(a1,a1),f926(a1,a1))),f857(f857(f10(f926(a1,a1),f927(a1,f927(f926(a1,a1),f926(a1,a1))),a1),f857(f9(a1,f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),f857(f857(f10(a915,f927(f926(a1,a1),f927(f926(a1,a1),f926(a1,a1))),a1),f96(f926(a1,a1))),f857(f857(f9(a1,a1,a915),a324),f2(a1))))),f857(f857(f9(a1,a1,f926(a1,a1)),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f78(a1))),f2(a1))))),f857(f857(f9(a1,f927(a1,a1),f927(a1,f926(a1,a1))),f857(f857(f10(f927(a1,f926(a1,a1)),f927(f927(a1,a1),f927(a1,f926(a1,a1))),a1),f10(a1,f926(a1,a1),a1)),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f857(f857(f9(a1,a1,a1),f857(f857(f10(a1,f927(a1,a1),a1),f3(a1)),f78(a1))),f77(a1))))),f857(f3(a1),f857(f75(a1),x104702))))),f52(x104701,x104702)))),f45(x104701,x104702))
% 15.02/14.80 [5909]~P120(x59091)+~P94(x59091)+E(f857(f75(x59091),f857(f857(f243(x59091),f857(f103(x59091),a97)),x59092)),f77(x59091))
% 15.02/14.80 [6415]~P143(x64151)+~P106(f857(f857(f235(a1),x64152),f2(a1)))+E(f857(f78(x64151),f857(f100(x64151),f857(a104,f857(f78(a1),x64152)))),f857(f102(x64151),x64152))
% 15.02/14.80 [6620]P106(f857(f857(f234(a99),x66201),f77(a99)))+E(f857(f857(f79(a99),f77(a99)),f271(x66201,f857(f857(f35(a99),x66202),x66201))),f271(x66201,x66202))+P106(f857(f857(f235(a99),x66202),x66201))
% 15.02/14.80 [7226]~P93(x72261)+~P106(f857(f857(f328(x72261),x72262),f109(x72261)))+~E(f857(f857(f79(x72261),f857(f857(f79(x72261),f77(x72261)),x72262)),x72262),f2(x72261))
% 15.02/14.80 [7342]~P106(f857(f857(f234(a1),x73422),f2(a1)))+~P106(f857(f857(f235(a1),x73421),f2(a1)))+E(f857(f250(a1,a1),f857(a50,f46(f857(f78(a1),x73421),f857(f78(a1),x73422)))),f857(f857(f35(a1),x73421),x73422))
% 15.02/14.80 [7359]~P106(f857(f857(f234(a1),x73592),f2(a1)))+~P106(f857(f857(f235(a1),x73591),f2(a1)))+E(f857(f255(a1,a1),f857(a50,f46(f857(f78(a1),x73591),f857(f78(a1),x73592)))),f44(a1,x73591,x73592))
% 15.02/14.80 [7367]~P106(f857(f857(f235(a1),x73672),f2(a1)))+E(f857(f250(a1,a1),f857(a50,f49(f857(f78(a1),x73671),f857(f78(a1),x73672)))),f857(f857(f35(a1),x73671),x73672))+~P106(f857(f857(f235(a1),f2(a1)),x73671))
% 15.02/14.80 [7385]~P106(f857(f857(f235(a1),x73852),f2(a1)))+E(f857(f255(a1,a1),f857(a50,f49(f857(f78(a1),x73851),f857(f78(a1),x73852)))),f44(a1,x73851,x73852))+~P106(f857(f857(f235(a1),f2(a1)),x73851))
% 15.02/14.80 [7438]E(f857(f857(f35(a1),f857(f857(f243(a1),x74381),x74382)),x74381),f857(f857(f243(a1),x74381),f857(f857(f3(a919),x74382),f857(a112,f2(a919)))))+~P106(f857(f857(f235(a919),f2(a919)),x74382))+~P106(f857(f857(f235(a1),f2(a1)),x74381))
% 15.02/14.80 [7540]~P106(f857(f857(f235(a919),f2(a919)),x75401))+~P106(f857(f857(f235(a919),f2(a919)),x75402))+P106(f857(f857(f235(a919),f857(f857(f3(a919),x75401),x75402)),x75401))
% 15.02/14.80 [7541]~P106(f857(f857(f235(a919),f2(a919)),x75411))+~P106(f857(f857(f235(a919),f77(a919)),x75412))+P106(f857(f857(f235(a919),f857(f857(f35(a919),x75411),x75412)),x75411))
% 15.02/14.80 [7542]~P106(f857(f857(f235(a1),f2(a1)),x75421))+~P106(f857(f857(f235(a1),f77(a1)),x75422))+P106(f857(f857(f235(a1),f857(f857(f35(a1),x75421),x75422)),x75421))
% 15.02/14.80 [7679]E(x76791,f2(a919))+~E(x76792,f2(a1))+~P106(f857(f857(f235(a1),f2(a1)),f857(f857(f243(a1),f857(f75(a1),x76792)),x76791)))
% 15.02/14.80 [8096]~E(x80962,f113(f920(x80961)))+E(f857(f190(f920(f920(x80961))),f179(x80961,x80962)),f2(a919))+~P14(a919,f857(f168(a919),f857(f857(f154(f920(x80961),a919),f190(f920(x80961))),x80962)))
% 15.02/14.80 [8349]P106(f857(x83491,x83492))+~P106(f857(x83491,f857(a106,f548(x83491,x83492))))+~P106(f857(f857(f328(f927(f926(a919,a919),a915)),x83492),a98))
% 15.02/14.80 [8365]E(x83651,f113(f920(x83652)))+E(f857(f190(f920(x83652)),f857(f857(f164(f920(x83652)),x83651),f2(a919))),f857(f190(f920(f920(x83652))),f179(x83652,x83651)))+~P14(a919,f857(f168(a919),f857(f857(f154(f920(x83652),a919),f190(f920(x83652))),x83651)))
% 15.02/14.80 [8505]~P40(x85051,x85052)+~P41(x85051,x85052)+P40(x85051,f857(f857(f3(f927(f926(x85051,x85051),a915)),x85052),f306(x85051,f189(f927(f926(x85051,x85051),a915)))))
% 15.02/14.80 [9076]~P106(f857(f60(x90761),f857(f261(x90761),x90762)))+~P106(f857(f60(x90761),f241(f927(x90761,a915))))+P106(f857(f60(x90761),f857(f261(x90761),f857(f857(f10(a915,a915,x90761),a321),x90762))))
% 15.02/14.80 [9140]E(f857(f857(f251(a919,a919),f857(a112,f857(f857(f35(a919),f857(f857(f3(a919),x91401),x91402)),x91402))),f44(a919,f857(f857(f3(a919),x91401),x91402),x91402)),f84(f926(a919,a919),f47(x91401,x91402)))+~P106(f857(f857(f235(a919),f2(a919)),x91402))+~P106(f857(f857(f234(a919),x91402),x91401))
% 15.02/14.80 [9422]~P106(f857(f60(x94221),f857(f261(x94221),x94222)))+P106(f857(f60(x94221),f241(f927(x94221,a915))))+~P106(f857(f60(x94221),f857(f261(x94221),f857(f857(f10(a915,a915,x94221),a321),x94222))))
% 15.02/14.80 [10148]P28(x101481,x101482)+~P39(x101481,f857(f250(f927(f926(x101481,x101481),a915),f927(f926(x101481,x101481),a915)),x101482))+~P106(f857(f857(f234(f927(f926(x101481,x101481),a915)),f857(f857(f288(x101481,x101481,x101481),f857(f250(f927(f926(x101481,x101481),a915),f927(f926(x101481,x101481),a915)),x101482)),f857(f255(f927(f926(x101481,x101481),a915),f927(f926(x101481,x101481),a915)),x101482))),f857(f250(f927(f926(x101481,x101481),a915),f927(f926(x101481,x101481),a915)),x101482)))
% 15.02/14.80 [10244]~E(f299(a919,f286(a919),f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x102442,x102441),f189(f927(a919,a915)))+~P106(f857(f857(f286(a919),x102442),x102441))+P106(f857(f857(f286(a919),x102441),x102442))
% 15.02/14.80 [10245]~E(f296(a919,f286(a919),f857(f857(f20(a919,f927(a919,a915),f927(a919,a915)),f857(f857(f10(f927(a919,f927(a915,a915)),f927(f927(a919,a915),f927(a919,a915)),a919),f20(a919,a915,a915)),f857(f857(f10(f927(a919,a915),f927(a919,f927(a915,a915)),a919),f857(f10(a915,f927(a915,a915),a919),a325)),f286(a919)))),f857(f857(f10(f927(a919,a915),f927(a919,a915),a919),f857(f10(a915,a915,a919),a321)),f857(f9(a919,a919,a915),f286(a919)))),x102452,x102451),f189(f927(a919,a915)))+~P106(f857(f857(f286(a919),x102452),x102451))+P106(f857(f857(f286(a919),x102451),x102452))
% 15.02/14.80 [7468]~P106(f857(f857(f235(a919),f2(a919)),x74682))+P106(f857(f857(f235(a919),x74681),x74682))+E(f857(a112,f857(f857(f35(a919),f857(f857(f3(a919),x74681),x74682)),x74682)),f857(f857(f35(a919),x74681),x74682))
% 15.02/14.80 [7605]~P106(f857(f857(f235(a919),f2(a919)),x76052))+~P106(f857(f857(f234(a919),x76052),x76051))+E(f857(a112,f857(f857(f35(a919),f857(f857(f3(a919),x76051),x76052)),x76052)),f857(f857(f35(a919),x76051),x76052))
% 15.02/14.80 [8568]~P94(x85681)+~P93(x85681)+~P29(x85681,f857(f103(x85681),f857(f857(f3(a1),f857(f857(f79(a1),x85682),x85682)),a97)))
% 15.02/14.80 [9329]E(x93291,f2(a919))+E(f857(f857(f256(a919,a919,f926(a919,a919)),f857(f857(f10(a919,f927(a919,f926(a919,a919)),a919),f251(a919,a919)),a112)),f84(f926(a919,a919),f47(f857(f857(f3(a919),x93292),x93291),x93291))),f84(f926(a919,a919),f47(x93292,x93291)))+P106(f857(f857(f235(a919),x93292),x93291))
% 15.02/14.80 [9510]~P40(x95101,x95102)+~P53(x95101,x95102)+P106(f857(f857(f234(f927(f926(x95101,x95101),a915)),f857(f857(f288(x95101,x95101,x95101),f857(f285(x95101,x95101),x95102)),x95102)),x95102))
% 15.02/14.80 [9771]P106(f857(x97712,f642(x97712,x97711)))+P106(f857(x97711,f642(x97712,x97711)))+E(f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x97711)),f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x97712)))
% 15.02/14.80 [9775]~P106(f857(x97752,f642(x97752,x97751)))+~P106(f857(x97751,f642(x97752,x97751)))+E(f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x97751)),f857(f261(a1),f857(f857(f20(a1,a915,a915),f857(f857(f10(a915,f927(a915,a915),a1),a325),f857(f234(a1),f2(a1)))),x97752)))
% 15.02/14.80 [7815]~P66(x78151)+~P94(x78151)+E(f857(f857(f290(x78151),x78152),f857(f103(x78151),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))),x78152)
% 15.02/14.80 [9455]~P94(x94551)+~E(f857(f103(x94551),x94552),f77(x94551))+P29(x94551,f857(f103(x94551),f857(f857(f79(a1),x94552),f857(f78(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.80 [9642]~P144(x96421)+~E(x96422,f77(x96421))+E(f857(f857(f243(x96421),x96422),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f77(x96421))
% 15.02/14.80 [9643]~P144(x96431)+~E(x96432,f2(x96431))+E(f857(f857(f243(x96431),x96432),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f2(x96431))
% 15.02/14.80 [9658]~P144(x96581)+~E(x96582,f857(f78(x96581),f77(x96581)))+E(f857(f857(f243(x96581),x96582),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f77(x96581))
% 15.02/14.80 [9708]~P94(x97081)+E(f857(f103(x97081),x97082),f77(x97081))+~P29(x97081,f857(f103(x97081),f857(f857(f79(a1),x97082),f857(f78(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.80 [10090]~P120(x100902)+E(x100901,f2(x100902))+P106(f857(f857(f235(x100902),f2(x100902)),f857(f857(f243(x100902),x100901),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.80 [10147]~P120(x101472)+~E(x101471,f2(x101472))+~P106(f857(f857(f235(x101472),f2(x101472)),f857(f857(f243(x101472),x101471),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.80 [10183]P106(f857(f857(f234(a1),x101831),f2(a1)))+P106(f857(f857(f235(a1),x101832),x101831))+E(f857(f42(x101831),f46(x101832,f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101831))),f46(x101832,x101831))
% 15.02/14.80 [10184]~P106(f857(f857(f235(a1),f2(a1)),x101841))+P106(f857(f857(f235(a1),x101842),x101841))+E(f857(f42(x101841),f46(x101842,f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101841))),f46(x101842,x101841))
% 15.02/14.80 [10185]P106(f857(f857(f234(a1),x101851),f2(a1)))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),x101852),x101851)))+E(f857(f42(x101851),f49(x101852,f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101851))),f49(x101852,x101851))
% 15.02/14.80 [10186]~P106(f857(f857(f235(a1),f2(a1)),x101861))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),x101862),x101861)))+E(f857(f42(x101861),f49(x101862,f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101861))),f49(x101862,x101861))
% 15.02/14.80 [10187]~P146(x101871)+~P106(f857(f857(f234(a1),f2(a1)),x101872))+E(f857(f100(x101871),f857(a104,f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x101872))),f857(f857(f79(x101871),f857(f100(x101871),f857(a104,x101872))),f857(f100(x101871),f857(a104,x101872))))
% 15.02/14.80 [5239]~P148(x52391,x52393,x52392)+~E(x52393,f2(a1))+P106(f857(x52391,x52392))
% 15.02/14.80 [5363]~P109(x53631)+~P14(x53631,x53633)+P14(x53631,f170(x53631,x53632,x53633))
% 15.02/14.80 [5364]~P109(x53641)+~P14(x53641,x53643)+P14(x53641,f177(x53641,x53642,x53643))
% 15.02/14.80 [4932]~P76(x49322)+~E(x49323,f857(f78(x49322),x49321))+E(x49321,f857(f78(x49322),x49323))
% 15.02/14.80 [4934]~P76(x49341)+~E(f857(f78(x49341),x49343),x49342)+E(f857(f78(x49341),x49342),x49343)
% 15.02/14.80 [5013]~P103(x50133)+E(x50131,x50132)+~E(f857(f100(x50133),x50131),f857(f100(x50133),x50132))
% 15.02/14.80 [5014]~P76(x50143)+E(x50141,x50142)+~E(f857(f78(x50143),x50141),f857(f78(x50143),x50142))
% 15.02/14.80 [5015]~P96(x50153)+E(x50151,x50152)+~E(f857(f78(x50153),x50151),f857(f78(x50153),x50152))
% 15.02/14.80 [5016]~P93(x50163)+E(x50161,x50162)+~E(f857(f102(x50163),x50161),f857(f102(x50163),x50162))
% 15.02/14.80 [5017]~P109(x50173)+E(x50171,x50172)+~E(f857(f281(x50173),x50171),f857(f281(x50173),x50172))
% 15.02/14.80 [5018]~P109(x50183)+E(x50181,x50182)+~E(f857(f300(x50183),x50181),f857(f300(x50183),x50182))
% 15.02/14.80 [5019]~P109(x50193)+E(x50191,x50192)+~E(f857(f282(x50193),x50191),f857(f282(x50193),x50192))
% 15.02/14.80 [5020]~P109(x50203)+E(x50201,x50202)+~E(f857(f303(x50203),x50201),f857(f303(x50203),x50202))
% 15.02/14.80 [5122]~P64(x51221)+~P106(f857(x51222,x51223))+P106(f857(f55(x51221),x51222))
% 15.02/14.80 [5158]~P64(x51583)+P106(f857(x51581,x51582))+~P106(f857(f56(x51583),x51581))
% 15.02/14.80 [5259]~P149(x52591,x52592,x52593)+~E(x52592,f2(a1))+P106(f857(x52591,f2(a1)))
% 15.02/14.80 [5298]~E(x52981,f2(a919))+E(f858(x52981,x52982,x52983),f189(f927(x52983,a915)))+~E(f857(f34(x52983),x52982),f857(a112,x52981))
% 15.02/14.80 [5447]~E(x54472,f2(a919))+E(f857(f250(a919,a919),x54471),f2(a919))+~P106(f857(f47(x54473,x54472),x54471))
% 15.02/14.80 [5491]P106(f857(x54911,x54912))+~E(x54913,f857(f100(a1),x54912))+~P106(f857(x54911,f857(a104,x54913)))
% 15.02/14.80 [5973]~E(x59733,f2(a919))+~P106(f857(x59731,x59732))+P106(f857(x59731,f44(a919,x59732,x59733)))
% 15.02/14.80 [6208]~P104(x62082)+~P104(x62081)+E(f131(x62081,x62082,f132(x62081,x62083),f132(x62082,x62083)),f132(f926(x62081,x62082),x62083))
% 15.02/14.80 [6397]~E(x63973,f2(a919))+P106(f857(x63971,x63972))+~P106(f857(x63971,f44(a919,x63972,x63973)))
% 15.02/14.80 [7082]E(x70821,f2(a919))+~P106(f857(x70822,f364(x70821,x70823,x70822)))+P106(f857(x70822,f44(a919,x70823,x70821)))
% 15.02/14.80 [7192]~P6(x71921)+~P106(f857(f857(f234(x71921),x71922),f381(x71923,x71922,x71921)))+P106(f857(f857(f234(x71921),x71922),f37(x71921,x71923)))
% 15.02/14.80 [7194]~P106(f857(x71941,x71942))+~P106(f857(x71941,f364(x71943,x71942,x71941)))+P106(f857(x71941,f44(a919,x71942,x71943)))
% 15.02/14.80 [7297]E(x72971,f113(x72972))+E(f857(f857(f151(x72972),f690(x72973,x72971,x72972)),f693(x72973,x72971,x72972)),x72971)+~P106(f857(f857(f328(f920(x72972)),x72971),f161(x72972,x72973)))
% 15.02/14.80 [7329]~P143(x73291)+~P106(f857(f857(f328(x73291),x73292),f109(x73291)))+P106(f857(f857(f328(x73291),f857(f857(f243(x73291),x73292),x73293)),f109(x73291)))
% 15.02/14.80 [7651]P39(x76511,x76512)+~P106(f857(f857(f328(x76511),x76513),f617(x76512,x76511)))+P106(f857(f857(f328(x76511),f640(x76512,x76511,x76513)),f617(x76512,x76511)))
% 15.02/14.80 [7919]E(x79191,f113(x79192))+~P106(f857(f857(f328(f920(x79192)),x79191),f161(x79192,x79193)))+P106(f857(f857(f328(f920(x79192)),f693(x79193,x79191,x79192)),f161(x79192,x79193)))
% 15.02/14.80 [7971]E(x79711,f2(a919))+E(f857(f857(f79(a919),f857(f857(f80(a919),x79711),f365(x79711,x79712,x79713))),f364(x79711,x79712,x79713)),x79712)+P106(f857(x79713,f44(a919,x79712,x79711)))
% 15.02/14.80 [8012]~P106(f857(x80123,x80122))+E(f857(f857(f79(a919),f857(f857(f80(a919),x80121),f365(x80121,x80122,x80123))),f364(x80121,x80122,x80123)),x80122)+P106(f857(x80123,f44(a919,x80122,x80121)))
% 15.02/14.80 [8152]P106(f857(f857(f235(a1),x81521),f372(x81522,x81523,x81521)))+P106(f857(f857(x81523,f857(f857(f35(a1),x81522),x81521)),f44(a1,x81522,x81521)))+~P106(f857(f857(f235(a1),x81521),f2(a1)))
% 15.02/14.80 [8420]P106(f857(f857(x84202,f857(f857(f35(a1),x84201),x84203)),f44(a1,x84201,x84203)))+~P106(f857(f857(f235(a1),x84203),f2(a1)))+P106(f857(f857(f234(a1),f372(x84201,x84202,x84203)),f2(a1)))
% 15.02/14.80 [8602]E(f857(f857(f79(a1),f857(f857(f80(a1),x86021),f375(x86022,x86023,x86021))),f372(x86022,x86023,x86021)),x86022)+P106(f857(f857(x86023,f857(f857(f35(a1),x86022),x86021)),f44(a1,x86022,x86021)))+~P106(f857(f857(f235(a1),x86021),f2(a1)))
% 15.02/14.80 [8839]~P106(f857(f857(x88391,f375(x88392,x88391,x88393)),f372(x88392,x88391,x88393)))+P106(f857(f857(x88391,f857(f857(f35(a1),x88392),x88393)),f44(a1,x88392,x88393)))+~P106(f857(f857(f235(a1),x88393),f2(a1)))
% 15.02/14.80 [9089]~P109(x90891)+~P14(x90891,x90893)+P14(x90891,f149(x90891,x90891,f7(x90891),x90892,x90893))
% 15.02/14.80 [9587]~P129(x95872)+E(x95871,f2(x95872))+~P106(f857(f857(f234(x95872),f857(f857(f79(x95872),f857(f857(f80(x95872),x95873),x95873)),f857(f857(f80(x95872),x95871),x95871))),f2(x95872)))
% 15.02/14.80 [9588]~P129(x95882)+E(x95881,f2(x95882))+~P106(f857(f857(f234(x95882),f857(f857(f79(x95882),f857(f857(f80(x95882),x95881),x95881)),f857(f857(f80(x95882),x95883),x95883))),f2(x95882)))
% 15.02/14.80 [10401]~P120(x104011)+~P106(f857(f857(f235(x104011),x104012),f2(x104011)))+P106(f857(f857(f235(x104011),f857(f857(f243(x104011),x104012),f857(a112,f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x104013)))),f2(x104011)))
% 15.02/14.80 [10411]~P120(x104112)+E(x104111,f2(x104112))+~P106(f857(f857(f234(x104112),f857(f857(f79(x104112),f857(f857(f243(x104112),x104113),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x104112),x104111),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f2(x104112)))
% 15.02/14.80 [10412]~P120(x104122)+E(x104121,f2(x104122))+~P106(f857(f857(f234(x104122),f857(f857(f79(x104122),f857(f857(f243(x104122),x104121),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x104122),x104123),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f2(x104122)))
% 15.02/14.80 [4968]~E(x49682,x49683)+~P69(x49681)+E(f857(f857(f3(x49681),x49682),x49683),f2(x49681))
% 15.02/14.80 [4969]~E(x49692,x49693)+~P76(x49691)+E(f857(f857(f3(x49691),x49692),x49693),f2(x49691))
% 15.02/14.80 [4982]~P140(x49821)+~E(x49823,f2(x49821))+E(f857(f857(f79(x49821),x49822),x49823),x49822)
% 15.02/14.80 [4999]~P142(x49991)+~E(x49993,f2(x49991))+E(f857(f857(f80(x49991),x49992),x49993),f2(x49991))
% 15.02/14.80 [5000]~P142(x50001)+~E(x50002,f2(x50001))+E(f857(f857(f80(x50001),x50002),x50003),f2(x50001))
% 15.02/14.80 [5022]~E(x50223,f113(x50221))+~E(x50222,f113(x50221))+E(f857(f857(f134(x50221),x50222),x50223),f113(x50221))
% 15.02/14.80 [5112]~P140(x51122)+E(x51121,f2(x51122))+~E(f857(f857(f79(x51122),x51123),x51121),x51123)
% 15.02/14.80 [5113]~P76(x51131)+~E(x51132,f857(f78(x51131),x51133))+E(f857(f857(f79(x51131),x51132),x51133),f2(x51131))
% 15.02/14.80 [5120]E(x51201,f113(x51202))+E(x51203,f2(a919))+~E(f857(f857(f175(x51202),x51203),x51201),f113(x51202))
% 15.02/14.80 [5126]~P69(x51263)+E(x51261,x51262)+~E(f857(f857(f3(x51263),x51261),x51262),f2(x51263))
% 15.02/14.80 [5127]~P76(x51273)+E(x51271,x51272)+~E(f857(f857(f3(x51273),x51271),x51272),f2(x51273))
% 15.02/14.80 [5140]~P144(x51402)+E(x51401,f2(x51402))+~E(f857(f857(f243(x51402),x51401),x51403),f2(x51402))
% 15.02/14.80 [5141]~P3(x51412)+E(x51411,f189(x51412))+~E(f857(f857(f110(x51412),x51413),x51411),f189(x51412))
% 15.02/14.80 [5142]~P3(x51422)+E(x51421,f189(x51422))+~E(f857(f857(f110(x51422),x51421),x51423),f189(x51422))
% 15.02/14.80 [5143]~P100(x51432)+E(x51431,f241(x51432))+~E(f857(f857(f101(x51432),x51433),x51431),f241(x51432))
% 15.02/14.80 [5144]~P100(x51442)+E(x51441,f241(x51442))+~E(f857(f857(f101(x51442),x51441),x51443),f241(x51442))
% 15.02/14.80 [5213]~P76(x52132)+E(x52131,f857(f78(x52132),x52133))+~E(f857(f857(f79(x52132),x52131),x52133),f2(x52132))
% 15.02/14.80 [5214]~P76(x52141)+E(f857(f78(x52141),x52142),x52143)+~E(f857(f857(f79(x52141),x52142),x52143),f2(x52141))
% 15.02/14.80 [5216]~E(x52162,x52163)+~P107(x52161)+P106(f857(f857(f234(x52161),x52162),x52163))
% 15.02/14.80 [5218]~E(x52182,x52183)+~P110(x52181)+P106(f857(f857(f234(x52181),x52182),x52183))
% 15.02/14.80 [5316]~P122(x53161)+~E(x53162,f857(f78(x53161),x53163))+E(f857(f857(f80(x53161),x53162),x53162),f857(f857(f80(x53161),x53163),x53163))
% 15.02/14.80 [5324]~P109(x53241)+~P14(x53241,x53243)+P14(x53241,f857(f857(f175(x53241),x53242),x53243))
% 15.02/14.80 [5325]~P109(x53251)+~P14(x53251,x53253)+P14(x53251,f857(f857(f138(x53251),x53252),x53253))
% 15.02/14.80 [5361]E(x53611,x53612)+E(x53613,f2(a919))+~E(f857(f857(f80(a919),x53613),x53611),f857(f857(f80(a919),x53613),x53612))
% 15.02/14.80 [5362]E(x53621,x53622)+E(x53623,f2(a919))+~E(f857(f857(f80(a919),x53621),x53623),f857(f857(f80(a919),x53622),x53623))
% 15.02/14.80 [5440]~E(x54402,x54403)+~P110(x54401)+E(f302(x54401,x54402,x54403),f857(f857(f308(x54401),x54402),f189(f927(x54401,a915))))
% 15.02/14.80 [5481]~P120(x54811)+~E(f857(f75(x54811),x54812),f857(f75(x54811),x54813))+P106(f857(f857(f286(x54811),x54812),x54813))
% 15.02/14.80 [5489]~E(x54891,x54892)+~P109(x54893)+~P106(f857(f857(f235(x54893),x54891),x54892))
% 15.02/14.80 [5490]~E(x54901,x54902)+~P110(x54903)+~P106(f857(f857(f235(x54903),x54901),x54902))
% 15.02/14.80 [5502]~P110(x55021)+E(f857(f301(x55021,x55022),x55023),f189(f927(x55021,a915)))+P106(f857(f857(f235(x55021),x55022),x55023))
% 15.02/14.80 [5550]~P110(x55501)+E(f302(x55501,x55502,x55503),f189(f927(x55501,a915)))+P106(f857(f857(f234(x55501),x55502),x55503))
% 15.02/14.80 [5551]~P110(x55511)+E(f304(x55511,x55512,x55513),f189(f927(x55511,a915)))+P106(f857(f857(f235(x55511),x55512),x55513))
% 15.02/14.80 [5552]~P110(x55521)+E(f189(f927(x55521,a915)),f302(x55521,x55522,x55523))+P106(f857(f857(f234(x55521),x55522),x55523))
% 15.02/14.80 [5553]~P110(x55531)+E(f189(f927(x55531,a915)),f304(x55531,x55532,x55533))+P106(f857(f857(f235(x55531),x55532),x55533))
% 15.02/14.80 [5561]~P101(x55611)+~E(f857(f857(f110(x55611),x55612),x55613),x55613)+P106(f857(f857(f234(x55611),x55612),x55613))
% 15.02/14.80 [5562]~P102(x55621)+~E(f857(f857(f101(x55621),x55622),x55623),x55622)+P106(f857(f857(f234(x55621),x55622),x55623))
% 15.02/14.80 [5563]~P109(x55631)+~E(f857(f857(f188(x55631),x55632),x55633),x55632)+P106(f857(f857(f234(x55631),x55632),x55633))
% 15.02/14.80 [5564]~P109(x55641)+~E(f857(f857(f233(x55641),x55642),x55643),x55643)+P106(f857(f857(f234(x55641),x55642),x55643))
% 15.02/14.80 [5583]~P109(x55831)+P14(x55831,x55832)+~P14(x55831,f857(f857(f151(x55831),x55833),x55832))
% 15.02/14.80 [5584]~P109(x55841)+P14(x55841,x55842)+~P14(x55841,f857(f857(f134(x55841),x55843),x55842))
% 15.02/14.80 [5585]~P109(x55851)+P14(x55851,x55852)+~P14(x55851,f857(f857(f134(x55851),x55852),x55853))
% 15.02/14.80 [5590]~P62(x55901)+~E(f44(x55901,x55903,x55902),f2(x55901))+P106(f857(f857(f286(x55901),x55902),x55903))
% 15.02/14.80 [5651]~P109(x56511)+P106(f857(f857(f234(x56511),x56513),x56512))+P106(f857(f857(f234(x56511),x56512),x56513))
% 15.02/14.80 [5656]~P109(x56561)+P106(f857(f857(f235(x56561),x56563),x56562))+P106(f857(f857(f234(x56561),x56562),x56563))
% 15.02/14.80 [5694]~P101(x56941)+E(f857(f857(f110(x56941),x56942),x56943),x56942)+~P106(f857(f857(f234(x56941),x56943),x56942))
% 15.02/14.80 [5696]~P101(x56961)+E(f857(f857(f110(x56961),x56962),x56963),x56963)+~P106(f857(f857(f234(x56961),x56962),x56963))
% 15.02/14.80 [5697]~P102(x56971)+E(f857(f857(f101(x56971),x56972),x56973),x56973)+~P106(f857(f857(f234(x56971),x56973),x56972))
% 15.02/14.80 [5699]~P102(x56991)+E(f857(f857(f101(x56991),x56992),x56993),x56992)+~P106(f857(f857(f234(x56991),x56992),x56993))
% 15.02/14.80 [5700]~P109(x57001)+E(f857(f857(f188(x57001),x57002),x57003),x57003)+~P106(f857(f857(f234(x57001),x57003),x57002))
% 15.02/14.80 [5702]~P109(x57021)+E(f857(f857(f188(x57021),x57022),x57023),x57022)+~P106(f857(f857(f234(x57021),x57022),x57023))
% 15.02/14.80 [5703]~P109(x57031)+E(f857(f857(f233(x57031),x57032),x57033),x57032)+~P106(f857(f857(f234(x57031),x57033),x57032))
% 15.02/14.80 [5705]~P109(x57051)+E(f857(f857(f233(x57051),x57052),x57053),x57053)+~P106(f857(f857(f234(x57051),x57052),x57053))
% 15.02/14.80 [5712]~P124(x57122)+E(x57121,f2(x57122))+E(f857(f857(f290(x57122),f857(f78(x57122),x57123)),f857(f78(x57122),x57121)),f857(f857(f290(x57122),x57123),x57121))
% 15.02/14.80 [5719]~P62(x57191)+E(f44(x57191,x57192,x57193),f2(x57191))+~P106(f857(f857(f286(x57191),x57193),x57192))
% 15.02/14.80 [5766]~P110(x57661)+E(f857(f301(x57661,x57662),x57663),f189(f927(x57661,a915)))+~P106(f857(f857(f234(x57661),x57663),x57662))
% 15.02/14.80 [5798]~P110(x57981)+E(f302(x57981,x57982,x57983),f189(f927(x57981,a915)))+~P106(f857(f857(f235(x57981),x57983),x57982))
% 15.02/14.80 [5799]~P110(x57991)+E(f305(x57991,x57992,x57993),f189(f927(x57991,a915)))+~P106(f857(f857(f234(x57991),x57993),x57992))
% 15.02/14.80 [5800]~P110(x58001)+E(f304(x58001,x58002,x58003),f189(f927(x58001,a915)))+~P106(f857(f857(f234(x58001),x58003),x58002))
% 15.02/14.80 [5852]~E(f857(f857(f3(a919),x58521),x58523),x58522)+E(x58521,f857(f857(f79(a919),x58522),x58523))+~P106(f857(f857(f234(a919),x58523),x58521))
% 15.02/14.80 [5853]~E(x58531,f857(f857(f79(a919),x58533),x58532))+E(f857(f857(f3(a919),x58531),x58532),x58533)+~P106(f857(f857(f234(a919),x58532),x58531))
% 15.02/14.80 [5898]~P106(f857(x58981,x58983))+P106(f857(x58981,f433(x58981,x58982)))+~P106(f857(f857(f234(a919),x58983),x58982))
% 15.02/14.80 [5899]~P106(f857(x58991,x58993))+P106(f857(x58991,f483(x58991,x58992)))+~P106(f857(f857(f235(a919),x58993),x58992))
% 15.02/14.80 [5907]~P110(x59071)+~E(f857(f301(x59071,x59072),x59073),f189(f927(x59071,a915)))+~P106(f857(f857(f235(x59071),x59072),x59073))
% 15.02/14.80 [5912]~P107(x59121)+~P106(f857(f857(f235(x59121),x59122),x59123))+P106(f857(f857(f234(x59121),x59122),x59123))
% 15.02/14.80 [5914]~P110(x59141)+~P106(f857(f857(f235(x59141),x59142),x59143))+P106(f857(f857(f234(x59141),x59142),x59143))
% 15.02/14.80 [6023]~P110(x60231)+~E(f302(x60231,x60232,x60233),f189(f927(x60231,a915)))+~P106(f857(f857(f234(x60231),x60232),x60233))
% 15.02/14.80 [6024]~P110(x60241)+~E(f304(x60241,x60242,x60243),f189(f927(x60241,a915)))+~P106(f857(f857(f235(x60241),x60242),x60243))
% 15.02/14.80 [6025]~P110(x60251)+~E(f189(f927(x60251,a915)),f302(x60251,x60252,x60253))+~P106(f857(f857(f234(x60251),x60252),x60253))
% 15.02/14.80 [6026]~P110(x60261)+~E(f189(f927(x60261,a915)),f304(x60261,x60262,x60263))+~P106(f857(f857(f235(x60261),x60262),x60263))
% 15.02/14.80 [6036]P106(f857(x60361,x60362))+~P106(f857(x60361,f437(x60361,x60363)))+~P106(f857(f857(f234(a919),x60362),x60363))
% 15.02/14.80 [6037]P106(f857(x60371,x60372))+~P106(f857(x60371,f490(x60371,x60373)))+~P106(f857(f857(f235(a919),x60372),x60373))
% 15.02/14.80 [6045]~E(x60451,f857(a112,x60453))+P106(f857(f857(f235(a919),x60451),f857(a112,x60452)))+~P106(f857(f857(f235(a919),x60453),x60452))
% 15.02/14.80 [6064]E(x60641,x60642)+~E(f857(f857(f80(a919),x60643),x60641),f857(f857(f80(a919),x60643),x60642))+~P106(f857(f857(f235(a919),f2(a919)),x60643))
% 15.02/14.80 [6124]E(f857(x61241,f889(x61241,x61242,x61243)),f77(a919))+~E(f857(f857(f8(x61243,a919),x61241),x61242),f77(a919))+~P106(f857(f60(x61243),x61242))
% 15.02/14.80 [6141]~P6(x61411)+P106(f857(f857(f234(x61411),x61412),f36(x61411,x61413)))+~P106(f857(f857(f328(x61411),x61412),x61413))
% 15.02/14.80 [6164]~P107(x61641)+~P106(f857(f857(f235(x61641),x61643),x61642))+~P106(f857(f857(f234(x61641),x61642),x61643))
% 15.02/14.80 [6168]~P107(x61681)+~P106(f857(f857(f235(x61681),x61683),x61682))+~P106(f857(f857(f235(x61681),x61682),x61683))
% 15.02/14.80 [6171]~P109(x61711)+~P106(f857(f857(f235(x61711),x61713),x61712))+~P106(f857(f857(f234(x61711),x61712),x61713))
% 15.02/14.80 [6172]~P109(x61721)+~P106(f857(f857(f235(x61721),x61723),x61722))+~P106(f857(f857(f235(x61721),x61722),x61723))
% 15.02/14.80 [6173]~P110(x61731)+~P106(f857(f857(f235(x61731),x61733),x61732))+~P106(f857(f857(f235(x61731),x61732),x61733))
% 15.02/14.80 [6193]~E(x61932,x61933)+~E(x61931,x61932)+E(f289(a919,f286(a919),x61931,x61932),f857(f857(f308(a919),x61933),f189(f927(a919,a915))))
% 15.02/14.80 [6200]~E(f857(x62002,f890(x62002,x62003,x62001)),f2(a919))+E(f857(f857(f8(x62001,a919),x62002),x62003),f2(a919))+~P106(f857(f60(x62001),x62003))
% 15.02/14.80 [6201]~E(f857(x62012,f797(x62012,x62013,x62011)),f77(a919))+E(f857(f857(f11(x62011,a919),x62012),x62013),f77(a919))+~P106(f857(f60(x62011),x62013))
% 15.02/14.80 [6217]~P108(x62171)+~P106(f857(f857(f234(x62171),x62173),x62172))+P106(f857(f857(f328(x62171),x62172),f857(f282(x62171),x62173)))
% 15.02/14.80 [6218]~P108(x62181)+~P106(f857(f857(f235(x62181),x62183),x62182))+P106(f857(f857(f328(x62181),x62182),f857(f303(x62181),x62183)))
% 15.02/14.80 [6219]~P108(x62191)+~P106(f857(f857(f235(x62191),x62192),x62193))+P106(f857(f857(f328(x62191),x62192),f857(f281(x62191),x62193)))
% 15.02/14.80 [6220]~P108(x62201)+~P106(f857(f857(f234(x62201),x62202),x62203))+P106(f857(f857(f328(x62201),x62202),f857(f300(x62201),x62203)))
% 15.02/14.80 [6221]~P120(x62211)+~P106(f857(f857(f286(x62211),x62212),x62213))+P106(f857(f857(f286(x62211),x62212),f857(f75(x62211),x62213)))
% 15.02/14.80 [6222]~P115(x62221)+~P106(f857(f857(f286(x62221),x62222),x62223))+P106(f857(f857(f286(x62221),x62222),f857(f78(x62221),x62223)))
% 15.02/14.80 [6234]E(f857(x62341,f891(x62341,x62342,x62343)),f857(a112,f2(a919)))+~E(f857(f857(f8(x62343,a919),x62341),x62342),f857(a112,f2(a919)))+~P106(f857(f60(x62343),x62342))
% 15.02/14.80 [6321]~P6(x63211)+~P106(f857(f857(f328(x63211),x63213),x63212))+P106(f857(f857(f234(x63211),f37(x63211,x63212)),x63213))
% 15.02/14.80 [6341]~P106(f857(f857(f234(a919),x63411),x63413))+P106(f857(f857(f234(a919),x63411),x63412))+~P106(f857(f857(f234(a919),x63413),x63412))
% 15.02/14.80 [6342]~P106(f857(f857(f234(a1),x63421),x63423))+P106(f857(f857(f234(a1),x63421),x63422))+~P106(f857(f857(f234(a1),x63423),x63422))
% 15.02/14.80 [6362]~P108(x63621)+~P106(f857(f857(f328(x63621),x63623),f857(f282(x63621),x63622)))+P106(f857(f857(f234(x63621),x63622),x63623))
% 15.02/14.80 [6363]~P108(x63631)+~P106(f857(f857(f328(x63631),x63632),f857(f300(x63631),x63633)))+P106(f857(f857(f234(x63631),x63632),x63633))
% 15.02/14.80 [6364]~P108(x63641)+~P106(f857(f857(f328(x63641),x63643),f857(f303(x63641),x63642)))+P106(f857(f857(f235(x63641),x63642),x63643))
% 15.02/14.80 [6365]~P108(x63651)+~P106(f857(f857(f328(x63651),x63652),f857(f281(x63651),x63653)))+P106(f857(f857(f235(x63651),x63652),x63653))
% 15.02/14.80 [6366]~P120(x63661)+~P106(f857(f857(f286(x63661),x63662),f857(f75(x63661),x63663)))+P106(f857(f857(f286(x63661),x63662),x63663))
% 15.02/14.80 [6367]~P115(x63671)+~P106(f857(f857(f286(x63671),x63672),f857(f78(x63671),x63673)))+P106(f857(f857(f286(x63671),x63672),x63673))
% 15.02/14.80 [6440]~P106(f857(x64401,x64402))+P106(f857(x64401,f783(x64401)))+~P106(f857(f857(f328(x64403),x64402),f241(f927(x64403,a915))))
% 15.02/14.80 [6586]~P67(x65861)+P106(f857(f857(f235(x65861),f2(x65861)),f907(x65863,x65862,x65861)))+P106(f857(f857(f234(x65861),x65862),x65863))
% 15.02/14.80 [6587]~P68(x65871)+P106(f857(f857(f235(x65871),f2(x65871)),f339(x65873,x65872,x65871)))+P106(f857(f857(f234(x65871),x65872),x65873))
% 15.02/14.80 [6653]~P80(x66531)+~P106(f857(f857(f234(x66531),x66533),f857(f78(x66531),x66532)))+P106(f857(f857(f234(x66531),x66532),f857(f78(x66531),x66533)))
% 15.02/14.80 [6655]~P80(x66551)+~P106(f857(f857(f235(x66551),x66553),f857(f78(x66551),x66552)))+P106(f857(f857(f235(x66551),x66552),f857(f78(x66551),x66553)))
% 15.02/14.80 [6667]~P106(f857(f857(f235(a919),x66671),x66673))+~P106(f857(f857(f235(a919),x66673),x66672))+P106(f857(f857(f235(a919),f857(a112,x66671)),x66672))
% 15.02/14.80 [6695]~P127(x66951)+P106(f857(f857(f234(x66951),f857(f100(x66951),x66952)),f857(f100(x66951),x66953)))+~P106(f857(f857(f234(a919),x66952),x66953))
% 15.02/14.80 [6696]~P120(x66961)+P106(f857(f857(f234(x66961),f857(f102(x66961),x66962)),f857(f102(x66961),x66963)))+~P106(f857(f857(f234(a1),x66962),x66963))
% 15.02/14.80 [6698]~P120(x66981)+P106(f857(f857(f235(x66981),f857(f102(x66981),x66982)),f857(f102(x66981),x66983)))+~P106(f857(f857(f235(a1),x66982),x66983))
% 15.02/14.80 [6699]~P127(x66991)+P106(f857(f857(f235(x66991),f857(f100(x66991),x66992)),f857(f100(x66991),x66993)))+~P106(f857(f857(f235(a919),x66992),x66993))
% 15.02/14.80 [6705]~P109(x67051)+E(f857(f857(f110(f927(x67051,a915)),f857(f281(x67051),x67052)),f857(f301(x67051,x67052),x67053)),f857(f281(x67051),x67053))+~P106(f857(f857(f234(x67051),x67052),x67053))
% 15.02/14.80 [6735]~P80(x67351)+~P106(f857(f857(f234(x67351),x67353),x67352))+P106(f857(f857(f234(x67351),f857(f78(x67351),x67352)),f857(f78(x67351),x67353)))
% 15.02/14.80 [6737]~P96(x67371)+~P106(f857(f857(f234(x67371),x67373),x67372))+P106(f857(f857(f234(x67371),f857(f78(x67371),x67372)),f857(f78(x67371),x67373)))
% 15.02/14.80 [6738]~P80(x67381)+~P106(f857(f857(f235(x67381),x67383),x67382))+P106(f857(f857(f235(x67381),f857(f78(x67381),x67382)),f857(f78(x67381),x67383)))
% 15.02/14.80 [6774]~P109(x67741)+E(f857(f857(f110(f927(x67741,a915)),f857(f281(x67741),x67742)),f302(x67741,x67742,x67743)),f857(f300(x67741),x67743))+~P106(f857(f857(f234(x67741),x67742),x67743))
% 15.02/14.80 [6775]~P109(x67751)+E(f857(f857(f110(f927(x67751,a915)),f857(f300(x67751),x67752)),f305(x67751,x67752,x67753)),f857(f281(x67751),x67753))+~P106(f857(f857(f235(x67751),x67752),x67753))
% 15.02/14.80 [6776]~P109(x67761)+E(f857(f857(f110(f927(x67761,a915)),f857(f300(x67761),x67762)),f304(x67761,x67762,x67763)),f857(f300(x67761),x67763))+~P106(f857(f857(f234(x67761),x67762),x67763))
% 15.02/14.80 [6809]~P109(x68091)+E(f857(f857(f110(f927(x68091,a915)),f857(f301(x68091,x68092),x68093)),f857(f282(x68091),x68093)),f857(f282(x68091),x68092))+~P106(f857(f857(f234(x68091),x68092),x68093))
% 15.02/14.80 [6965]~P109(x69651)+E(f857(f857(f110(f927(x69651,a915)),f302(x69651,x69652,x69653)),f857(f303(x69651),x69653)),f857(f282(x69651),x69652))+~P106(f857(f857(f234(x69651),x69652),x69653))
% 15.02/14.80 [6966]~P109(x69661)+E(f857(f857(f110(f927(x69661,a915)),f305(x69661,x69662,x69663)),f857(f282(x69661),x69663)),f857(f303(x69661),x69662))+~P106(f857(f857(f235(x69661),x69662),x69663))
% 15.02/14.80 [6967]~P109(x69671)+E(f857(f857(f110(f927(x69671,a915)),f304(x69671,x69672,x69673)),f857(f303(x69671),x69673)),f857(f303(x69671),x69672))+~P106(f857(f857(f234(x69671),x69672),x69673))
% 15.02/14.80 [6986]P106(f857(x69861,x69862))+~P106(f857(f857(f234(a919),x69862),x69863))+P106(f857(f857(f328(a919),f437(x69861,x69863)),f302(a919,f2(a919),x69863)))
% 15.02/14.80 [7020]E(x70201,x70202)+~E(f857(f857(f164(x70203),x70201),f639(x70203,x70202,x70201)),f857(f857(f164(x70203),x70202),f639(x70203,x70202,x70201)))+~E(f857(f190(f920(x70203)),x70201),f857(f190(f920(x70203)),x70202))
% 15.02/14.80 [7025]~E(x70253,f857(f857(f35(a919),x70251),x70252))+~P106(f857(f857(f235(a919),f2(a919)),x70252))+P106(f857(f857(f235(a919),x70251),f857(f857(f80(a919),x70252),f857(a112,x70253))))
% 15.02/14.80 [7041]~P106(f857(x70411,x70413))+~P106(f857(f857(f234(a919),x70413),x70412))+P106(f857(f857(f328(a919),f433(x70411,x70412)),f302(a919,f2(a919),x70412)))
% 15.02/14.80 [7080]~P106(f857(x70801,x70803))+P106(f857(x70801,f438(x70801,x70802)))+~P106(f857(f857(f328(a919),x70803),f302(a919,f2(a919),x70802)))
% 15.02/14.80 [7099]~P127(x70993)+~P106(f857(f857(f234(x70993),f857(f100(x70993),x70991)),f857(f100(x70993),x70992)))+P106(f857(f857(f234(a919),x70991),x70992))
% 15.02/14.80 [7100]~P120(x71003)+~P106(f857(f857(f234(x71003),f857(f102(x71003),x71001)),f857(f102(x71003),x71002)))+P106(f857(f857(f234(a1),x71001),x71002))
% 15.02/14.80 [7102]~P127(x71023)+~P106(f857(f857(f235(x71023),f857(f100(x71023),x71021)),f857(f100(x71023),x71022)))+P106(f857(f857(f235(a919),x71021),x71022))
% 15.02/14.80 [7103]~P120(x71033)+~P106(f857(f857(f235(x71033),f857(f102(x71033),x71031)),f857(f102(x71033),x71032)))+P106(f857(f857(f235(a1),x71031),x71032))
% 15.02/14.80 [7120]~P127(x71201)+~P106(f857(f857(f235(x71201),f77(x71201)),x71202))+P106(f857(f857(f235(x71201),f77(x71201)),f857(f857(f243(x71201),x71202),f857(a112,x71203))))
% 15.02/14.80 [7123]~P80(x71231)+~P106(f857(f857(f234(x71231),f857(f78(x71231),x71233)),f857(f78(x71231),x71232)))+P106(f857(f857(f234(x71231),x71232),x71233))
% 15.02/14.80 [7124]~P96(x71241)+~P106(f857(f857(f234(x71241),f857(f78(x71241),x71243)),f857(f78(x71241),x71242)))+P106(f857(f857(f234(x71241),x71242),x71243))
% 15.02/14.80 [7125]~P80(x71251)+~P106(f857(f857(f235(x71251),f857(f78(x71251),x71253)),f857(f78(x71251),x71252)))+P106(f857(f857(f235(x71251),x71252),x71253))
% 15.02/14.80 [7149]P106(f857(x71491,x71492))+~P106(f857(x71491,f439(x71491,x71493)))+~P106(f857(f857(f328(a919),x71492),f302(a919,f2(a919),x71493)))
% 15.02/14.80 [7170]~P67(x71701)+P106(f857(f857(f235(x71701),f907(x71703,x71702,x71701)),f77(x71701)))+P106(f857(f857(f234(x71701),x71702),x71703))
% 15.02/14.80 [7189]~E(f44(a919,x71893,x71892),f44(a919,x71891,x71892))+E(f857(f857(f79(a919),x71891),f857(f857(f80(a919),x71892),f379(x71891,x71892,x71893))),x71893)+~P106(f857(f857(f234(a919),x71891),x71893))
% 15.02/14.80 [7245]E(f857(f857(f8(x72451,a919),x72452),x72453),f2(a919))+~P106(f857(f60(x72451),x72453))+P106(f857(f857(f328(x72451),f890(x72452,x72453,x72451)),x72453))
% 15.02/14.80 [7246]E(f857(f857(f11(x72461,a919),x72462),x72463),f77(a919))+~P106(f857(f60(x72461),x72463))+P106(f857(f857(f328(x72461),f797(x72462,x72463,x72461)),x72463))
% 15.02/14.80 [7268]~P109(x72681)+~P106(f857(f857(f234(x72681),x72682),x72683))+P106(f857(f857(f234(f927(x72681,a915)),f857(f281(x72681),x72682)),f857(f281(x72681),x72683)))
% 15.02/14.80 [7269]~P110(x72691)+~P106(f857(f857(f234(x72691),x72692),x72693))+P106(f857(f857(f234(f927(x72691,a915)),f857(f300(x72691),x72692)),f857(f300(x72691),x72693)))
% 15.02/14.80 [7270]~P110(x72701)+~P106(f857(f857(f234(x72701),x72703),x72702))+P106(f857(f857(f234(f927(x72701,a915)),f857(f282(x72701),x72702)),f857(f282(x72701),x72703)))
% 15.02/14.80 [7271]~P109(x72711)+~P106(f857(f857(f234(x72711),x72713),x72712))+P106(f857(f857(f234(f927(x72711,a915)),f857(f303(x72711),x72712)),f857(f303(x72711),x72713)))
% 15.02/14.80 [7272]~P109(x72721)+~P106(f857(f857(f235(x72721),x72722),x72723))+P106(f857(f857(f235(f927(x72721,a915)),f857(f281(x72721),x72722)),f857(f281(x72721),x72723)))
% 15.02/14.80 [7283]~P6(x72831)+P106(f857(f857(f234(x72831),x72832),f37(x72831,x72833)))+P106(f857(f857(f328(x72831),f381(x72833,x72832,x72831)),x72833))
% 15.02/14.80 [7289]~P80(x72891)+P106(f857(f857(f234(x72891),f857(f857(f3(x72891),x72892),x72893)),f2(x72891)))+~P106(f857(f857(f234(x72891),x72892),x72893))
% 15.02/14.80 [7290]~P80(x72901)+P106(f857(f857(f235(x72901),f857(f857(f3(x72901),x72902),x72903)),f2(x72901)))+~P106(f857(f857(f235(x72901),x72902),x72903))
% 15.02/14.80 [7332]P106(f857(x73321,x73322))+P106(f857(f857(f234(a919),f439(x73321,x73323)),x73323))+~P106(f857(f857(f328(a919),x73322),f302(a919,f2(a919),x73323)))
% 15.02/14.80 [7374]~E(f857(f857(f8(x73741,a919),x73742),x73743),f77(a919))+~P106(f857(f60(x73741),x73743))+P106(f857(f857(f328(x73741),f889(x73742,x73743,x73741)),x73743))
% 15.02/14.80 [7375]~P106(f857(x73751,x73753))+P106(f857(f857(f234(a919),f438(x73751,x73752)),x73752))+~P106(f857(f857(f328(a919),x73753),f302(a919,f2(a919),x73752)))
% 15.02/14.80 [7415]~P6(x74151)+P106(f857(f857(f328(x74151),f879(x74153,x74152,x74151)),x74152))+P106(f857(f857(f234(x74151),f36(x74151,x74152)),x74153))
% 15.02/14.80 [7449]~E(f857(f857(f8(x74491,a919),x74492),x74493),f857(a112,f2(a919)))+~P106(f857(f60(x74491),x74493))+P106(f857(f857(f328(x74491),f891(x74492,x74493,x74491)),x74493))
% 15.02/14.80 [7460]E(x74601,f2(a919))+P106(f857(x74602,f44(a919,x74603,x74601)))+P106(f857(f857(f235(a919),f364(x74601,x74603,x74602)),x74601))
% 15.02/14.80 [7569]~P106(f857(x75691,x75692))+P106(f857(x75691,f44(a919,x75692,x75693)))+P106(f857(f857(f235(a919),f364(x75693,x75692,x75691)),x75693))
% 15.02/14.80 [7683]E(x76831,f113(x76832))+~P106(f857(f857(f328(f920(x76832)),x76831),f161(x76832,x76833)))+P106(f857(f857(f328(x76832),f690(x76833,x76831,x76832)),x76833))
% 15.02/14.80 [7705]~P109(x77051)+E(f857(f857(f110(f927(x77051,a915)),f857(f857(f308(x77051),x77052),f189(f927(x77051,a915)))),f305(x77051,x77052,x77053)),f857(f301(x77051,x77052),x77053))+~P106(f857(f857(f235(x77051),x77052),x77053))
% 15.02/14.80 [7727]~P109(x77271)+E(f857(f857(f110(f927(x77271,a915)),f857(f857(f308(x77271),x77272),f189(f927(x77271,a915)))),f304(x77271,x77272,x77273)),f302(x77271,x77272,x77273))+~P106(f857(f857(f234(x77271),x77272),x77273))
% 15.02/14.80 [7837]~P109(x78371)+P106(f857(f857(f234(x78371),x78372),x78373))+~P106(f857(f857(f234(f927(x78371,a915)),f857(f303(x78371),x78373)),f857(f303(x78371),x78372)))
% 15.02/14.80 [7838]~P110(x78381)+P106(f857(f857(f234(x78381),x78382),x78383))+~P106(f857(f857(f234(f927(x78381,a915)),f857(f282(x78381),x78383)),f857(f282(x78381),x78382)))
% 15.02/14.80 [7839]~P109(x78391)+P106(f857(f857(f234(x78391),x78392),x78393))+~P106(f857(f857(f234(f927(x78391,a915)),f857(f281(x78391),x78392)),f857(f281(x78391),x78393)))
% 15.02/14.80 [7840]~P110(x78401)+P106(f857(f857(f234(x78401),x78402),x78403))+~P106(f857(f857(f234(f927(x78401,a915)),f857(f300(x78401),x78402)),f857(f300(x78401),x78403)))
% 15.02/14.80 [7841]~P109(x78411)+P106(f857(f857(f235(x78411),x78412),x78413))+~P106(f857(f857(f235(f927(x78411,a915)),f857(f281(x78411),x78412)),f857(f281(x78411),x78413)))
% 15.02/14.80 [7864]~P80(x78641)+~P106(f857(f857(f234(x78641),f857(f857(f3(x78641),x78642),x78643)),f2(x78641)))+P106(f857(f857(f234(x78641),x78642),x78643))
% 15.02/14.80 [7865]~P80(x78651)+~P106(f857(f857(f235(x78651),f857(f857(f3(x78651),x78652),x78653)),f2(x78651)))+P106(f857(f857(f235(x78651),x78652),x78653))
% 15.02/14.80 [8019]E(x80191,f2(a919))+~E(f857(f142(a919,a919,f79(a919),x80192),x80193),f2(a919))+~P106(f857(f857(f328(a919),x80191),f857(f172(a919),x80193)))
% 15.02/14.80 [8023]~P6(x80231)+~P106(f857(f857(f234(x80231),f879(x80233,x80232,x80231)),x80233))+P106(f857(f857(f234(x80231),f36(x80231,x80232)),x80233))
% 15.02/14.80 [8178]P106(f857(f857(f234(a1),f2(a1)),f373(x81781,x81782,x81783)))+P106(f857(f857(x81782,f857(f857(f35(a1),x81781),x81783)),f44(a1,x81781,x81783)))+~P106(f857(f857(f235(a1),f2(a1)),x81783))
% 15.02/14.80 [8266]E(x82661,x82662)+~E(f857(f190(f920(x82663)),x82661),f857(f190(f920(x82663)),x82662))+~P106(f857(f857(f256(x82663,x82663,a915),a324),f665(x82663,x82661,x82662)))
% 15.02/14.80 [8336]~P39(x83362,x83363)+E(x83361,f189(f927(x83362,a915)))+~P106(f857(f857(f234(f927(x83362,a915)),x83361),f857(f284(x83362,x83362,x83363),x83361)))
% 15.02/14.80 [8367]~P68(x83671)+~P106(f857(f857(f234(x83671),x83672),f857(f857(f79(x83671),x83673),f339(x83673,x83672,x83671))))+P106(f857(f857(f234(x83671),x83672),x83673))
% 15.02/14.80 [8402]P54(x84021,x84022,x84023)+P106(f857(f857(f328(x84021),f574(x84023,x84022,x84021)),x84022))+P106(f857(f857(f328(f926(x84021,x84021)),f575(x84023,x84022,x84021)),x84023))
% 15.02/14.80 [8423]P106(f857(f857(x84232,f857(f857(f35(a1),x84231),x84233)),f44(a1,x84231,x84233)))+~P106(f857(f857(f235(a1),f2(a1)),x84233))+P106(f857(f857(f235(a1),f373(x84231,x84232,x84233)),x84233))
% 15.02/14.80 [8447]E(f857(f309(a919,a919,f857(f857(f9(a919,a919,a919),f3(a919)),x84471)),f857(f301(a919,x84472),x84473)),f189(f927(a919,a915)))+P106(f857(f857(f235(a919),x84471),x84473))+P106(f857(f857(f235(a919),x84472),x84473))
% 15.02/14.80 [8557]E(f857(f309(a919,a919,f857(f857(f9(a919,a919,a919),f3(a919)),x85571)),f857(f301(a919,x85572),x85573)),f857(f857(f308(a919),f2(a919)),f189(f927(a919,a915))))+P106(f857(f857(f235(a919),x85571),x85573))+~P106(f857(f857(f235(a919),x85572),x85573))
% 15.02/14.80 [8571]~P109(x85711)+E(f149(x85711,x85711,f7(x85711),x85712,x85713),x85713)+~P106(f857(f857(f328(x85711),x85712),f857(f172(x85711),x85713)))
% 15.02/14.80 [8584]P26(x85841,x85841,x85842,x85843)+~P106(f857(f60(x85841),x85843))+~P106(f857(f857(f234(f927(x85841,a915)),x85843),f857(f309(x85841,x85841,x85842),x85843)))
% 15.02/14.80 [8610]E(f857(f857(f79(a1),f857(f857(f80(a1),x86101),f374(x86102,x86103,x86101))),f373(x86102,x86103,x86101)),x86102)+P106(f857(f857(x86103,f857(f857(f35(a1),x86102),x86101)),f44(a1,x86102,x86101)))+~P106(f857(f857(f235(a1),f2(a1)),x86101))
% 15.02/14.80 [8846]~P106(f857(f857(x88461,f374(x88462,x88461,x88463)),f373(x88462,x88461,x88463)))+P106(f857(f857(x88461,f857(f857(f35(a1),x88462),x88463)),f44(a1,x88462,x88463)))+~P106(f857(f857(f235(a1),f2(a1)),x88463))
% 15.02/14.80 [9739]~P106(f857(f60(x97391),x97392))+~P106(f857(f857(f328(x97391),x97393),x97392))+P106(f857(f857(f235(a919),f857(f34(x97391),f857(f857(f3(f927(x97391,a915)),x97392),f857(f857(f308(x97391),x97393),f189(f927(x97391,a915)))))),f857(f34(x97391),x97392)))
% 15.02/14.80 [10344]P54(x103441,x103442,x103443)+~P106(f857(f857(f256(x103441,x103441,a915),f857(f857(f9(x103441,f927(x103441,a915),f927(x103441,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x103441,a915),f927(x103441,a915)),x103441),f10(a915,a915,x103441)),f857(f857(f10(a915,f927(a915,a915),x103441),a325),f857(f857(f9(x103441,f927(x103441,a915),a915),f328(x103441)),x103442)))),f857(f857(f9(x103441,f927(x103441,a915),a915),f328(x103441)),x103442))),f575(x103443,x103442,x103441)))+P106(f857(f857(f328(x103441),f574(x103443,x103442,x103441)),x103442))
% 15.02/14.80 [5673]~P124(x56732)+E(x56731,f2(x56732))+E(f857(f857(f290(x56732),x56733),f857(f78(x56732),x56731)),f857(f78(x56732),f857(f857(f290(x56732),x56733),x56731)))
% 15.02/14.80 [5814]~E(x58143,f189(f927(x58141,a915)))+~E(x58142,f189(f927(x58141,a915)))+E(f857(f857(f110(f927(x58141,a915)),x58142),x58143),f189(f927(x58141,a915)))
% 15.02/14.80 [5872]~E(x58723,f2(a919))+~P106(f857(x58721,f2(a919)))+P106(f857(x58721,f857(f857(f35(a919),x58722),x58723)))
% 15.02/14.80 [6015]~P68(x60152)+E(x60151,f2(x60152))+E(f857(f857(f290(x60152),f857(f75(x60152),x60153)),f857(f75(x60152),x60151)),f857(f75(x60152),f857(f857(f290(x60152),x60153),x60151)))
% 15.02/14.80 [6134]~P62(x61341)+E(f857(f857(f80(x61341),x61342),f857(f857(f35(x61341),x61343),x61342)),x61343)+~P106(f857(f857(f286(x61341),x61342),x61343))
% 15.02/14.80 [6189]~P106(f857(f60(x61891),x61893))+E(f857(f34(x61891),f857(f857(f308(x61891),x61892),x61893)),f857(a112,f857(f34(x61891),x61893)))+P106(f857(f857(f328(x61891),x61892),x61893))
% 15.02/14.80 [6269]~E(x62692,f2(a919))+P106(f857(x62691,f2(a919)))+~P106(f857(x62691,f857(f857(f35(a919),x62693),x62692)))
% 15.02/14.80 [6286]~P106(f857(f60(x62861),x62863))+E(f857(f34(x62861),f857(f857(f308(x62861),x62862),x62863)),f857(f34(x62861),x62863))+~P106(f857(f857(f328(x62861),x62862),x62863))
% 15.02/14.80 [6323]~P106(f857(f60(x63231),x63233))+E(f857(f34(x63231),f857(f857(f308(x63231),x63232),x63233)),f857(f857(f79(a919),f77(a919)),f857(f34(x63231),x63233)))+P106(f857(f857(f328(x63231),x63232),x63233))
% 15.02/14.80 [6330]~P63(x63301)+E(f857(f857(f35(x63301),x63302),f857(f78(x63301),x63303)),f857(f78(x63301),f857(f857(f35(x63301),x63302),x63303)))+~P106(f857(f857(f286(x63301),x63303),x63302))
% 15.02/14.80 [6441]E(f857(f857(f79(a919),x64411),f892(x64411,x64412,x64413)),x64412)+~P106(f857(x64413,f2(a919)))+P106(f857(x64413,f857(f857(f3(a919),x64412),x64411)))
% 15.02/14.80 [6442]E(f857(f857(f79(a919),x64421),f893(x64421,x64422,x64423)),x64422)+~P106(f857(x64423,f2(a919)))+P106(f857(x64423,f857(f857(f3(a919),x64422),x64421)))
% 15.02/14.80 [6465]~P63(x64651)+E(f857(f857(f35(x64651),f857(f78(x64651),x64652)),x64653),f857(f78(x64651),f857(f857(f35(x64651),x64652),x64653)))+~P106(f857(f857(f286(x64651),x64653),x64652))
% 15.02/14.80 [6489]~P6(x64891)+~P106(f857(f60(x64891),x64893))+E(f857(f857(f63(x64891,x64891,f110(x64891)),x64892),x64893),f857(f857(f110(x64891),x64892),f36(x64891,x64893)))
% 15.02/14.80 [6490]~P6(x64901)+~P106(f857(f60(x64901),x64903))+E(f857(f857(f63(x64901,x64901,f101(x64901)),x64902),x64903),f857(f857(f101(x64901),x64902),f37(x64901,x64903)))
% 15.02/14.80 [6496]~P94(x64961)+~E(f857(f103(x64961),x64962),f857(f103(x64961),x64963))+P29(x64961,f857(f103(x64961),f857(f857(f79(a1),x64962),f857(f78(a1),x64963))))
% 15.02/14.80 [6505]~P143(x65051)+E(f857(f857(f3(x65051),f857(f100(x65051),x65052)),f857(f100(x65051),x65053)),f857(f100(x65051),f857(f857(f3(a919),x65052),x65053)))+~P106(f857(f857(f234(a919),x65053),x65052))
% 15.02/14.80 [6512]~P120(x65121)+~P106(f857(f857(f286(x65121),x65122),x65123))+P106(f857(f857(f286(x65121),f857(f75(x65121),x65122)),x65123))
% 15.02/14.80 [6513]~P115(x65131)+~P106(f857(f857(f286(x65131),x65132),x65133))+P106(f857(f857(f286(x65131),f857(f78(x65131),x65132)),x65133))
% 15.02/14.80 [6597]E(f857(f857(f79(a919),x65971),f892(x65971,x65972,x65973)),x65972)+P106(f857(f857(f235(a919),x65972),x65971))+P106(f857(x65973,f857(f857(f3(a919),x65972),x65971)))
% 15.02/14.80 [6598]E(f857(f857(f79(a919),x65981),f893(x65981,x65982,x65983)),x65982)+P106(f857(f857(f235(a919),x65982),x65981))+P106(f857(x65983,f857(f857(f3(a919),x65982),x65981)))
% 15.02/14.80 [6612]~P120(x66121)+E(f857(f857(f80(x66121),f857(f75(x66121),x66122)),x66123),f857(f75(x66121),f857(f857(f80(x66121),x66122),x66123)))+~P106(f857(f857(f234(x66121),f2(x66121)),x66123))
% 15.02/14.80 [6613]~P67(x66131)+E(f857(f857(f290(x66131),f857(f75(x66131),x66132)),x66133),f857(f75(x66131),f857(f857(f290(x66131),x66132),x66133)))+~P106(f857(f857(f235(x66131),f2(x66131)),x66133))
% 15.02/14.80 [6621]~P2(x66211)+~P106(f857(f60(x66211),x66213))+E(f857(f857(f63(x66211,x66211,f110(x66211)),x66212),x66213),f12(x66211,f857(f857(f308(x66211),x66212),x66213)))
% 15.02/14.80 [6622]~P2(x66221)+~P106(f857(f60(x66221),x66223))+E(f857(f857(f63(x66221,x66221,f101(x66221)),x66222),x66223),f13(x66221,f857(f857(f308(x66221),x66222),x66223)))
% 15.02/14.80 [6623]~P109(x66231)+~P106(f857(f60(x66231),x66233))+E(f857(f857(f63(x66231,x66231,f188(x66231)),x66232),x66233),f16(x66231,f857(f857(f308(x66231),x66232),x66233)))
% 15.02/14.80 [6624]~P109(x66241)+~P106(f857(f60(x66241),x66243))+E(f857(f857(f63(x66241,x66241,f233(x66241)),x66242),x66243),f17(x66241,f857(f857(f308(x66241),x66242),x66243)))
% 15.02/14.80 [6669]E(x66691,f113(x66692))+~E(f179(x66692,x66693),f113(f920(x66692)))+~P106(f857(f857(f328(f920(x66692)),x66691),f857(f172(f920(x66692)),x66693)))
% 15.02/14.80 [6713]~P106(f857(f137(x67131),x67133))+P106(f857(f857(f328(x67131),x67132),f857(f172(x67131),x67133)))+P106(f857(f137(x67131),f857(f857(f151(x67131),x67132),x67133)))
% 15.02/14.80 [6724]~P97(x67241)+~P106(f857(f60(x67241),x67243))+E(f857(f62(x67241,f80(x67241)),f857(f857(f308(x67241),x67242),x67243)),f857(f857(f63(x67241,x67241,f80(x67241)),x67242),x67243))
% 15.02/14.80 [6746]~P109(x67461)+~P106(f857(f60(x67461),x67463))+E(f14(x67461,f188(x67461),f857(f857(f308(x67461),x67462),x67463)),f857(f857(f63(x67461,x67461,f188(x67461)),x67462),x67463))
% 15.02/14.80 [6747]~P109(x67471)+~P106(f857(f60(x67471),x67473))+E(f15(x67471,f233(x67471),f857(f857(f308(x67471),x67472),x67473)),f857(f857(f63(x67471,x67471,f233(x67471)),x67472),x67473))
% 15.02/14.80 [6749]P106(f857(x67491,f2(a919)))+~P106(f857(f857(f235(a919),x67492),x67493))+~P106(f857(x67491,f857(f857(f3(a919),x67492),x67493)))
% 15.02/14.80 [6770]~P87(x67701)+P106(f857(f857(f234(x67701),x67702),x67703))+~P106(f857(f857(f234(x67701),f857(f75(x67701),x67702)),x67703))
% 15.02/14.80 [6771]~P120(x67711)+P106(f857(f857(f235(x67711),x67712),x67713))+~P106(f857(f857(f235(x67711),f857(f75(x67711),x67712)),x67713))
% 15.02/14.80 [6772]~P120(x67721)+P106(f857(f857(f286(x67721),x67722),x67723))+~P106(f857(f857(f286(x67721),f857(f75(x67721),x67722)),x67723))
% 15.02/14.80 [6773]~P115(x67731)+P106(f857(f857(f286(x67731),x67732),x67733))+~P106(f857(f857(f286(x67731),f857(f78(x67731),x67732)),x67733))
% 15.02/14.80 [6790]E(x67901,f113(x67902))+E(f857(f141(x67902),f857(f857(f138(x67902),x67903),x67901)),f857(f857(f164(x67902),x67901),x67903))+~P106(f857(f857(f235(a919),x67903),f857(f190(f920(x67902)),x67901)))
% 15.02/14.80 [6842]~P106(f857(x68421,x68423))+P106(f857(x68421,f491(x68421,x68422)))+~P106(f857(f857(f328(a919),x68423),f857(f301(a919,f2(a919)),x68422)))
% 15.02/14.80 [6862]P106(f857(x68621,x68622))+~P106(f857(f857(f235(a919),x68622),x68623))+P106(f857(f857(f328(a919),f490(x68621,x68623)),f857(f301(a919,f2(a919)),x68623)))
% 15.02/14.80 [6877]~P127(x68771)+~P106(f857(f857(f234(x68771),f77(x68771)),x68772))+P106(f857(f857(f234(x68771),f77(x68771)),f857(f857(f243(x68771),x68772),x68773)))
% 15.02/14.80 [6879]~P127(x68791)+~P106(f857(f857(f234(x68791),f2(x68791)),x68792))+P106(f857(f857(f234(x68791),f2(x68791)),f857(f857(f243(x68791),x68792),x68793)))
% 15.02/14.80 [6881]~P127(x68811)+~P106(f857(f857(f235(x68811),f2(x68811)),x68812))+P106(f857(f857(f235(x68811),f2(x68811)),f857(f857(f243(x68811),x68812),x68813)))
% 15.02/14.80 [6905]~P106(f857(x69051,x69053))+~P106(f857(f857(f235(a919),x69053),x69052))+P106(f857(f857(f328(a919),f483(x69051,x69052)),f857(f301(a919,f2(a919)),x69052)))
% 15.02/14.80 [6913]P106(f857(f60(x69131),x69132))+~P106(f857(f60(x69131),x69133))+~P106(f857(f857(f234(f927(x69131,a915)),x69132),x69133))
% 15.02/14.80 [6920]~P106(f857(f857(f286(a919),x69201),x69202))+~P106(f857(f857(f286(a919),x69201),x69203))+P106(f857(f857(f286(a919),x69201),f857(f857(f3(a919),x69202),x69203)))
% 15.02/14.80 [6921]P106(f857(x69211,x69212))+~P106(f857(x69211,f492(x69211,x69213)))+~P106(f857(f857(f328(a919),x69212),f857(f301(a919,f2(a919)),x69213)))
% 15.02/14.80 [6934]E(x69341,f2(a919))+P106(f857(x69342,f370(x69341,x69343,x69342)))+~P106(f857(x69342,f857(f857(f35(a919),x69343),x69341)))
% 15.02/14.80 [6942]~P129(x69422)+E(x69421,f2(x69422))+~E(f857(f857(f79(x69422),f857(f857(f80(x69422),x69423),x69423)),f857(f857(f80(x69422),x69421),x69421)),f2(x69422))
% 15.02/14.80 [6943]~P129(x69432)+E(x69431,f2(x69432))+~E(f857(f857(f79(x69432),f857(f857(f80(x69432),x69431),x69431)),f857(f857(f80(x69432),x69433),x69433)),f2(x69432))
% 15.02/14.80 [6987]E(x69871,f2(a919))+~P106(f857(x69872,f371(x69871,x69873,x69872)))+P106(f857(x69872,f857(f857(f35(a919),x69873),x69871)))
% 15.02/14.80 [6992]~P109(x69921)+~P14(x69921,x69923)+P14(x69921,f857(f857(f148(x69921,x69921,f7(x69921)),x69922),x69923))
% 15.02/14.80 [7034]P106(f857(x70341,f370(x70342,x70343,x70341)))+P106(f857(x70341,f2(a919)))+~P106(f857(x70341,f857(f857(f35(a919),x70343),x70342)))
% 15.02/14.80 [7040]~P94(x70401)+E(f857(f103(x70401),x70402),f857(f103(x70401),x70403))+~P29(x70401,f857(f103(x70401),f857(f857(f79(a1),x70402),f857(f78(a1),x70403))))
% 15.02/14.80 [7106]E(x71061,f2(a1))+E(x71062,f2(a1))+~P106(f857(f48(x71062,x71062),f857(f857(f251(a1,a1),x71063),x71061)))
% 15.02/14.80 [7107]E(x71071,f77(a1))+E(x71072,f2(a1))+~P106(f857(f48(x71072,x71072),f857(f857(f251(a1,a1),x71071),x71073)))
% 15.02/14.80 [7122]P106(f857(x71221,x71222))+P106(f857(f857(f235(a919),f492(x71221,x71223)),x71223))+~P106(f857(f857(f328(a919),x71222),f857(f301(a919,f2(a919)),x71223)))
% 15.02/14.80 [7145]~P106(f857(x71451,f892(x71453,x71452,x71451)))+~P106(f857(x71451,f2(a919)))+P106(f857(x71451,f857(f857(f3(a919),x71452),x71453)))
% 15.02/14.80 [7146]~P106(f857(x71461,f893(x71463,x71462,x71461)))+~P106(f857(x71461,f2(a919)))+P106(f857(x71461,f857(f857(f3(a919),x71462),x71463)))
% 15.02/14.80 [7147]~P106(f857(x71471,f371(x71473,x71472,x71471)))+~P106(f857(x71471,f2(a919)))+P106(f857(x71471,f857(f857(f35(a919),x71472),x71473)))
% 15.02/14.80 [7166]~P106(f857(x71661,x71663))+P106(f857(f857(f235(a919),f491(x71661,x71662)),x71662))+~P106(f857(f857(f328(a919),x71663),f857(f301(a919,f2(a919)),x71662)))
% 15.02/14.80 [7167]E(f857(f857(f3(a919),f857(f857(f3(a919),x71671),x71672)),f857(f857(f3(a919),x71673),x71672)),f857(f857(f3(a919),x71671),x71673))+~P106(f857(f857(f234(a919),x71672),x71671))+~P106(f857(f857(f234(a919),x71672),x71673))
% 15.02/14.80 [7202]~P80(x72021)+~P106(f857(f857(f234(x72021),f857(f78(x72021),x72023)),x72022))+P106(f857(f857(f234(x72021),f857(f78(x72021),x72022)),x72023))
% 15.02/14.80 [7204]~P87(x72041)+~P106(f857(f857(f234(x72041),f857(f75(x72041),x72042)),x72043))+P106(f857(f857(f234(x72041),f857(f78(x72041),x72042)),x72043))
% 15.02/14.80 [7206]~P80(x72061)+~P106(f857(f857(f235(x72061),f857(f78(x72061),x72063)),x72062))+P106(f857(f857(f235(x72061),f857(f78(x72061),x72062)),x72063))
% 15.02/14.80 [7207]~P120(x72071)+~P106(f857(f857(f235(x72071),f857(f75(x72071),x72072)),x72073))+P106(f857(f857(f235(x72071),f857(f78(x72071),x72072)),x72073))
% 15.02/14.80 [7240]~P106(f857(x72403,f892(x72402,x72401,x72403)))+P106(f857(f857(f235(a919),x72401),x72402))+P106(f857(x72403,f857(f857(f3(a919),x72401),x72402)))
% 15.02/14.80 [7241]~P106(f857(x72413,f893(x72412,x72411,x72413)))+P106(f857(f857(f235(a919),x72411),x72412))+P106(f857(x72413,f857(f857(f3(a919),x72411),x72412)))
% 15.02/14.80 [7293]~E(f881(x72933,x72932,x72931),f882(x72933,x72932,x72931))+E(f857(f857(f101(f927(x72931,a915)),x72932),f36(f927(x72931,a915),x72933)),f189(f927(x72931,a915)))+P106(f857(f857(f328(f927(x72931,a915)),x72932),x72933))
% 15.02/14.80 [7301]~P106(f857(f60(x73011),x73013))+P106(f857(f60(x73011),f37(f927(x73011,a915),x73012)))+~P106(f857(f857(f328(f927(x73011,a915)),x73013),x73012))
% 15.02/14.80 [7361]~P109(x73611)+E(f857(f857(f110(f927(x73611,a915)),f857(f301(x73611,x73612),x73613)),f857(f857(f308(x73611),x73613),f189(f927(x73611,a915)))),f302(x73611,x73612,x73613))+~P106(f857(f857(f234(x73611),x73612),x73613))
% 15.02/14.80 [7364]E(x73641,f2(a919))+P106(f857(f857(f235(a919),f376(x73641,x73643,x73642)),x73641))+P106(f857(x73642,f857(f857(f35(a919),x73643),x73641)))
% 15.02/14.80 [7393]P106(f857(f857(f235(a919),f857(f190(f920(x73931)),x73932)),f785(x73933,x73931)))+~P106(f857(f60(f920(x73931)),x73933))+~P106(f857(f857(f328(f920(x73931)),x73932),x73933))
% 15.02/14.80 [7399]E(x73991,x73992)+~P106(f857(f857(f234(f927(x73993,a915)),x73991),x73992))+P106(f857(f857(f235(f927(x73993,a915)),x73991),x73992))
% 15.02/14.80 [7412]E(x74121,x74122)+~E(f857(f190(f920(x74123)),x74121),f857(f190(f920(x74123)),x74122))+P106(f857(f857(f235(a919),f639(x74123,x74121,x74122)),f857(f190(f920(x74123)),x74122)))
% 15.02/14.80 [7461]P9(x74611,x74612,x74613)+~E(f857(f263(x74611,x74611),x74613),x74612)+~E(f857(f857(f288(x74611,x74611,x74611),f857(f285(x74611,x74611),x74613)),x74613),x74613)
% 15.02/14.80 [7539]~P106(f857(x75391,f2(a919)))+P106(f857(f857(f235(a919),f376(x75393,x75392,x75391)),x75393))+P106(f857(x75391,f857(f857(f35(a919),x75392),x75393)))
% 15.02/14.80 [7548]~P109(x75481)+E(f857(f857(f110(f927(x75481,a915)),f305(x75481,x75482,x75483)),f857(f857(f308(x75481),x75483),f189(f927(x75481,a915)))),f304(x75481,x75482,x75483))+~P106(f857(f857(f235(x75481),x75482),x75483))
% 15.02/14.80 [7640]~P106(f857(f60(x76401),x76403))+P106(f857(f857(f234(a919),f857(f34(x76401),x76402)),f857(f34(x76401),x76403)))+~P106(f857(f857(f234(f927(x76401,a915)),x76402),x76403))
% 15.02/14.80 [7641]~P106(f857(f60(x76411),x76413))+P106(f857(f857(f235(a919),f857(f34(x76411),x76412)),f857(f34(x76411),x76413)))+~P106(f857(f857(f235(f927(x76411,a915)),x76412),x76413))
% 15.02/14.80 [7772]E(x77721,x77722)+~P106(f857(f857(f234(f927(x77723,a915)),x77722),x77721))+~P106(f857(f857(f234(f927(x77723,a915)),x77721),x77722))
% 15.02/14.80 [7775]~P109(x77751)+P14(x77751,x77752)+~P14(x77751,f857(f857(f148(x77751,x77751,f7(x77751)),x77753),x77752))
% 15.02/14.80 [7846]~P106(f857(f857(f235(a919),x78463),x78462))+~P106(f857(f857(f235(a919),x78463),x78461))+P106(f857(f857(f235(a919),f857(f857(f3(a919),x78461),x78462)),f857(f857(f3(a919),x78461),x78463)))
% 15.02/14.80 [7847]~P106(f857(f857(f234(a919),x78472),x78471))+~P106(f857(f857(f235(a919),x78471),x78473))+P106(f857(f857(f235(a919),f857(f857(f3(a919),x78471),x78472)),f857(f857(f3(a919),x78473),x78472)))
% 15.02/14.80 [7862]~P106(f857(f857(f235(a1),x78622),f2(a1)))+~P106(f857(f857(f234(a1),x78623),x78621))+P106(f857(f857(f234(a1),f857(f857(f35(a1),x78621),x78622)),f857(f857(f35(a1),x78623),x78622)))
% 15.02/14.80 [7879]~P106(f857(f857(f235(a919),f2(a919)),x78793))+~P106(f857(f857(f234(a919),x78793),x78792))+P106(f857(f857(f234(a919),f857(f857(f35(a919),x78791),x78792)),f857(f857(f35(a919),x78791),x78793)))
% 15.02/14.80 [7880]~P106(f857(f857(f235(a1),f2(a1)),x78802))+~P106(f857(f857(f234(a1),x78801),x78803))+P106(f857(f857(f234(a1),f857(f857(f35(a1),x78801),x78802)),f857(f857(f35(a1),x78803),x78802)))
% 15.02/14.80 [7884]~P106(f857(f857(f235(a919),f2(a919)),x78842))+~P106(f857(f857(f235(a919),x78841),x78843))+P106(f857(f857(f235(a919),f857(f857(f80(a919),x78841),x78842)),f857(f857(f80(a919),x78843),x78842)))
% 15.02/14.80 [7885]~P106(f857(f857(f235(a919),f2(a919)),x78851))+~P106(f857(f857(f235(a919),x78852),x78853))+P106(f857(f857(f235(a919),f857(f857(f80(a919),x78851),x78852)),f857(f857(f80(a919),x78851),x78853)))
% 15.02/14.80 [7886]~P106(f857(f857(f235(a1),f2(a1)),x78861))+~P106(f857(f857(f235(a1),x78862),x78863))+P106(f857(f857(f235(a1),f857(f857(f80(a1),x78861),x78862)),f857(f857(f80(a1),x78861),x78863)))
% 15.02/14.80 [7934]E(x79341,f2(a919))+E(f857(f857(f79(a919),f857(f857(f80(a919),x79341),f371(x79341,x79342,x79343))),f376(x79341,x79342,x79343)),x79342)+P106(f857(x79343,f857(f857(f35(a919),x79342),x79341)))
% 15.02/14.80 [7993]E(f857(f857(f79(a919),f857(f857(f80(a919),x79931),f371(x79931,x79932,x79933))),f376(x79931,x79932,x79933)),x79932)+~P106(f857(x79933,f2(a919)))+P106(f857(x79933,f857(f857(f35(a919),x79932),x79931)))
% 15.02/14.80 [8010]~P106(f857(f60(x80101),x80103))+P106(f857(f857(f328(x80101),f898(x80102,x80103,x80101)),x80103))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f11(x80101,a919),x80102),x80103)))
% 15.02/14.80 [8011]~P106(f857(f60(x80111),x80113))+P106(f857(f857(f328(x80111),f911(x80112,x80113,x80111)),x80113))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f11(x80111,a919),x80112),x80113)))
% 15.02/14.80 [8111]E(x81111,f2(a919))+P106(f857(f857(f286(a919),x81112),x81113))+~P106(f857(f857(f286(a919),f857(f857(f80(a919),x81111),x81112)),f857(f857(f80(a919),x81111),x81113)))
% 15.02/14.80 [8301]E(x83011,f189(f927(x83012,a915)))+E(x83011,f857(f857(f308(x83012),x83013),f189(f927(x83012,a915))))+~P106(f857(f857(f234(f927(x83012,a915)),x83011),f857(f857(f308(x83012),x83013),f189(f927(x83012,a915)))))
% 15.02/14.80 [8337]~P106(f857(f857(f235(a919),f77(a919)),x83373))+P106(f857(f857(f234(a919),x83371),x83372))+~P106(f857(f857(f286(a919),f857(f857(f243(a919),x83373),x83371)),f857(f857(f243(a919),x83373),x83372)))
% 15.02/14.80 [8339]~P106(f857(f857(f235(a919),f2(a919)),x83393))+P106(f857(f857(f234(a919),x83391),x83392))+~P106(f857(f857(f234(a919),f857(f857(f80(a919),x83393),x83391)),f857(f857(f80(a919),x83393),x83392)))
% 15.02/14.80 [8340]~P106(f857(f857(f235(a919),f2(a919)),x83403))+P106(f857(f857(f234(a919),x83401),x83402))+~P106(f857(f857(f234(a919),f857(f857(f80(a919),x83401),x83403)),f857(f857(f80(a919),x83402),x83403)))
% 15.02/14.80 [8342]~P106(f857(f857(f235(a919),f2(a919)),x83423))+P106(f857(f857(f235(a919),x83421),x83422))+~P106(f857(f857(f235(a919),f857(f857(f243(a919),x83423),x83421)),f857(f857(f243(a919),x83423),x83422)))
% 15.02/14.80 [8344]~P106(f857(f857(f235(a919),f2(a919)),x83443))+P106(f857(f857(f286(a919),x83441),x83442))+~P106(f857(f857(f286(a919),f857(f857(f80(a919),x83443),x83441)),f857(f857(f80(a919),x83443),x83442)))
% 15.02/14.80 [8383]~E(f857(f857(f101(f927(x83831,a915)),f882(x83833,x83832,x83831)),f881(x83833,x83832,x83831)),f189(f927(x83831,a915)))+E(f857(f857(f101(f927(x83831,a915)),x83832),f36(f927(x83831,a915),x83833)),f189(f927(x83831,a915)))+P106(f857(f857(f328(f927(x83831,a915)),x83832),x83833))
% 15.02/14.80 [8397]E(x83971,f113(x83972))+~E(f857(f142(f920(x83972),f920(x83972),f134(x83972),f113(x83972)),x83973),f113(x83972))+~P106(f857(f857(f328(f920(x83972)),x83971),f857(f172(f920(x83972)),x83973)))
% 15.02/14.80 [8452]E(x84521,f189(f927(f927(x84522,a915),a915)))+P106(f857(f857(f328(f927(x84522,a915)),f384(x84523,x84521,x84522)),x84521))+P106(f857(f857(f234(f927(x84522,a915)),f37(f927(x84522,a915),x84521)),x84523))
% 15.02/14.80 [8458]~P72(x84581)+~P77(x84581)+E(f857(f857(f8(a1,x84581),f857(f857(f10(a919,x84581,a1),x84582),a104)),f857(f309(a919,a1,f100(a1)),x84583)),f857(f857(f8(a919,x84581),x84582),x84583))
% 15.02/14.80 [8459]~P72(x84591)+~P77(x84591)+E(f857(f857(f11(a1,x84591),f857(f857(f10(a919,x84591,a1),x84592),a104)),f857(f309(a919,a1,f100(a1)),x84593)),f857(f857(f11(a919,x84591),x84592),x84593))
% 15.02/14.80 [8501]~P106(f857(f60(x85011),x85013))+~P106(f857(f857(f235(a919),f2(a919)),f857(x85012,f898(x85012,x85013,x85011))))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f11(x85011,a919),x85012),x85013)))
% 15.02/14.80 [8502]~P106(f857(f60(x85021),x85023))+~P106(f857(f857(f235(a919),f2(a919)),f857(x85022,f911(x85022,x85023,x85021))))+P106(f857(f857(f235(a919),f2(a919)),f857(f857(f11(x85021,a919),x85022),x85023)))
% 15.02/14.80 [8538]~P66(x85382)+E(x85381,f77(x85382))+E(f857(f857(f290(x85382),f857(f857(f3(x85382),f857(f857(f243(x85382),x85381),x85383)),f77(x85382))),f857(f857(f3(x85382),x85381),f77(x85382))),f857(f857(f8(a919,x85382),f857(f243(x85382),x85381)),f857(f301(a919,f2(a919)),x85383)))
% 15.02/14.80 [8595]E(x85951,f2(a919))+~P106(f857(x85953,f857(f857(f35(a919),x85952),x85951)))+P106(f857(f857(f235(a919),x85952),f857(f857(f80(a919),x85951),f857(a112,f370(x85951,x85952,x85953)))))
% 15.02/14.80 [8613]P106(f857(x86131,f2(a919)))+~P106(f857(x86131,f857(f857(f35(a919),x86132),x86133)))+P106(f857(f857(f235(a919),x86132),f857(f857(f80(a919),x86133),f857(a112,f370(x86133,x86132,x86131)))))
% 15.02/14.80 [8651]E(x86511,f2(a919))+~P106(f857(x86513,f857(f857(f35(a919),x86512),x86511)))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x86511),f370(x86511,x86512,x86513))),x86512))
% 15.02/14.80 [8682]P106(f857(x86821,f2(a919)))+~P106(f857(x86821,f857(f857(f35(a919),x86823),x86822)))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x86822),f370(x86822,x86823,x86821))),x86823))
% 15.02/14.80 [8690]~P109(x86901)+E(f857(f857(f148(x86901,x86901,f7(x86901)),x86902),x86903),f149(x86901,x86901,f7(x86901),x86902,x86903))+P106(f857(f857(f328(x86901),x86902),f857(f172(x86901),x86903)))
% 15.02/14.80 [8725]~E(f857(x87253,f585(x87252,x87253,x87251)),f857(x87253,f588(x87252,x87253,x87251)))+~P61(x87251,f857(x87253,f586(x87252,x87253,x87251)))+P61(x87251,f857(f857(f39(x87252,f927(x87251,f927(x87251,a915))),f241(f927(x87252,a915))),x87253))
% 15.02/14.80 [8734]E(x87341,f189(f927(f927(x87342,a915),a915)))+~P106(f857(f857(f234(f927(x87342,a915)),f384(x87343,x87341,x87342)),x87343))+P106(f857(f857(f234(f927(x87342,a915)),f37(f927(x87342,a915),x87341)),x87343))
% 15.02/14.80 [8794]~P68(x87941)+~P106(f857(f857(f235(x87941),x87942),x87943))+P106(f857(f857(f235(x87941),x87942),f857(f857(f290(x87941),f857(f857(f79(x87941),x87942),x87943)),f857(f857(f79(x87941),f77(x87941)),f77(x87941)))))
% 15.02/14.80 [8852]~P106(f857(f857(x88521,f385(x88521,x88523,x88522)),f387(x88521,x88523,x88522)))+P106(f857(f857(x88521,x88522),x88523))+~P106(f857(f314(f926(a1,a1),a51),f857(f857(f251(a1,a1),x88522),x88523)))
% 15.02/14.80 [8853]~P106(f857(f857(x88531,f389(x88531,x88533,x88532)),f390(x88531,x88533,x88532)))+P106(f857(f857(x88531,x88532),x88533))+~P106(f857(f314(f926(a1,a1),a57),f857(f857(f251(a1,a1),x88532),x88533)))
% 15.02/14.80 [8854]~P106(f857(f857(x88541,f393(x88541,x88543,x88542)),f394(x88541,x88543,x88542)))+P106(f857(f857(x88541,x88542),x88543))+~P106(f857(f314(f926(a919,a919),a220),f857(f857(f251(a919,a919),x88542),x88543)))
% 15.02/14.80 [8855]~P106(f857(f857(x88551,f402(x88551,x88553,x88552)),f404(x88551,x88553,x88552)))+P106(f857(f857(x88551,x88552),x88553))+~P106(f857(f314(f926(a1,a1),a222),f857(f857(f251(a1,a1),x88552),x88553)))
% 15.02/14.80 [8856]~P106(f857(f857(x88561,f676(x88561,x88563,x88562)),f679(x88561,x88563,x88562)))+P106(f857(f857(x88561,x88562),x88563))+~P106(f857(f314(f926(a1,a1),a182),f857(f857(f251(a1,a1),x88562),x88563)))
% 15.02/14.80 [8857]~P106(f857(f857(x88571,f772(x88571,x88573,x88572)),f773(x88571,x88573,x88572)))+P106(f857(f857(x88571,x88572),x88573))+~P106(f857(f314(f926(a1,a1),a133),f857(f857(f251(a1,a1),x88572),x88573)))
% 15.02/14.80 [9130]P106(f857(f857(x91301,x91302),x91303))+P106(f857(f314(f926(a919,a919),a220),f857(f857(f251(a919,a919),f393(x91301,x91303,x91302)),f394(x91301,x91303,x91302))))+~P106(f857(f314(f926(a919,a919),a220),f857(f857(f251(a919,a919),x91302),x91303)))
% 15.02/14.80 [9131]P106(f857(f857(x91311,x91312),x91313))+P106(f857(f314(f926(a1,a1),a51),f857(f857(f251(a1,a1),f385(x91311,x91313,x91312)),f387(x91311,x91313,x91312))))+~P106(f857(f314(f926(a1,a1),a51),f857(f857(f251(a1,a1),x91312),x91313)))
% 15.02/14.80 [9132]P106(f857(f857(x91321,x91322),x91323))+P106(f857(f314(f926(a1,a1),a57),f857(f857(f251(a1,a1),f389(x91321,x91323,x91322)),f390(x91321,x91323,x91322))))+~P106(f857(f314(f926(a1,a1),a57),f857(f857(f251(a1,a1),x91322),x91323)))
% 15.02/14.80 [9133]P106(f857(f857(x91331,x91332),x91333))+P106(f857(f314(f926(a1,a1),a222),f857(f857(f251(a1,a1),f402(x91331,x91333,x91332)),f404(x91331,x91333,x91332))))+~P106(f857(f314(f926(a1,a1),a222),f857(f857(f251(a1,a1),x91332),x91333)))
% 15.02/14.80 [9134]P106(f857(f857(x91341,x91342),x91343))+P106(f857(f314(f926(a1,a1),a182),f857(f857(f251(a1,a1),f676(x91341,x91343,x91342)),f679(x91341,x91343,x91342))))+~P106(f857(f314(f926(a1,a1),a182),f857(f857(f251(a1,a1),x91342),x91343)))
% 15.02/14.80 [9135]P106(f857(f857(x91351,x91352),x91353))+P106(f857(f314(f926(a1,a1),a133),f857(f857(f251(a1,a1),f772(x91351,x91353,x91352)),f773(x91351,x91353,x91352))))+~P106(f857(f314(f926(a1,a1),a133),f857(f857(f251(a1,a1),x91352),x91353)))
% 15.02/14.80 [9468]~P106(f857(f60(x94681),x94683))+P106(f857(f857(f328(f926(f927(x94681,a915),f927(x94681,a915))),f857(f857(f251(f927(x94681,a915),f927(x94681,a915)),x94682),x94683)),f313(x94681)))+~P106(f857(f857(f235(f927(x94681,a915)),x94682),x94683))
% 15.02/14.80 [9543]~P61(x95431,f857(x95433,f586(x95432,x95433,x95431)))+P61(x95431,f857(f857(f39(x95432,f927(x95431,f927(x95431,a915))),f241(f927(x95432,a915))),x95433))+~E(f857(f857(f101(f927(x95431,a915)),f248(x95431,x95431,f857(x95433,f585(x95432,x95433,x95431)))),f249(x95431,x95431,f857(x95433,f588(x95432,x95433,x95431)))),f189(f927(x95431,a915)))
% 15.02/14.80 [9752]P54(x97521,x97522,x97523)+P106(f857(f857(f328(f926(x97521,x97521)),f575(x97523,x97522,x97521)),x97523))+~P106(f857(f857(f328(f926(x97521,x97521)),f857(f857(f251(x97521,x97521),f574(x97523,x97522,x97521)),f574(x97523,x97522,x97521))),x97523))
% 15.02/14.80 [10347]P54(x103471,x103472,x103473)+~P106(f857(f857(f256(x103471,x103471,a915),f857(f857(f9(x103471,f927(x103471,a915),f927(x103471,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x103471,a915),f927(x103471,a915)),x103471),f10(a915,a915,x103471)),f857(f857(f10(a915,f927(a915,a915),x103471),a325),f857(f857(f9(x103471,f927(x103471,a915),a915),f328(x103471)),x103472)))),f857(f857(f9(x103471,f927(x103471,a915),a915),f328(x103471)),x103472))),f575(x103473,x103472,x103471)))+~P106(f857(f857(f328(f926(x103471,x103471)),f857(f857(f251(x103471,x103471),f574(x103473,x103472,x103471)),f574(x103473,x103472,x103471))),x103473))
% 15.02/14.80 [5854]~P62(x58542)+E(x58541,f2(x58542))+E(f857(f857(f35(x58542),f857(f857(f80(x58542),x58543),x58541)),x58541),x58543)
% 15.02/14.80 [5855]~P62(x58552)+E(x58551,f2(x58552))+E(f857(f857(f35(x58552),f857(f857(f80(x58552),x58551),x58553)),x58551),x58553)
% 15.02/14.80 [6506]~P62(x65061)+E(f857(f857(f80(x65061),f857(f857(f35(x65061),x65062),x65063)),x65063),x65062)+~P106(f857(f857(f286(x65061),x65063),x65062))
% 15.02/14.80 [6668]~P72(x66681)+~E(f857(x66682,f2(a919)),f2(x66681))+E(f857(f857(f8(a919,x66681),x66682),f857(f301(a919,f857(a112,f2(a919))),x66683)),f857(f857(f8(a919,x66681),x66682),f857(f301(a919,f2(a919)),x66683)))
% 15.02/14.80 [6802]~P62(x68022)+E(x68021,f2(x68022))+E(f857(f857(f35(x68022),f857(f857(f79(x68022),x68023),x68021)),x68021),f857(f857(f79(x68022),f857(f857(f35(x68022),x68023),x68021)),f77(x68022)))
% 15.02/14.80 [6803]~P62(x68032)+E(x68031,f2(x68032))+E(f857(f857(f35(x68032),f857(f857(f79(x68032),x68031),x68033)),x68031),f857(f857(f79(x68032),f857(f857(f35(x68032),x68033),x68031)),f77(x68032)))
% 15.02/14.80 [7023]~P106(f857(x70233,f2(a1)))+P106(f857(f857(f234(a919),x70231),x70232))+P106(f857(x70233,f857(f100(a1),f857(f857(f3(a919),x70232),x70231))))
% 15.02/14.80 [7128]P106(f857(f857(f235(a919),x71282),x71281))+P106(f857(f857(f234(a919),x71281),x71282))+P106(f857(x71283,f857(f100(a1),f857(f857(f3(a919),x71282),x71281))))
% 15.02/14.80 [7200]E(f857(f857(f79(a919),f857(f103(a919),x72001)),f857(f857(f79(a919),f857(f103(a919),x72002)),x72003)),f857(f857(f79(a919),f857(f103(a919),x72001)),x72003))+P106(f857(a194,f857(f103(a1),x72001)))+~P106(f857(a194,f857(f103(a1),x72002)))
% 15.02/14.80 [7280]~E(x72802,f857(f857(f35(a919),x72803),x72801))+~P106(f857(f857(f235(a919),f2(a919)),x72801))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x72801),x72802)),x72803))
% 15.02/14.80 [7396]~P106(f857(f60(x73961),x73963))+~P106(f857(f60(x73961),x73962))+P106(f857(f60(x73961),f857(f857(f110(f927(x73961,a915)),x73962),x73963)))
% 15.02/14.80 [7446]~P40(x74461,x74463)+~P40(x74461,x74462)+P40(x74461,f857(f857(f101(f927(f926(x74461,x74461),a915)),x74462),x74463))
% 15.02/14.80 [7447]~P53(x74471,x74473)+~P53(x74471,x74472)+P53(x74471,f857(f857(f110(f927(f926(x74471,x74471),a915)),x74472),x74473))
% 15.02/14.80 [7448]~P53(x74481,x74483)+~P53(x74481,x74482)+P53(x74481,f857(f857(f101(f927(f926(x74481,x74481),a915)),x74482),x74483))
% 15.02/14.80 [7689]~P109(x76891)+~P106(f857(f60(x76891),x76892))+E(f139(x76891,f857(f857(f3(f927(x76891,a915)),x76892),f857(f857(f308(x76891),x76893),f189(f927(x76891,a915))))),f170(x76891,x76893,f139(x76891,x76892)))
% 15.02/14.80 [7751]P106(f857(x77511,f2(a1)))+~P106(f857(f857(f235(a919),x77512),x77513))+~P106(f857(x77511,f857(f100(a1),f857(f857(f3(a919),x77512),x77513))))
% 15.02/14.80 [7769]~P106(f857(f60(x77691),x77692))+E(f857(f34(x77691),f857(f857(f3(f927(x77691,a915)),x77692),f857(f857(f308(x77691),x77693),f189(f927(x77691,a915))))),f857(f34(x77691),x77692))+P106(f857(f857(f328(x77691),x77693),x77692))
% 15.02/14.80 [7902]~P127(x79021)+~P106(f857(f857(f235(x79021),f77(x79021)),x79022))+P106(f857(f857(f235(x79021),f77(x79021)),f857(f857(f80(x79021),x79022),f857(f857(f243(x79021),x79022),x79023))))
% 15.02/14.80 [7944]~P106(f857(f60(x79441),x79443))+E(f857(f857(f3(a919),f857(f34(x79441),x79442)),f857(f34(x79441),x79443)),f857(f34(x79441),f857(f857(f3(f927(x79441,a915)),x79442),x79443)))+~P106(f857(f857(f234(f927(x79441,a915)),x79443),x79442))
% 15.02/14.80 [8001]~P106(f857(f857(f234(a919),x80012),x80013))+~P106(f857(f857(f234(a919),x80011),f857(f857(f3(a919),x80013),x80012)))+P106(f857(f857(f234(a919),f857(f857(f79(a919),x80011),x80012)),x80013))
% 15.02/14.80 [8054]P106(f857(f60(x80541),x80542))+~P106(f857(f60(x80541),x80543))+~P106(f857(f60(x80541),f857(f857(f3(f927(x80541,a915)),x80542),x80543)))
% 15.02/14.80 [8060]~P106(f857(f60(x80601),x80602))+E(f857(f34(x80601),f857(f857(f3(f927(x80601,a915)),x80602),f857(f857(f308(x80601),x80603),f189(f927(x80601,a915))))),f857(f857(f3(a919),f857(f34(x80601),x80602)),f77(a919)))+~P106(f857(f857(f328(x80601),x80603),x80602))
% 15.02/14.80 [8136]P61(x81361,x81362)+~P61(x81361,x81363)+~P106(f857(f857(f234(f927(x81361,f927(x81361,a915))),x81362),x81363))
% 15.02/14.80 [8177]~P106(f857(f857(f234(a919),x81773),x81772))+P106(f857(f857(f234(a919),x81771),f857(f857(f3(a919),x81772),x81773)))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),x81771),x81773)),x81772))
% 15.02/14.80 [8195]P39(x81951,x81952)+~P39(x81951,x81953)+~P106(f857(f857(f234(f927(f926(x81951,x81951),a915)),x81952),x81953))
% 15.02/14.80 [8196]P59(x81961,x81962)+~P59(x81961,x81963)+~P106(f857(f857(f234(f927(f926(x81961,x81961),a915)),x81962),x81963))
% 15.02/14.80 [8197]P41(x81971,x81972)+~P41(x81971,x81973)+~P106(f857(f857(f234(f927(f926(x81971,x81971),a915)),x81972),x81973))
% 15.02/14.80 [8430]~P127(x84301)+~P106(f857(f857(f235(x84301),f77(x84301)),x84302))+P106(f857(f857(f235(x84301),f857(f857(f243(x84301),x84302),x84303)),f857(f857(f80(x84301),x84302),f857(f857(f243(x84301),x84302),x84303))))
% 15.02/14.80 [8520]~P106(f857(x85201,f2(a1)))+~P106(f857(x85201,f857(f857(f3(a1),f857(f100(a1),x85202)),f857(f100(a1),x85203))))+P106(f857(x85201,f857(f100(a1),f857(f857(f3(a919),x85202),x85203))))
% 15.02/14.80 [8535]~P106(f857(f857(f234(a919),x85353),x85352))+P106(f857(x85351,f857(f857(f3(a1),f857(f100(a1),x85352)),f857(f100(a1),x85353))))+~P106(f857(x85351,f857(f100(a1),f857(f857(f3(a919),x85352),x85353))))
% 15.02/14.80 [8554]P106(f857(f857(f235(a919),x85541),x85542))+~P106(f857(x85543,f857(f857(f3(a1),f857(f100(a1),x85541)),f857(f100(a1),x85542))))+P106(f857(x85543,f857(f100(a1),f857(f857(f3(a919),x85541),x85542))))
% 15.02/14.80 [8607]~P129(x86072)+E(x86071,f2(x86072))+P106(f857(f857(f235(x86072),f2(x86072)),f857(f857(f79(x86072),f857(f857(f80(x86072),x86073),x86073)),f857(f857(f80(x86072),x86071),x86071))))
% 15.02/14.80 [8608]~P129(x86082)+E(x86081,f2(x86082))+P106(f857(f857(f235(x86082),f2(x86082)),f857(f857(f79(x86082),f857(f857(f80(x86082),x86081),x86081)),f857(f857(f80(x86082),x86083),x86083))))
% 15.02/14.80 [8707]~P106(f857(f857(f235(a919),f2(a919)),x87071))+~P106(f857(f857(f235(a1),x87072),x87073))+P106(f857(f857(f235(a1),f857(f857(f80(a1),f857(f100(a1),x87071)),x87072)),f857(f857(f80(a1),f857(f100(a1),x87071)),x87073)))
% 15.02/14.80 [8763]E(f857(f857(f101(f927(x87631,a915)),x87632),f36(f927(x87631,a915),x87633)),f189(f927(x87631,a915)))+P106(f857(f857(f328(f927(x87631,a915)),x87632),x87633))+P106(f857(f857(f328(f927(x87631,a915)),f882(x87633,x87632,x87631)),f857(f857(f308(f927(x87631,a915)),x87632),x87633)))
% 15.02/14.80 [8764]E(f857(f857(f101(f927(x87641,a915)),x87642),f36(f927(x87641,a915),x87643)),f189(f927(x87641,a915)))+P106(f857(f857(f328(f927(x87641,a915)),x87642),x87643))+P106(f857(f857(f328(f927(x87641,a915)),f881(x87643,x87642,x87641)),f857(f857(f308(f927(x87641,a915)),x87642),x87643)))
% 15.02/14.80 [8793]E(x87931,x87932)+~E(f857(f190(f920(x87933)),x87931),f857(f190(f920(x87933)),x87932))+P106(f857(f857(f328(f926(x87933,x87933)),f665(x87933,x87931,x87932)),f857(f172(f926(x87933,x87933)),f857(f857(f181(x87933,x87933),x87932),x87931))))
% 15.02/14.80 [9043]E(f306(x90431,x90432),f306(x90431,x90433))+~P106(f857(f857(f234(f927(f926(x90431,x90431),a915)),x90433),f306(x90431,x90432)))+~P106(f857(f857(f234(f927(f926(x90431,x90431),a915)),x90432),x90433))
% 15.02/14.80 [9110]~P54(x91101,f241(f927(x91101,a915)),x91103)+P106(f857(f857(f234(f927(f926(f920(x91101),f920(x91101)),a915)),f157(x91101,x91102)),f158(x91101,x91103)))+~P106(f857(f857(f234(f927(f926(x91101,x91101),a915)),x91102),x91103))
% 15.02/14.80 [9305]P39(x93051,x93052)+~P106(f857(f857(f328(x93051),x93053),f617(x93052,x93051)))+P106(f857(f857(f328(f926(x93051,x93051)),f857(f857(f251(x93051,x93051),f640(x93052,x93051,x93053)),x93053)),x93052))
% 15.02/14.80 [9340]~P106(f857(f60(x93401),x93402))+P106(f857(f60(f927(x93401,a915)),f857(f857(f59(x93401),x93402),x93403)))+~P106(f857(f857(f234(f927(f926(x93401,x93401),a915)),x93403),f857(f857(f253(x93401,x93401),x93402),f857(f18(f927(x93401,a915),x93401),x93402))))
% 15.02/14.80 [9376]P54(x93761,x93762,x93763)+P106(f857(f857(f328(x93761),f539(x93763,x93762,x93761)),x93762))+~P106(f857(f857(f234(f927(f926(x93761,x93761),a915)),x93763),f857(f857(f253(x93761,x93761),x93762),f857(f18(f927(x93761,a915),x93761),x93762))))
% 15.02/14.80 [9377]P54(x93771,x93772,x93773)+P106(f857(f857(f328(x93771),f549(x93772,x93773,x93771)),x93772))+~P106(f857(f857(f234(f927(f926(x93771,x93771),a915)),x93773),f857(f857(f253(x93771,x93771),x93772),f857(f18(f927(x93771,a915),x93771),x93772))))
% 15.02/14.80 [9411]~P68(x94111)+~P106(f857(f857(f235(x94111),x94112),x94113))+P106(f857(f857(f235(x94111),f857(f857(f290(x94111),f857(f857(f79(x94111),x94112),x94113)),f857(f857(f79(x94111),f77(x94111)),f77(x94111)))),x94113))
% 15.02/14.80 [9441]~P67(x94411)+P106(f857(f857(f234(x94411),x94412),x94413))+~P106(f857(f857(f234(x94411),f857(f857(f80(x94411),f907(x94413,x94412,x94411)),x94412)),x94413))
% 15.02/14.80 [9578]E(f857(f190(f920(f920(x95781))),f857(f136(f920(x95781),f857(f857(f10(a919,a915,f920(x95781)),f857(f235(a919),x95782)),f190(f920(x95781)))),f179(x95781,x95783))),f857(f190(f920(x95781)),f857(f857(f164(f920(x95781)),x95783),x95782)))+~P14(a919,f857(f168(a919),f857(f857(f154(f920(x95781),a919),f190(f920(x95781))),x95783)))+~P106(f857(f857(f235(a919),x95782),f857(f190(f920(f920(x95781))),x95783)))
% 15.02/14.80 [9699]~P39(x96991,x96992)+P28(x96991,f857(f857(f251(f927(f926(x96991,x96991),a915),f927(f926(x96991,x96991),a915)),x96992),x96993))+~P106(f857(f857(f234(f927(f926(x96991,x96991),a915)),f857(f857(f288(x96991,x96991,x96991),x96992),x96993)),x96992))
% 15.02/14.80 [9705]E(f857(f857(f154(f920(x97051),x97051),f857(f857(f9(f920(x97051),a919,x97051),f164(x97051)),x97052)),f857(f136(f920(x97051),f857(f857(f10(a919,a915,f920(x97051)),f857(f235(a919),x97052)),f190(f920(x97051)))),f179(x97051,x97053))),f857(f857(f164(f920(x97051)),x97053),x97052))+~P14(a919,f857(f168(a919),f857(f857(f154(f920(x97051),a919),f190(f920(x97051))),x97053)))+~P106(f857(f857(f235(a919),x97052),f857(f190(f920(f920(x97051))),x97053)))
% 15.02/14.80 [9840]P54(x98401,x98402,x98403)+~P106(f857(f857(f328(f926(x98401,x98401)),f857(f857(f251(x98401,x98401),f539(x98403,x98402,x98401)),f539(x98403,x98402,x98401))),x98403))+~P106(f857(f857(f234(f927(f926(x98401,x98401),a915)),x98403),f857(f857(f253(x98401,x98401),x98402),f857(f18(f927(x98401,a915),x98401),x98402))))
% 15.02/14.80 [9841]P54(x98411,x98412,x98413)+~P106(f857(f857(f328(f926(x98411,x98411)),f857(f857(f251(x98411,x98411),f549(x98412,x98413,x98411)),f549(x98412,x98413,x98411))),x98413))+~P106(f857(f857(f234(f927(f926(x98411,x98411),a915)),x98413),f857(f857(f253(x98411,x98411),x98412),f857(f18(f927(x98411,a915),x98411),x98412))))
% 15.02/14.80 [10009]~P143(x100091)+~P126(x100091)+E(f857(f857(f290(x100091),f857(f102(x100091),f857(f857(f72(f926(a1,a1),a1,x100092,f250(a1,a1)),f213(x100092)),x100093))),f857(f102(x100091),f857(f857(f72(f926(a1,a1),a1,x100092,f255(a1,a1)),f213(x100092)),x100093))),f223(x100092,x100091,x100093))
% 15.02/14.80 [10215]~E(x102153,f2(a919))+~E(f857(f190(f920(x102151)),f857(f857(f164(f920(x102151)),x102152),f713(x102153,x102151,x102152))),x102153)+E(f857(f857(f154(a919,f920(x102151)),f857(f857(f9(a919,f920(a919),f920(x102151)),f857(f857(f10(f927(a919,x102151),f927(f920(a919),f920(x102151)),a919),f154(a919,x102151)),f857(f9(a919,a919,x102151),f857(f857(f10(f920(x102151),f927(a919,x102151),a919),f164(x102151)),f857(f164(f920(x102151)),x102152))))),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(f920(x102151))),x102152))))),f139(a919,f857(f301(a919,f2(a919)),x102153))),f179(x102151,x102152))
% 15.02/14.80 [10216]E(x102161,f113(f920(x102162)))+~E(f857(f190(f920(x102162)),f857(f857(f164(f920(x102162)),x102161),f713(x102163,x102162,x102161))),x102163)+E(f857(f857(f154(a919,f920(x102162)),f857(f857(f9(a919,f920(a919),f920(x102162)),f857(f857(f10(f927(a919,x102162),f927(f920(a919),f920(x102162)),a919),f154(a919,x102162)),f857(f9(a919,a919,x102162),f857(f857(f10(f920(x102162),f927(a919,x102162),a919),f164(x102162)),f857(f164(f920(x102162)),x102161))))),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(f920(x102162))),x102161))))),f139(a919,f857(f301(a919,f2(a919)),x102163))),f179(x102162,x102161))
% 15.02/14.80 [10217]~E(x102173,f2(a919))+E(f857(f857(f154(a919,f920(x102171)),f857(f857(f9(a919,f920(a919),f920(x102171)),f857(f857(f10(f927(a919,x102171),f927(f920(a919),f920(x102171)),a919),f154(a919,x102171)),f857(f9(a919,a919,x102171),f857(f857(f10(f920(x102171),f927(a919,x102171),a919),f164(x102171)),f857(f164(f920(x102171)),x102172))))),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(f920(x102171))),x102172))))),f139(a919,f857(f301(a919,f2(a919)),x102173))),f179(x102171,x102172))+P106(f857(f857(f235(a919),f713(x102173,x102171,x102172)),f857(f190(f920(f920(x102171))),x102172)))
% 15.02/14.80 [10218]E(x102181,f113(f920(x102182)))+E(f857(f857(f154(a919,f920(x102182)),f857(f857(f9(a919,f920(a919),f920(x102182)),f857(f857(f10(f927(a919,x102182),f927(f920(a919),f920(x102182)),a919),f154(a919,x102182)),f857(f9(a919,a919,x102182),f857(f857(f10(f920(x102182),f927(a919,x102182),a919),f164(x102182)),f857(f164(f920(x102182)),x102181))))),f139(a919,f857(f301(a919,f2(a919)),f857(f190(f920(f920(x102182))),x102181))))),f139(a919,f857(f301(a919,f2(a919)),x102183))),f179(x102182,x102181))+P106(f857(f857(f235(a919),f713(x102183,x102182,x102181)),f857(f190(f920(f920(x102182))),x102181)))
% 15.02/14.80 [7941]E(f857(f857(f79(a919),f857(f103(a919),x79411)),f857(f857(f79(a919),f857(f103(a919),x79412)),x79413)),f857(f857(f79(a919),f857(f103(a919),f857(f857(f79(a1),x79411),x79412))),x79413))+P106(f857(a194,f857(f103(a1),x79411)))+P106(f857(a194,f857(f103(a1),x79412)))
% 15.02/14.80 [8699]~P106(f857(f60(x86991),x86992))+~P106(f857(f857(f328(x86991),x86993),x86992))+E(f857(a112,f857(f34(x86991),f857(f857(f3(f927(x86991,a915)),x86992),f857(f857(f308(x86991),x86993),f189(f927(x86991,a915)))))),f857(f34(x86991),x86992))
% 15.02/14.80 [8715]~P106(f857(f60(x87151),x87152))+~P106(f857(f857(f328(x87151),x87153),x87152))+E(f857(f857(f79(a919),f77(a919)),f857(f34(x87151),f857(f857(f3(f927(x87151,a915)),x87152),f857(f857(f308(x87151),x87153),f189(f927(x87151,a915)))))),f857(f34(x87151),x87152))
% 15.02/14.80 [8802]~P109(x88021)+~P106(f857(f60(x88021),x88023))+E(f857(f857(f148(x88021,x88021,f7(x88021)),x88022),f139(x88021,f857(f857(f3(f927(x88021,a915)),x88023),f857(f857(f308(x88021),x88022),f189(f927(x88021,a915)))))),f139(x88021,f857(f857(f308(x88021),x88022),x88023)))
% 15.02/14.80 [8968]~P106(f857(f60(x89681),x89683))+~P106(f857(f60(x89681),x89682))+E(f857(f857(f79(a919),f857(f34(x89681),f857(f857(f110(f927(x89681,a915)),x89682),x89683))),f857(f34(x89681),f857(f857(f101(f927(x89681,a915)),x89682),x89683))),f857(f857(f79(a919),f857(f34(x89681),x89682)),f857(f34(x89681),x89683)))
% 15.02/14.80 [10164]~P26(x101641,f927(f927(x101641,a915),a915),f857(f857(f9(x101641,f927(f926(x101641,x101641),a915),f927(f927(x101641,a915),a915)),f857(f857(f10(f927(x101641,a915),f927(f927(f926(x101641,x101641),a915),f927(f927(x101641,a915),a915)),x101641),f59(x101641)),f857(f857(f9(x101641,f927(x101641,a915),f927(x101641,a915)),f308(x101641)),f189(f927(x101641,a915))))),x101643),x101642)+~P106(f857(f60(x101641),x101642))+E(f857(f34(f927(x101641,a915)),f857(f857(f59(x101641),x101642),x101643)),f857(f34(x101641),x101642))
% 15.02/14.80 [8209]~P94(x82091)+P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x82093)))+E(f857(f857(f243(x82091),x82092),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),x82093),x82093)),a97))),f77(x82091))
% 15.02/14.80 [9681]~P94(x96811)+~P106(f857(f857(f234(a1),f2(a1)),f857(f103(a1),x96813)))+E(f857(f857(f243(x96811),x96812),f857(f103(a919),f857(f857(f3(a1),f857(f857(f79(a1),x96813),x96813)),a97))),f857(f857(f85(x96811,x96811),f857(f857(f243(x96811),x96812),f857(f103(a919),x96813))),f857(f857(f20(x96811,x96811,x96811),f857(f857(f10(x96811,f927(x96811,x96811),x96811),f80(x96811)),f857(f80(x96811),x96812))),f7(x96811))))
% 15.02/14.80 [10072]~P106(f857(f137(x100721),x100723))+~P106(f857(f857(f328(x100721),x100722),f857(f172(x100721),x100723)))+E(f857(f857(f138(x100721),f857(f190(f920(x100721)),f177(x100721,f857(f857(f10(a915,a915,x100721),a321),f857(f857(f9(x100721,x100721,a915),a324),x100722)),f857(f168(x100721),x100723)))),f857(f168(x100721),x100723)),f857(f857(f151(x100721),x100722),f857(f168(x100721),f177(x100721,f857(f857(f10(a915,a915,x100721),a321),f857(f857(f9(x100721,x100721,a915),a324),x100722)),x100723))))
% 15.02/14.80 [10134]P106(f857(f857(f234(f927(f926(x101341,x101341),a915)),f306(x101341,x101342)),x101343))+~P106(f857(f857(f234(f927(f926(x101341,x101341),a915)),f306(x101341,f189(f927(f926(x101341,x101341),a915)))),x101343))+~P106(f857(f857(f234(f927(f926(x101341,x101341),a915)),f857(f857(f288(x101341,x101341,x101341),f857(f857(f101(f927(f926(x101341,x101341),a915)),f306(x101341,x101342)),x101343)),x101342)),x101343))
% 15.02/14.80 [9989]~P106(f857(f60(x99891),f857(f261(x99891),x99893)))+~P106(f857(f60(x99891),f857(f261(x99891),x99892)))+P106(f857(f60(x99891),f857(f261(x99891),f857(f857(f20(x99891,a915,a915),f857(f857(f10(a915,f927(a915,a915),x99891),a326),x99892)),x99893))))
% 15.02/14.80 [10281]P106(f857(f857(f234(f927(f926(x102811,x102811),a915)),f857(f857(f288(x102811,x102811,x102811),x102812),f306(x102811,x102812))),x102813))+~P106(f857(f857(f234(f927(f926(x102811,x102811),a915)),x102812),x102813))+~P106(f857(f857(f234(f927(f926(x102811,x102811),a915)),f857(f857(f288(x102811,x102811,x102811),f857(f857(f101(f927(f926(x102811,x102811),a915)),f857(f857(f288(x102811,x102811,x102811),x102812),f306(x102811,x102812))),x102813)),x102812)),x102813))
% 15.02/14.80 [10231]~P120(x102312)+E(x102311,f2(x102312))+~E(f857(f857(f79(x102312),f857(f857(f243(x102312),x102313),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x102312),x102311),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f2(x102312))
% 15.02/14.80 [10232]~P120(x102322)+E(x102321,f2(x102322))+~E(f857(f857(f79(x102322),f857(f857(f243(x102322),x102321),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x102322),x102323),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f2(x102322))
% 15.02/14.80 [10237]~P106(f857(f137(x102371),x102373))+~P106(f857(f857(f328(x102371),x102372),f857(f172(x102371),x102373)))+E(f857(f168(x102371),f857(f171(x102371),f857(f857(f138(x102371),f857(f190(f920(x102371)),f177(x102371,f857(f857(f10(a915,a915,x102371),a321),f857(f857(f9(x102371,x102371,a915),a324),x102372)),x102373))),x102373))),f177(x102371,f857(f857(f10(a915,a915,x102371),a321),f857(f857(f9(x102371,x102371,a915),a324),x102372)),f857(f168(x102371),x102373)))
% 15.02/14.80 [10329]~P120(x103292)+E(x103291,f2(x103292))+P106(f857(f857(f235(x103292),f2(x103292)),f857(f857(f79(x103292),f857(f857(f243(x103292),x103293),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103292),x103291),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))))
% 15.02/14.80 [10330]~P120(x103302)+E(x103301,f2(x103302))+P106(f857(f857(f235(x103302),f2(x103302)),f857(f857(f79(x103302),f857(f857(f243(x103302),x103301),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103302),x103303),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))))
% 15.02/14.80 [10385]~P120(x103851)+P106(f857(f857(f234(x103851),f2(x103851)),x103852))+~P106(f857(f857(f234(x103851),f2(x103851)),f857(f857(f243(x103851),x103852),f857(a112,f857(f857(f80(a919),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),x103853)))))
% 15.02/14.80 [5686]~P25(x56861,x56864,x56863)+P25(x56861,x56862,x56863)+~P25(x56861,x56862,x56864)
% 15.02/14.80 [5150]~E(x51502,f89(x51503,x51501))+P106(f857(x51501,x51502))+~P106(f857(x51501,x51504))
% 15.02/14.80 [5395]E(f67(x53953,x53952,x53954),x53952)+E(x53951,f739(x53952,x53953,x53954))+~P106(f857(x53954,x53951))
% 15.02/14.80 [6725]E(f67(x67251,x67252,x67253),f84(x67251,x67253))+~E(f775(x67252,x67251,x67253,x67254),x67254)+~P106(f857(x67253,x67254))
% 15.02/14.80 [6935]~P39(x69352,x69354)+~P39(x69351,x69353)+P39(f926(x69351,x69352),f318(x69351,x69352,x69353,x69354))
% 15.02/14.80 [6936]~P40(x69362,x69364)+~P40(x69361,x69363)+P40(f926(x69361,x69362),f318(x69361,x69362,x69363,x69364))
% 15.02/14.80 [5335]~P8(x53354,x53351)+~E(f857(x53351,x53352),f857(x53351,x53353))+P106(f857(f857(x53351,x53352),x53353))
% 15.02/14.80 [5499]~P8(x54994,x54991)+E(f857(x54991,x54992),f857(x54991,x54993))+~P106(f857(f857(x54991,x54992),x54993))
% 15.02/14.80 [5500]~P16(x55004,x55001)+E(f857(x55001,x55002),f857(x55001,x55003))+~P106(f857(f857(x55001,x55002),x55003))
% 15.02/14.80 [5593]~P19(x55933,x55934,x55931)+E(f857(x55931,x55932),f857(f62(x55933,x55934),x55932))+~P106(f857(f60(x55933),x55932))
% 15.02/14.80 [5594]~P10(x55943,x55944,x55941)+E(f857(x55941,x55942),f857(f62(x55943,x55944),x55942))+~P106(f857(f60(x55943),x55942))
% 15.02/14.80 [5721]~P8(x57214,x57211)+~P106(f857(f857(x57211,x57213),x57212))+P106(f857(f857(x57211,x57212),x57213))
% 15.02/14.80 [5722]~P52(x57224,x57221)+~P106(f857(f857(x57221,x57223),x57222))+P106(f857(f857(x57221,x57222),x57223))
% 15.02/14.80 [5723]~P16(x57234,x57231)+~P106(f857(f857(x57231,x57233),x57232))+P106(f857(f857(x57231,x57232),x57233))
% 15.02/14.80 [5724]~P16(x57243,x57241)+P106(f857(f857(x57241,x57242),x57242))+~P106(f857(f857(x57241,x57244),x57242))
% 15.02/14.80 [5725]~P16(x57253,x57251)+P106(f857(f857(x57251,x57252),x57252))+~P106(f857(f857(x57251,x57252),x57254))
% 15.02/14.80 [5796]E(x57961,x57962)+~E(f857(f250(x57963,x57964),x57961),f857(f250(x57963,x57964),x57962))+~E(f857(f255(x57963,x57964),x57961),f857(f255(x57963,x57964),x57962))
% 15.02/14.80 [5823]E(x58231,x58232)+~P106(f857(f47(x58233,x58234),x58232))+~P106(f857(f47(x58233,x58234),x58231))
% 15.02/14.80 [6014]~P72(x60142)+E(f232(x60141,x60142,x60143,x60144),f2(x60142))+P106(f857(f60(x60141),x60144))
% 15.02/14.80 [6062]~P8(x60623,x60622)+~P106(f857(x60621,x60624))+P106(f857(x60621,f819(x60621,x60622,x60623)))
% 15.02/14.80 [6159]~P106(f857(f314(x61591,x61592),x61594))+P106(f857(f314(x61591,x61592),x61593))+~P106(f857(f857(x61592,x61593),x61594))
% 15.02/14.80 [6970]~P31(x69701,x69703,x69704)+P106(f857(x69701,x69702))+~P106(f857(f857(f328(a1),x69702),f302(a1,x69703,x69704)))
% 15.02/14.80 [7163]~P8(x71631,x71633)+~P106(f857(x71632,x71634))+P106(f857(f857(f328(x71631),f819(x71632,x71633,x71631)),f269(x71631,x71633)))
% 15.02/14.80 [8049]E(x80491,f2(a919))+~P106(f857(x80492,x80493))+P106(f857(x80492,f770(x80492,x80493,x80491,x80494)))
% 15.02/14.80 [8131]~P109(x81312)+~P106(f857(f137(x81311),x81314))+P106(f857(f137(x81311),f150(x81311,x81312,x81313,x81314)))
% 15.02/14.80 [8176]E(f67(x81761,x81762,x81763),f84(x81761,x81763))+~P106(f857(x81763,x81764))+P106(f857(x81763,f775(x81762,x81761,x81763,x81764)))
% 15.02/14.80 [8357]~P106(f857(f60(x83572),x83574))+~P106(f857(f60(x83571),x83573))+P106(f857(f60(f925(x83571,x83572)),f312(x83571,x83572,x83573,x83574)))
% 15.02/14.80 [8358]~P106(f857(f137(x83582),x83584))+~P106(f857(f137(x83581),x83583))+P106(f857(f137(f926(x83581,x83582)),f58(x83581,x83582,x83583,x83584)))
% 15.02/14.80 [8361]P106(f857(f857(f328(f920(x83611)),f857(f857(f134(x83611),x83612),x83613)),f161(x83611,x83614)))+~P106(f857(f857(f328(f920(x83611)),x83613),f161(x83611,x83614)))+~P106(f857(f857(f328(f920(x83611)),x83612),f161(x83611,x83614)))
% 15.02/14.80 [8637]E(x86371,f2(a919))+P106(f857(x86372,x86373))+~P106(f857(x86372,f771(x86372,x86373,x86371,x86374)))
% 15.02/14.80 [8674]~P109(x86743)+~P106(f857(f137(x86741),f150(x86741,x86743,x86744,x86742)))+P106(f857(f137(x86741),x86742))
% 15.02/14.80 [8957]~P106(f857(f857(f328(f926(x89571,x89571)),f857(f857(f251(x89571,x89571),x89572),x89574)),f306(x89571,x89573)))+P106(f857(f857(f328(x89571),x89572),f315(x89571,x89573)))+~P106(f857(f857(f328(x89571),x89574),f315(x89571,x89573)))
% 15.02/14.80 [5319]~P72(x53192)+E(f857(f857(f8(x53191,x53192),x53193),x53194),f2(x53192))+P106(f857(f60(x53191),x53194))
% 15.02/14.80 [5322]~P77(x53222)+E(f857(f857(f11(x53221,x53222),x53223),x53224),f77(x53222))+P106(f857(f60(x53221),x53224))
% 15.02/14.80 [5463]~P73(x54633)+E(x54631,x54632)+~E(f857(f857(f79(x54633),x54634),x54631),f857(f857(f79(x54633),x54634),x54632))
% 15.02/14.80 [5464]~P74(x54643)+E(x54641,x54642)+~E(f857(f857(f79(x54643),x54644),x54641),f857(f857(f79(x54643),x54644),x54642))
% 15.02/14.80 [5466]~P73(x54663)+E(x54661,x54662)+~E(f857(f857(f79(x54663),x54661),x54664),f857(f857(f79(x54663),x54662),x54664))
% 15.02/14.80 [5560]~P123(x55601)+~E(x55603,f857(f857(f80(x55601),x55602),x55604))+P106(f857(f857(f286(x55601),x55602),x55603))
% 15.02/14.80 [5588]~P6(x55883)+E(x55881,f189(f927(x55882,a915)))+E(f857(f857(f38(x55882,x55883),x55881),f857(f18(x55883,x55882),x55884)),x55884)
% 15.02/14.80 [5589]~P6(x55893)+E(x55891,f189(f927(x55892,a915)))+E(f857(f857(f39(x55892,x55893),x55891),f857(f18(x55893,x55892),x55894)),x55894)
% 15.02/14.80 [5742]~E(x57424,f189(f927(x57421,a915)))+~E(x57424,f857(f857(f308(x57421),x57422),x57423))+P106(f857(f857(f328(x57421),x57422),x57423))
% 15.02/14.80 [5809]~P110(x58093)+E(x58091,x58092)+~E(f302(x58093,x58094,x58091),f857(f857(f308(x58093),x58092),f189(f927(x58093,a915))))
% 15.02/14.80 [5810]~P110(x58103)+E(x58101,x58102)+~E(f302(x58103,x58101,x58102),f857(f857(f308(x58103),x58104),f189(f927(x58103,a915))))
% 15.02/14.80 [5870]~P37(x58703,x58701,x58704)+P37(x58703,x58701,f857(f857(f151(x58703),x58702),x58704))+P106(f857(x58701,x58702))
% 15.02/14.80 [5972]~P33(x59721,x59722,x59724)+~P106(f857(x59722,x59723))+P33(x59721,x59722,f857(f857(f151(x59721),x59723),x59724))
% 15.02/14.80 [6114]P106(f857(x61141,x61142))+~P106(f857(f247(x61143,x61141),x61144))+~P106(f857(f857(f328(x61143),x61142),x61144))
% 15.02/14.80 [6123]~P33(x61231,x61232,x61234)+~P33(x61231,x61232,x61233)+P33(x61231,x61232,f857(f857(f134(x61231),x61233),x61234))
% 15.02/14.80 [6138]P35(x61381,x61382,x61383)+~P35(x61381,x61382,f857(f857(f151(x61381),x61384),x61383))+P106(f857(x61382,x61384))
% 15.02/14.80 [6139]P37(x61391,x61392,x61393)+~P37(x61391,x61392,f857(f857(f151(x61391),x61394),x61393))+P106(f857(x61392,x61394))
% 15.02/14.80 [6214]P35(x62141,x62142,x62143)+P35(x62141,x62142,x62144)+~P35(x62141,x62142,f857(f857(f134(x62141),x62144),x62143))
% 15.02/14.80 [6235]~P72(x62351)+E(f857(f857(f8(a919,x62351),x62352),f857(f301(a919,x62353),f857(a112,x62354))),f2(x62351))+~P106(f857(f857(f235(a919),x62354),x62353))
% 15.02/14.80 [6240]~P63(x62401)+~E(f44(x62401,x62402,x62403),f44(x62401,x62404,x62403))+E(f44(x62401,f857(f78(x62401),x62402),x62403),f44(x62401,f857(f78(x62401),x62404),x62403))
% 15.02/14.80 [6312]P106(f857(x63121,x63122))+~E(f857(f136(x63123,x63121),x63124),x63124)+~P106(f857(f857(f328(x63123),x63122),f857(f172(x63123),x63124)))
% 15.02/14.80 [6332]~E(f857(f857(f79(a919),x63323),x63322),f857(f857(f79(a919),x63321),x63324))+~P106(f857(f857(f235(a919),x63323),x63324))+P106(f857(f857(f235(a919),x63321),x63322))
% 15.02/14.80 [6338]P35(x63381,x63382,x63383)+~P106(f857(x63382,x63384))+~P106(f857(f857(f328(x63381),x63384),f857(f172(x63381),x63383)))
% 15.02/14.80 [6379]~P33(x63793,x63791,x63794)+P106(f857(x63791,x63792))+~P106(f857(f857(f328(x63793),x63792),f857(f172(x63793),x63794)))
% 15.02/14.80 [6381]~E(f857(f136(x63811,x63812),x63813),f113(x63811))+~P106(f857(x63812,x63814))+~P106(f857(f857(f328(x63811),x63814),f857(f172(x63811),x63813)))
% 15.02/14.80 [6382]~E(f177(x63823,x63821,x63824),x63824)+P106(f857(x63821,x63822))+~P106(f857(f857(f328(x63823),x63822),f857(f172(x63823),x63824)))
% 15.02/14.80 [6408]~E(x64084,f189(f927(x64082,a915)))+~E(x64083,f189(f927(x64081,a915)))+E(f312(x64081,x64082,x64083,x64084),f189(f927(f925(x64081,x64082),a915)))
% 15.02/14.80 [6558]P106(f857(x65581,x65582))+~P106(f857(f160(x65583,x65581),x65584))+~P106(f857(f857(f328(x65583),x65582),f857(f172(x65583),x65584)))
% 15.02/14.80 [6694]~P32(x66941,x66943,x66944)+P106(f857(x66941,x66942))+~P106(f857(f857(f328(a919),x66942),f857(f301(a919,x66943),x66944)))
% 15.02/14.80 [6832]~P72(x68321)+E(f857(f857(f8(a919,x68321),x68322),f302(a919,x68323,f857(a112,x68324))),f2(x68321))+~P106(f857(f857(f235(a919),f857(a112,x68324)),x68323))
% 15.02/14.80 [6973]~P109(x69731)+E(f857(f857(f3(f927(x69731,a915)),f857(f301(x69731,x69732),x69733)),f857(f301(x69731,x69732),x69734)),f857(f301(x69731,x69734),x69733))+~P106(f857(f857(f234(x69731),x69732),x69734))
% 15.02/14.80 [7044]~E(x70443,x70444)+E(x70441,f2(a919))+P106(f857(f857(f328(x70442),x70443),f857(f172(x70442),f169(x70442,x70441,x70444))))
% 15.02/14.80 [7326]~P106(f857(f857(f328(f920(x73261)),x73264),f161(x73261,x73263)))+P106(f857(f857(f328(x73261),x73262),x73263))+~P106(f857(f857(f328(x73261),x73262),f857(f172(x73261),x73264)))
% 15.02/14.80 [7333]~P39(x73331,x73332)+P106(f857(f857(f328(x73331),f618(x73332,x73331,x73333)),x73333))+~P106(f857(f857(f328(x73331),x73334),x73333))
% 15.02/14.80 [7390]~P72(x73901)+E(f857(f857(f857(f64(x73901,x73902,f79(x73901)),x73903),f2(x73901)),x73904),f857(f857(f8(x73902,x73901),x73903),x73904))+~P106(f857(f60(x73902),x73904))
% 15.02/14.80 [7392]~P77(x73921)+E(f857(f857(f857(f64(x73921,x73922,f80(x73921)),x73923),f77(x73921)),x73924),f857(f857(f11(x73922,x73921),x73923),x73924))+~P106(f857(f60(x73922),x73924))
% 15.02/14.80 [7421]P26(x74211,x74212,x74213,x74214)+~E(f857(f34(x74212),f857(f309(x74211,x74212,x74213),x74214)),f857(f34(x74211),x74214))+~P106(f857(f60(x74211),x74214))
% 15.02/14.80 [7611]~P72(x76111)+E(f857(f857(f79(x76111),f857(x76112,x76113)),f857(f857(f8(a919,x76111),x76112),f304(a919,x76113,x76114))),f857(f857(f8(a919,x76111),x76112),f302(a919,x76113,x76114)))+~P106(f857(f857(f234(a919),x76113),x76114))
% 15.02/14.80 [7621]~P72(x76211)+~P26(x76212,x76211,x76213,x76214)+E(f857(f857(f8(x76211,x76211),f31(x76211)),f857(f309(x76212,x76211,x76213),x76214)),f857(f857(f8(x76212,x76211),x76213),x76214))
% 15.02/14.80 [7622]~P77(x76221)+~P26(x76222,x76221,x76223,x76224)+E(f857(f857(f11(x76221,x76221),f31(x76221)),f857(f309(x76222,x76221,x76223),x76224)),f857(f857(f11(x76222,x76221),x76223),x76224))
% 15.02/14.80 [7671]E(f857(f34(f925(x76711,x76712)),f312(x76711,x76712,x76713,x76714)),f857(f857(f79(a919),f857(f34(x76711),x76713)),f857(f34(x76712),x76714)))+~P106(f857(f60(x76712),x76714))+~P106(f857(f60(x76711),x76713))
% 15.02/14.80 [7752]E(x77521,x77522)+P106(f857(f857(f328(x77523),x77521),f857(f172(x77523),f170(x77523,x77522,x77524))))+~P106(f857(f857(f328(x77523),x77521),f857(f172(x77523),x77524)))
% 15.02/14.80 [7980]~P72(x79801)+E(f857(f857(f79(x79801),f857(f857(f8(a919,x79801),x79802),f857(f301(a919,x79803),x79804))),f857(x79802,x79804)),f857(f857(f8(a919,x79801),x79802),f857(f301(a919,x79803),f857(a112,x79804))))+P106(f857(f857(f235(a919),x79804),x79803))
% 15.02/14.80 [8029]~P26(x80291,x80292,x80293,f241(f927(x80291,a915)))+~P106(f857(f60(x80292),x80294))+P106(f857(f60(x80291),f857(f310(x80291,x80292,x80293),x80294)))
% 15.02/14.80 [8146]P106(f857(f857(f328(f920(x81461)),f857(f857(f151(x81461),x81462),x81463)),f161(x81461,x81464)))+~P106(f857(f857(f328(f920(x81461)),x81463),f161(x81461,x81464)))+~P106(f857(f857(f328(x81461),x81462),x81464))
% 15.02/14.80 [8233]~E(f857(f309(x82333,x82331,x82334),f241(f927(x82333,a915))),f241(f927(x82331,a915)))+P106(f857(f60(x82331),x82332))+~P106(f857(f60(x82333),f857(f310(x82333,x82331,x82334),x82332)))
% 15.02/14.80 [8327]~P26(x83271,x83273,x83274,x83272)+P106(f857(f60(x83271),x83272))+~P106(f857(f60(x83273),f857(f309(x83271,x83273,x83274),x83272)))
% 15.02/14.80 [8351]~E(x83512,x83513)+P106(f857(f857(f328(f926(x83511,x83511)),f857(f857(f251(x83511,x83511),x83512),x83513)),f262(x83511,x83514)))+~P106(f857(f857(f328(x83511),x83512),x83514))
% 15.02/14.80 [8384]~P72(x83841)+E(f857(f857(f79(x83841),f857(f857(f8(a919,x83841),x83842),f302(a919,x83843,x83844))),f857(x83842,f857(a112,x83844))),f857(f857(f8(a919,x83841),x83842),f302(a919,x83843,f857(a112,x83844))))+P106(f857(f857(f235(a919),f857(a112,x83844)),x83843))
% 15.02/14.80 [8444]P106(f857(x84441,x84442))+~P106(f857(x84441,f857(f857(f164(x84443),x84444),f662(x84441,x84444,x84443))))+~P106(f857(f857(f328(x84443),x84442),f857(f172(x84443),x84444)))
% 15.02/14.80 [8583]~P106(f857(f857(f328(x85831),x85832),f315(x85831,x85834)))+P106(f857(f857(f328(f920(x85831)),f857(f857(f151(x85831),x85832),x85833)),f315(f920(x85831),f157(x85831,x85834))))+~P106(f857(f857(f328(f920(x85831)),x85833),f315(f920(x85831),f157(x85831,x85834))))
% 15.02/14.80 [8598]~P26(x85982,x85983,x85984,f532(x85984,x85983,x85982,x85981))+P26(x85982,x85983,x85984,f37(f927(x85982,a915),x85981))+E(x85981,f189(f927(f927(x85982,a915),a915)))
% 15.02/14.80 [8866]E(x88661,x88662)+~P106(f857(f857(f328(f926(x88663,x88663)),f857(f857(f251(x88663,x88663),x88661),x88662)),f306(x88663,x88664)))+P106(f857(f857(f328(x88663),x88661),f857(f263(x88663,x88663),x88664)))
% 15.02/14.80 [9144]E(x91441,f2(a919))+P106(f857(x91442,x91443))+P106(f857(f857(f328(x91444),f771(x91442,x91443,x91441,x91444)),f857(f172(x91444),f169(x91444,x91441,x91443))))
% 15.02/14.80 [9156]E(x91561,f2(a919))+~P106(f857(x91563,x91564))+P106(f857(f857(f328(x91562),f770(x91563,x91564,x91561,x91562)),f857(f172(x91562),f169(x91562,x91561,x91564))))
% 15.02/14.80 [9158]~P27(x91581,x91582,x91583,f241(f927(x91581,a915)),f241(f927(x91582,a915)))+~P106(f857(f60(x91582),x91584))+P106(f857(f60(x91581),f857(f310(x91581,x91582,x91583),x91584)))
% 15.02/14.80 [9161]P26(x91612,x91613,x91614,f37(f927(x91612,a915),x91611))+E(x91611,f189(f927(f927(x91612,a915),a915)))+P106(f857(f857(f328(f927(x91612,a915)),f532(x91614,x91613,x91612,x91611)),x91611))
% 15.02/14.80 [9276]~P27(x92763,x92761,x92764,f241(f927(x92763,a915)),f241(f927(x92761,a915)))+P106(f857(f60(x92761),x92762))+~P106(f857(f60(x92763),f857(f310(x92763,x92761,x92764),x92762)))
% 15.02/14.80 [9293]P106(f857(f60(x92931),x92932))+~P106(f857(f60(x92934),f857(f309(x92931,x92934,x92933),x92932)))+P106(f857(f857(f328(x92931),f576(x92933,x92934,x92932,x92931)),x92932))
% 15.02/14.80 [9387]~P6(x93872)+E(f857(f857(f63(x93871,x93872,f857(f857(f10(x93872,f927(x93872,x93872),x93871),f101(x93872)),x93873)),f241(x93872)),x93874),f857(f857(f38(x93871,x93872),x93874),x93873))+~P106(f857(f60(x93871),x93874))
% 15.02/14.80 [9388]~P6(x93882)+E(f857(f857(f63(x93881,x93882,f857(f857(f10(x93882,f927(x93882,x93882),x93881),f110(x93882)),x93883)),f189(x93882)),x93884),f857(f857(f39(x93881,x93882),x93884),x93883))+~P106(f857(f60(x93881),x93884))
% 15.02/14.80 [9418]~P106(f857(f857(f286(a919),x94183),x94184))+P106(f857(f857(f286(a919),x94181),x94182))+P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x94181,x94182)),f289(a919,f286(a919),x94183,x94184)))
% 15.02/14.80 [9473]P106(f857(x94731,x94732))+~P106(f857(x94731,f857(f857(f164(x94733),x94734),f701(x94732,x94731,x94734,x94733))))+~P106(f857(f857(f328(x94733),x94732),f857(f172(x94733),x94734)))
% 15.02/14.80 [9494]E(x94941,x94942)+~P106(f857(f857(f328(f926(x94943,x94943)),f857(f857(f251(x94943,x94943),x94941),x94942)),f306(x94943,x94944)))+P106(f857(f857(f328(f926(x94943,x94943)),f857(f857(f251(x94943,x94943),x94941),x94942)),f857(f857(f288(x94943,x94943,x94943),x94944),f306(x94943,x94944))))
% 15.02/14.80 [9544]~E(f857(f190(f920(x95441)),x95442),f857(f190(f920(x95441)),x95443))+~P106(f857(f857(f328(f926(f920(x95441),f920(x95441))),f857(f857(f251(f920(x95441),f920(x95441)),x95442),x95443)),f147(x95441,x95444)))+P106(f857(f857(f328(f926(f920(x95441),f920(x95441))),f857(f857(f251(f920(x95441),f920(x95441)),x95442),x95443)),f145(x95441,x95444)))
% 15.02/14.80 [9667]P106(f857(f857(f286(a919),x96671),x96672))+~P106(f857(f857(f286(a919),x96673),x96671))+~P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x96673,x96671)),f289(a919,f286(a919),x96674,x96672)))
% 15.02/14.80 [9668]P106(f857(f857(f286(a919),x96681),x96682))+~P106(f857(f857(f286(a919),x96682),x96683))+~P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x96682,x96683)),f289(a919,f286(a919),x96681,x96684)))
% 15.02/14.80 [9788]P33(x97881,f857(f857(f20(x97881,a915,a915),f857(f857(f10(a915,f927(a915,a915),x97881),a326),f857(f857(f10(a915,a915,x97881),a321),x97882))),f857(a324,x97883)),x97884)+~P106(f857(x97882,x97883))+~P37(x97881,x97882,f857(f857(f151(x97881),x97883),x97884))
% 15.02/14.80 [9953]~P33(x99531,f857(f857(f20(x99531,a915,a915),f857(f857(f10(a915,f927(a915,a915),x99531),a326),f857(f857(f10(a915,a915,x99531),a321),x99532))),f857(a324,x99533)),x99534)+~P106(f857(x99532,x99533))+P37(x99531,x99532,f857(f857(f151(x99531),x99533),x99534))
% 15.02/14.80 [9957]~P37(x99571,x99572,x99574)+~P33(x99571,f857(f857(f20(x99571,a915,a915),f857(f857(f10(a915,f927(a915,a915),x99571),a326),f857(f857(f10(a915,a915,x99571),a321),x99572))),f857(a324,x99573)),x99574)+P37(x99571,x99572,f857(f857(f151(x99571),x99573),x99574))
% 15.02/14.80 [9990]~P69(x99901)+E(f857(f857(f8(a919,x99901),f857(f857(f20(a919,x99901,x99901),f857(f857(f10(x99901,f927(x99901,x99901),a919),f3(x99901)),x99902)),f857(f857(f10(a919,x99901,a919),x99902),f857(f857(f9(a919,a919,a919),f79(a919)),f77(a919))))),f302(a919,x99903,x99904)),f2(x99901))+P106(f857(f857(f234(a919),x99903),x99904))
% 15.02/14.80 [10230]~P39(x102302,x102304)+~P26(x102302,x102301,x102303,f241(f927(x102302,a915)))+P39(x102301,f857(f309(f926(x102302,x102302),f926(x102301,x102301),f257(x102302,x102301,x102302,x102301,x102303,x102303)),x102304))
% 15.02/14.80 [10423]~E(f857(f190(f920(x104231)),x104233),f857(f190(f920(x104231)),x104232))+P106(f857(f857(f328(f926(f920(x104231),f920(x104231))),f857(f857(f251(f920(x104231),f920(x104231)),x104232),x104233)),f158(x104231,x104234)))+~P106(f857(f857(f256(x104231,x104231,a915),f857(f857(f9(x104231,f927(f926(x104231,x104231),a915),f927(x104231,a915)),f857(f857(f10(f927(x104231,f927(f927(f926(x104231,x104231),a915),a915)),f927(f927(f926(x104231,x104231),a915),f927(x104231,a915)),x104231),f9(x104231,f927(f926(x104231,x104231),a915),a915)),f857(f857(f10(f927(x104231,f926(x104231,x104231)),f927(x104231,f927(f927(f926(x104231,x104231),a915),a915)),x104231),f857(f10(f926(x104231,x104231),f927(f927(f926(x104231,x104231),a915),a915),x104231),f328(f926(x104231,x104231)))),f251(x104231,x104231)))),x104234)),f666(x104234,x104233,x104232,x104231)))
% 15.02/14.80 [6293]~P62(x62931)+~E(x62932,f2(x62931))+E(f857(f857(f35(x62931),f857(f857(f80(x62931),x62932),x62933)),f857(f857(f80(x62931),x62932),x62934)),f2(x62931))
% 15.02/14.80 [6335]E(x63351,f113(x63352))+E(x63353,f857(f857(f3(a919),f857(f190(f920(x63352)),x63351)),f77(a919)))+E(f144(x63352,f857(f857(f159(x63352,x63351),x63353),x63354)),f144(x63352,x63351))
% 15.02/14.80 [6370]E(x63701,x63702)+P106(f857(x63703,x63702))+~P106(f857(f857(f857(f308(x63704),x63701),x63703),x63702))
% 15.02/14.80 [6386]~P72(x63861)+~P106(f857(f137(x63862),x63864))+E(f857(f165(x63861),f857(f857(f154(x63862,x63861),x63863),x63864)),f857(f857(f8(x63862,x63861),x63863),f857(f172(x63862),x63864)))
% 15.02/14.80 [6401]~P77(x64012)+~P106(f857(f60(x64011),x64014))+E(f857(f857(f11(x64011,x64012),f857(f18(x64012,x64011),x64013)),x64014),f857(f857(f243(x64012),x64013),f857(f34(x64011),x64014)))
% 15.02/14.80 [6454]~P65(x64542)+E(x64541,f2(x64542))+E(f857(f857(f290(x64542),f857(f857(f80(x64542),x64543),x64541)),f857(f857(f80(x64542),x64544),x64541)),f857(f857(f290(x64542),x64543),x64544))
% 15.02/14.80 [6455]~P65(x64552)+E(x64551,f2(x64552))+E(f857(f857(f290(x64552),f857(f857(f80(x64552),x64551),x64553)),f857(f857(f80(x64552),x64551),x64554)),f857(f857(f290(x64552),x64553),x64554))
% 15.02/14.80 [6456]~P62(x64562)+E(x64561,f2(x64562))+E(f857(f857(f35(x64562),f857(f857(f80(x64562),x64563),x64561)),f857(f857(f80(x64562),x64564),x64561)),f857(f857(f35(x64562),x64563),x64564))
% 15.02/14.80 [6458]~P62(x64582)+E(x64581,f2(x64582))+E(f857(f857(f35(x64582),f857(f857(f80(x64582),x64581),x64583)),f857(f857(f80(x64582),x64581),x64584)),f857(f857(f35(x64582),x64583),x64584))
% 15.02/14.80 [6526]P106(f857(x65261,x65262))+~E(x65263,f857(f857(f79(a919),x65264),x65262))+~P106(f857(x65261,f857(f857(f3(a919),x65263),x65264)))
% 15.02/14.80 [6611]~P106(f857(x66112,x66113))+~P106(f857(f160(x66111,x66112),x66114))+P106(f857(f160(x66111,x66112),f857(f857(f151(x66111),x66113),x66114)))
% 15.02/14.80 [6651]E(x66511,f113(x66512))+~E(x66513,f857(f857(f3(a919),f857(f190(f920(x66512)),x66511)),f77(a919)))+E(f144(x66512,f857(f857(f159(x66512,x66511),x66513),x66514)),x66514)
% 15.02/14.80 [6674]~P101(x66741)+~P106(f857(f857(f234(x66741),x66742),x66744))+P106(f857(f857(f234(x66741),x66742),f857(f857(f110(x66741),x66743),x66744)))
% 15.02/14.80 [6675]~P101(x66751)+~P106(f857(f857(f234(x66751),x66752),x66753))+P106(f857(f857(f234(x66751),x66752),f857(f857(f110(x66751),x66753),x66754)))
% 15.02/14.80 [6677]~P109(x66771)+~P106(f857(f857(f234(x66771),x66772),x66774))+P106(f857(f857(f234(x66771),x66772),f857(f857(f233(x66771),x66773),x66774)))
% 15.02/14.80 [6679]~P109(x66791)+~P106(f857(f857(f234(x66791),x66792),x66793))+P106(f857(f857(f234(x66791),x66792),f857(f857(f233(x66791),x66793),x66794)))
% 15.02/14.80 [6680]~P101(x66801)+~P106(f857(f857(f235(x66801),x66802),x66804))+P106(f857(f857(f235(x66801),x66802),f857(f857(f110(x66801),x66803),x66804)))
% 15.02/14.80 [6681]~P101(x66811)+~P106(f857(f857(f235(x66811),x66812),x66813))+P106(f857(f857(f235(x66811),x66812),f857(f857(f110(x66811),x66813),x66814)))
% 15.02/14.80 [6683]~P109(x66831)+~P106(f857(f857(f235(x66831),x66832),x66834))+P106(f857(f857(f235(x66831),x66832),f857(f857(f233(x66831),x66833),x66834)))
% 15.02/14.80 [6685]~P109(x66851)+~P106(f857(f857(f235(x66851),x66852),x66853))+P106(f857(f857(f235(x66851),x66852),f857(f857(f233(x66851),x66853),x66854)))
% 15.02/14.80 [6686]~P113(x66861)+~P106(f857(f857(f286(x66861),x66862),x66864))+P106(f857(f857(f286(x66861),x66862),f857(f857(f80(x66861),x66863),x66864)))
% 15.02/14.80 [6687]~P113(x66871)+~P106(f857(f857(f286(x66871),x66872),x66873))+P106(f857(f857(f286(x66871),x66872),f857(f857(f80(x66871),x66873),x66874)))
% 15.02/14.80 [6777]~E(f857(f857(f164(x67771),x67772),x67773),x67774)+E(f857(f857(f159(x67771,x67772),x67773),x67774),x67772)+~P106(f857(f857(f235(a919),x67773),f857(f190(f920(x67771)),x67772)))
% 15.02/14.80 [6816]P106(f857(x68161,x68162))+~P106(f857(x68163,x68162))+~P106(f857(f857(f234(f927(x68164,a915)),x68163),x68161))
% 15.02/14.80 [6849]~E(f857(f857(f159(x68491,x68492),x68493),x68494),x68492)+E(f857(f857(f164(x68491),x68492),x68493),x68494)+~P106(f857(f857(f235(a919),x68493),f857(f190(f920(x68491)),x68492)))
% 15.02/14.80 [6863]~P106(f857(f160(x68631,x68632),x68634))+~P106(f857(f160(x68631,x68632),x68633))+P106(f857(f160(x68631,x68632),f857(f857(f134(x68631),x68633),x68634)))
% 15.02/14.80 [6969]E(x69691,f189(f927(x69692,a915)))+E(x69693,f189(f927(x69694,a915)))+~E(f857(f857(f253(x69694,x69692),x69693),f857(f18(f927(x69692,a915),x69694),x69691)),f189(f927(f926(x69694,x69692),a915)))
% 15.02/14.80 [6989]E(x69891,x69892)+P106(f857(f857(f328(x69893),x69891),x69894))+~P106(f857(f857(f328(x69893),x69891),f857(f857(f308(x69893),x69892),x69894)))
% 15.02/14.80 [7006]~P109(x70061)+P106(f857(f857(f234(x70061),x70062),x70063))+~P106(f857(f857(f234(x70061),x70062),f857(f857(f188(x70061),x70064),x70063)))
% 15.02/14.80 [7008]~P109(x70081)+P106(f857(f857(f234(x70081),x70082),x70083))+~P106(f857(f857(f234(x70081),x70082),f857(f857(f188(x70081),x70083),x70084)))
% 15.02/14.80 [7010]~P102(x70101)+P106(f857(f857(f234(x70101),x70102),x70103))+~P106(f857(f857(f234(x70101),x70102),f857(f857(f101(x70101),x70104),x70103)))
% 15.02/14.80 [7012]~P102(x70121)+P106(f857(f857(f234(x70121),x70122),x70123))+~P106(f857(f857(f234(x70121),x70122),f857(f857(f101(x70121),x70123),x70124)))
% 15.02/14.80 [7013]~P109(x70131)+P106(f857(f857(f235(x70131),x70132),x70133))+~P106(f857(f857(f235(x70131),x70132),f857(f857(f188(x70131),x70134),x70133)))
% 15.02/14.80 [7014]~P109(x70141)+P106(f857(f857(f235(x70141),x70142),x70143))+~P106(f857(f857(f235(x70141),x70142),f857(f857(f188(x70141),x70143),x70144)))
% 15.02/14.80 [7035]~E(f857(f857(f164(x70351),x70353),x70354),x70352)+P106(f857(f857(f328(x70351),x70352),f857(f172(x70351),x70353)))+~P106(f857(f857(f235(a919),x70354),f857(f190(f920(x70351)),x70353)))
% 15.02/14.80 [7045]~P109(x70451)+~P14(x70451,f857(f857(f151(x70451),x70452),f857(f857(f151(x70451),x70453),x70454)))+P106(f857(f857(f234(x70451),x70452),x70453))
% 15.02/14.80 [7190]~P33(x71902,x71901,x71903)+P106(f857(x71901,f857(f857(f164(x71902),x71903),x71904)))+~P106(f857(f857(f235(a919),x71904),f857(f190(f920(x71902)),x71903)))
% 15.02/14.80 [7208]E(x72081,f2(a1))+E(f857(f857(f35(a1),x72082),x72081),x72083)+~P106(f857(f48(x72082,x72081),f857(f857(f251(a1,a1),x72083),x72084)))
% 15.02/14.80 [7229]E(f44(a1,x72292,x72291),x72293)+E(x72291,f2(a1))+~P106(f857(f48(x72292,x72291),f857(f857(f251(a1,a1),x72294),x72293)))
% 15.02/14.80 [7350]P106(f857(f857(f328(x73501),x73502),x73503))+~P106(f857(f857(f328(x73501),x73502),x73504))+~P106(f857(f857(f235(f927(x73501,a915)),x73504),x73503))
% 15.02/14.80 [7351]P106(f857(f857(f328(x73511),x73512),x73513))+~P106(f857(f857(f328(x73511),x73512),x73514))+~P106(f857(f857(f234(f927(x73511,a915)),x73514),x73513))
% 15.02/14.80 [7362]~P122(x73621)+~E(x73623,f2(x73621))+P106(f857(f857(f286(x73621),f857(f857(f80(x73621),x73622),x73623)),f857(f857(f80(x73621),x73624),x73623)))
% 15.02/14.80 [7363]~P122(x73631)+~E(x73632,f2(x73631))+P106(f857(f857(f286(x73631),f857(f857(f80(x73631),x73632),x73633)),f857(f857(f80(x73631),x73632),x73634)))
% 15.02/14.80 [7465]P35(x74651,x74652,x74653)+~P106(f857(x74652,f857(f857(f164(x74651),x74653),x74654)))+~P106(f857(f857(f235(a919),x74654),f857(f190(f920(x74651)),x74653)))
% 15.02/14.80 [7577]~P108(x75772)+~P106(f857(f857(f235(f927(x75771,x75772)),x75773),x75774))+P106(f857(f857(f234(f927(x75771,x75772)),x75773),x75774))
% 15.02/14.80 [7660]~P25(x76601,x76602,x76604)+P25(x76601,x76602,f857(f857(f308(f918(x76601)),x76603),x76604))+~P25(x76601,x76602,f857(f857(f308(f918(x76601)),x76603),f189(f927(f918(x76601),a915))))
% 15.02/14.80 [7702]~P106(f857(f857(f328(x77021),x77022),x77024))+P106(f857(f857(f328(x77021),x77022),f36(f927(x77021,a915),x77023)))+~P106(f857(f857(f328(f927(x77021,a915)),x77024),x77023))
% 15.02/14.80 [7730]~P85(x77301)+~P106(f857(f857(f234(x77301),x77303),x77304))+P106(f857(f857(f234(x77301),f857(f857(f79(x77301),x77302),x77303)),f857(f857(f79(x77301),x77302),x77304)))
% 15.02/14.80 [7731]~P86(x77311)+~P106(f857(f857(f234(x77311),x77313),x77314))+P106(f857(f857(f234(x77311),f857(f857(f79(x77311),x77312),x77313)),f857(f857(f79(x77311),x77312),x77314)))
% 15.02/14.80 [7732]~P85(x77321)+~P106(f857(f857(f234(x77321),x77322),x77324))+P106(f857(f857(f234(x77321),f857(f857(f79(x77321),x77322),x77323)),f857(f857(f79(x77321),x77324),x77323)))
% 15.02/14.80 [7733]~P86(x77331)+~P106(f857(f857(f234(x77331),x77332),x77334))+P106(f857(f857(f234(x77331),f857(f857(f79(x77331),x77332),x77333)),f857(f857(f79(x77331),x77334),x77333)))
% 15.02/14.80 [7734]~P84(x77341)+~P106(f857(f857(f235(x77341),x77343),x77344))+P106(f857(f857(f235(x77341),f857(f857(f79(x77341),x77342),x77343)),f857(f857(f79(x77341),x77342),x77344)))
% 15.02/14.80 [7735]~P85(x77351)+~P106(f857(f857(f235(x77351),x77353),x77354))+P106(f857(f857(f235(x77351),f857(f857(f79(x77351),x77352),x77353)),f857(f857(f79(x77351),x77352),x77354)))
% 15.02/14.80 [7736]~P84(x77361)+~P106(f857(f857(f235(x77361),x77362),x77364))+P106(f857(f857(f235(x77361),f857(f857(f79(x77361),x77362),x77363)),f857(f857(f79(x77361),x77364),x77363)))
% 15.02/14.80 [7737]~P85(x77371)+~P106(f857(f857(f235(x77371),x77372),x77374))+P106(f857(f857(f235(x77371),f857(f857(f79(x77371),x77372),x77373)),f857(f857(f79(x77371),x77374),x77373)))
% 15.02/14.80 [7738]~P122(x77381)+~P106(f857(f857(f286(x77381),x77383),x77384))+P106(f857(f857(f286(x77381),f857(f857(f80(x77381),x77382),x77383)),f857(f857(f80(x77381),x77382),x77384)))
% 15.02/14.80 [7739]~P122(x77391)+~P106(f857(f857(f286(x77391),x77392),x77394))+P106(f857(f857(f286(x77391),f857(f857(f80(x77391),x77392),x77393)),f857(f857(f80(x77391),x77394),x77393)))
% 15.02/14.80 [7746]~P111(x77461)+~P95(x77461)+E(f857(f857(f3(x77461),f857(f857(f80(x77461),x77462),f857(f103(x77461),x77463))),f857(f857(f80(x77461),x77464),f857(f103(x77461),x77463))),f857(f857(f80(x77461),f857(f857(f3(x77461),x77462),x77464)),f857(f103(x77461),x77463)))
% 15.02/14.80 [7747]~P141(x77471)+~P95(x77471)+E(f857(f857(f79(x77471),f857(f857(f80(x77471),x77472),f857(f103(x77471),x77473))),f857(f857(f80(x77471),x77474),f857(f103(x77471),x77473))),f857(f857(f80(x77471),f857(f857(f79(x77471),x77472),x77474)),f857(f103(x77471),x77473)))
% 15.02/14.80 [7783]~P72(x77831)+E(f857(f857(f79(x77831),f857(x77832,x77833)),f857(f857(f8(a919,x77831),x77832),f302(a919,f857(a112,x77833),x77834))),f857(f857(f8(a919,x77831),x77832),f302(a919,x77833,x77834)))+~P106(f857(f857(f234(a919),x77833),x77834))
% 15.02/14.80 [7795]~P26(x77952,x77951,x77953,f857(f172(x77952),x77954))+~P106(f857(f137(x77952),x77954))+P106(f857(f137(x77951),f857(f857(f154(x77952,x77951),x77953),x77954)))
% 15.02/14.80 [7844]~P106(f857(f857(f234(a919),x78442),x78444))+~P106(f857(f857(f234(a919),x78441),x78443))+P106(f857(f857(f234(a919),f857(f857(f80(a919),x78441),x78442)),f857(f857(f80(a919),x78443),x78444)))
% 15.02/14.80 [7845]~P106(f857(f857(f234(a919),x78452),x78454))+~P106(f857(f857(f234(a919),x78451),x78453))+P106(f857(f857(f234(a919),f857(f857(f79(a919),x78451),x78452)),f857(f857(f79(a919),x78453),x78454)))
% 15.02/14.80 [7848]~P106(f857(f857(f235(a919),x78482),x78484))+~P106(f857(f857(f235(a919),x78481),x78483))+P106(f857(f857(f235(a919),f857(f857(f79(a919),x78481),x78482)),f857(f857(f79(a919),x78483),x78484)))
% 15.02/14.80 [7849]~P106(f857(f857(f234(a1),x78492),x78494))+~P106(f857(f857(f235(a1),x78491),x78493))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x78491),x78492)),f857(f857(f79(a1),x78493),x78494)))
% 15.02/14.80 [7897]P106(f857(f857(f328(x78971),x78972),x78973))+~P106(f857(f857(f328(x78971),x78972),f37(f927(x78971,a915),x78974)))+~P106(f857(f857(f328(f927(x78971,a915)),x78973),x78974))
% 15.02/14.80 [7913]~P106(f857(x79131,f660(x79131,x79133,x79132)))+P106(f857(x79131,f857(f857(f164(x79132),x79133),x79134)))+~P106(f857(f857(f235(a919),x79134),f857(f190(f920(x79132)),x79133)))
% 15.02/14.80 [7918]P106(f857(x79181,x79182))+~P106(f857(f857(f328(x79184),x79182),f857(f172(x79184),x79183)))+P106(f857(f857(f235(a919),f662(x79181,x79183,x79184)),f857(f190(f920(x79184)),x79183)))
% 15.02/14.80 [7965]~P108(x79651)+~P106(f857(f857(f235(f927(x79652,x79651)),x79654),x79653))+~P106(f857(f857(f234(f927(x79652,x79651)),x79653),x79654))
% 15.02/14.80 [8008]~P106(f857(x80084,x80082))+~P106(f857(f857(f328(x80081),x80082),x80083))+P106(f857(f857(f328(x80081),x80082),f857(f857(f101(f927(x80081,a915)),x80083),f857(f261(x80081),x80084))))
% 15.02/14.80 [8153]~P106(f857(f857(f328(x81531),x81533),x81534))+~P106(f857(f857(f235(f927(x81531,a915)),x81532),x81534))+P106(f857(f857(f235(f927(x81531,a915)),x81532),f857(f857(f308(x81531),x81533),x81534)))
% 15.02/14.80 [8155]E(f857(f857(f101(f927(x81551,a915)),x81552),x81553),f189(f927(x81551,a915)))+~E(f857(f857(f101(f927(x81551,a915)),f36(f927(x81551,a915),x81554)),x81553),f189(f927(x81551,a915)))+~P106(f857(f857(f328(f927(x81551,a915)),x81552),x81554))
% 15.02/14.80 [8229]P106(f857(f857(f328(x82291),x82292),x82293))+~P106(f857(f857(f234(f927(x82291,a915)),x82293),f857(f857(f308(x82291),x82292),x82294)))+P106(f857(f857(f234(f927(x82291,a915)),x82293),x82294))
% 15.02/14.80 [8246]P106(f857(f857(f328(x82462),f660(x82461,x82463,x82462)),f857(f172(x82462),x82463)))+P106(f857(x82461,f857(f857(f164(x82462),x82463),x82464)))+~P106(f857(f857(f235(a919),x82464),f857(f190(f920(x82462)),x82463)))
% 15.02/14.80 [8254]~P106(f857(f857(f234(f927(x82541,a915)),x82542),x82544))+P106(f857(f857(f234(f927(x82541,a915)),x82542),x82543))+~P106(f857(f857(f234(f927(x82541,a915)),x82544),x82543))
% 15.02/14.80 [8255]~P106(f857(f857(f235(f927(x82551,a915)),x82552),x82554))+~P106(f857(f857(f234(f927(x82551,a915)),x82554),x82553))+P106(f857(f857(f235(f927(x82551,a915)),x82552),x82553))
% 15.02/14.80 [8256]~P106(f857(f857(f234(f927(x82561,a915)),x82562),x82564))+~P106(f857(f857(f235(f927(x82561,a915)),x82564),x82563))+P106(f857(f857(f235(f927(x82561,a915)),x82562),x82563))
% 15.02/14.80 [8257]~P106(f857(f857(f235(f927(x82571,a915)),x82572),x82574))+P106(f857(f857(f235(f927(x82571,a915)),x82572),x82573))+~P106(f857(f857(f235(f927(x82571,a915)),x82574),x82573))
% 15.02/14.80 [8300]~P106(f857(f857(f328(x83001),x83004),x83003))+~P106(f857(f857(f235(f927(x83001,a915)),x83002),f857(f857(f308(x83001),x83004),x83003)))+P106(f857(f857(f235(f927(x83001,a915)),x83002),x83003))
% 15.02/14.80 [8311]~P85(x83111)+P106(f857(f857(f234(x83111),x83112),x83113))+~P106(f857(f857(f234(x83111),f857(f857(f79(x83111),x83114),x83112)),f857(f857(f79(x83111),x83114),x83113)))
% 15.02/14.80 [8313]~P85(x83131)+P106(f857(f857(f234(x83131),x83132),x83133))+~P106(f857(f857(f234(x83131),f857(f857(f79(x83131),x83132),x83134)),f857(f857(f79(x83131),x83133),x83134)))
% 15.02/14.80 [8315]~P85(x83151)+P106(f857(f857(f235(x83151),x83152),x83153))+~P106(f857(f857(f235(x83151),f857(f857(f79(x83151),x83154),x83152)),f857(f857(f79(x83151),x83154),x83153)))
% 15.02/14.80 [8317]~P85(x83171)+P106(f857(f857(f235(x83171),x83172),x83173))+~P106(f857(f857(f235(x83171),f857(f857(f79(x83171),x83172),x83174)),f857(f857(f79(x83171),x83173),x83174)))
% 15.02/14.80 [8368]P106(f857(x83681,x83682))+~E(f857(f857(f138(x83683),f857(f190(f920(x83683)),f177(x83683,x83681,x83684))),x83684),f113(x83683))+~P106(f857(f857(f328(x83683),x83682),f857(f172(x83683),x83684)))
% 15.02/14.80 [8486]P106(f857(x84861,x84862))+~P106(f857(f857(f328(x84863),x84862),f857(f172(x84863),x84864)))+P106(f857(f857(f235(a919),f857(f190(f920(x84863)),f857(f136(x84863,x84861),x84864))),f857(f190(f920(x84863)),x84864)))
% 15.02/14.80 [8973]~P106(f857(x89731,f753(x89731,x89733,x89732,x89734)))+P106(f857(x89731,f857(f857(f164(x89732),x89733),x89734)))+~P106(f857(f857(f235(a919),x89734),f857(f190(f920(x89732)),x89733)))
% 15.02/14.80 [8997]~P26(x89974,x89973,x89971,f241(f927(x89974,a915)))+E(f857(x89971,f502(x89972,x89971,x89973,x89974)),x89972)+~P106(f857(f857(f328(x89973),x89972),f857(f309(x89974,x89973,x89971),f241(f927(x89974,a915)))))
% 15.02/14.80 [9065]E(f177(x90651,x90652,x90653),f857(f857(f175(x90651),x90654),x90653))+P106(f857(f857(f235(a919),f724(x90652,x90653,x90651,x90654)),x90654))+P106(f857(f857(f235(a919),x90654),f857(f190(f920(x90651)),x90653)))
% 15.02/14.80 [9068]E(f177(x90681,x90682,x90683),f857(f857(f175(x90681),x90684),x90683))+P106(f857(f857(f235(a919),f724(x90682,x90683,x90681,x90684)),x90684))+P106(f857(x90682,f857(f857(f164(x90681),x90683),x90684)))
% 15.02/14.80 [9103]P106(f857(x91031,x91032))+~P106(f857(f857(f328(x91034),x91032),f857(f172(x91034),x91033)))+P106(f857(f857(f235(a919),f701(x91032,x91031,x91033,x91034)),f857(f190(f920(x91034)),x91033)))
% 15.02/14.80 [9105]E(f177(x91051,x91052,x91053),f857(f857(f175(x91051),x91054),x91053))+P106(f857(f857(f235(a919),x91054),f857(f190(f920(x91051)),x91053)))+P106(f857(f857(f235(a919),f724(x91052,x91053,x91051,x91054)),f857(f190(f920(x91051)),x91053)))
% 15.02/14.80 [9112]E(f177(x91121,x91122,x91123),f857(f857(f175(x91121),x91124),x91123))+P106(f857(x91122,f857(f857(f164(x91121),x91123),x91124)))+P106(f857(f857(f235(a919),f724(x91122,x91123,x91121,x91124)),f857(f190(f920(x91121)),x91123)))
% 15.02/14.80 [9137]~P127(x91374)+P106(f857(f857(f328(x91371),f346(x91372,x91373,x91371,x91374)),x91373))+P106(f857(f857(f235(x91374),f2(x91374)),f857(f857(f11(x91371,x91374),x91372),x91373)))
% 15.02/14.80 [9138]~P127(x91384)+P106(f857(f857(f328(x91381),f347(x91382,x91383,x91381,x91384)),x91383))+P106(f857(f857(f234(x91384),f2(x91384)),f857(f857(f11(x91381,x91384),x91382),x91383)))
% 15.02/14.80 [9163]~P106(f857(f60(x91631),x91634))+P106(f857(f857(f328(x91631),f537(x91632,x91633,x91634,x91631)),x91634))+P106(f857(f60(f926(x91631,x91633)),f857(f857(f253(x91631,x91633),x91634),x91632)))
% 15.02/14.80 [9195]P106(f857(f857(f328(x91952),f753(x91951,x91953,x91952,x91954)),f857(f172(x91952),x91953)))+P106(f857(x91951,f857(f857(f164(x91952),x91953),x91954)))+~P106(f857(f857(f235(a919),x91954),f857(f190(f920(x91952)),x91953)))
% 15.02/14.80 [9324]P106(f857(f857(f234(a919),x93244),f857(f190(f920(x93242)),f177(x93242,x93243,x93241))))+P106(f857(f857(f235(a919),f725(x93241,x93242,x93243,x93244)),x93244))+~P106(f857(f857(f234(a919),x93244),f857(f190(f920(x93242)),x93241)))
% 15.02/14.80 [9477]E(f177(x94771,x94772,x94773),f857(f857(f175(x94771),x94774),x94773))+~P106(f857(x94772,f857(f857(f164(x94771),x94773),f724(x94772,x94773,x94771,x94774))))+P106(f857(f857(f235(a919),x94774),f857(f190(f920(x94771)),x94773)))
% 15.02/14.80 [9484]E(f177(x94841,x94842,x94843),f857(f857(f175(x94841),x94844),x94843))+~P106(f857(x94842,f857(f857(f164(x94841),x94843),f724(x94842,x94843,x94841,x94844))))+P106(f857(x94842,f857(f857(f164(x94841),x94843),x94844)))
% 15.02/14.80 [9488]~P106(f857(f60(x94881),x94883))+~P106(f857(f60(x94882),f857(x94884,f537(x94884,x94882,x94883,x94881))))+P106(f857(f60(f926(x94881,x94882)),f857(f857(f253(x94881,x94882),x94883),x94884)))
% 15.02/14.80 [9496]~P127(x94961)+~P106(f857(f857(f234(x94961),f2(x94961)),f857(x94963,f347(x94963,x94964,x94962,x94961))))+P106(f857(f857(f234(x94961),f2(x94961)),f857(f857(f11(x94962,x94961),x94963),x94964)))
% 15.02/14.80 [9497]~P127(x94971)+~P106(f857(f857(f235(x94971),f2(x94971)),f857(x94973,f346(x94973,x94974,x94972,x94971))))+P106(f857(f857(f235(x94971),f2(x94971)),f857(f857(f11(x94972,x94971),x94973),x94974)))
% 15.02/14.80 [9505]~E(f857(f190(f920(x95054)),x95052),f857(f190(f920(x95054)),x95053))+P106(f857(f857(f328(f926(f920(x95054),f920(x95054))),f857(f857(f251(f920(x95054),f920(x95054)),x95053),x95052)),f158(x95054,x95051)))+P106(f857(f857(f235(a919),f649(x95051,x95052,x95053,x95054)),f857(f190(f920(x95054)),x95053)))
% 15.02/14.80 [9557]~P106(f857(x95573,f857(f857(f164(x95572),x95574),f725(x95574,x95572,x95573,x95571))))+P106(f857(f857(f234(a919),x95571),f857(f190(f920(x95572)),f177(x95572,x95573,x95574))))+~P106(f857(f857(f234(a919),x95571),f857(f190(f920(x95572)),x95574)))
% 15.02/14.80 [9638]E(f857(f857(f175(x96381),f661(x96382,x96383,x96384,x96381)),x96383),f857(f857(f175(x96381),f661(x96382,x96383,x96384,x96381)),x96384))+~P106(f857(f857(f328(f926(f920(x96381),f920(x96381))),f857(f857(f251(f920(x96381),f920(x96381)),x96384),x96383)),f147(x96381,x96382)))+P106(f857(f857(f235(a919),f857(f190(f920(x96381)),x96384)),f857(f190(f920(x96381)),x96383)))
% 15.02/14.80 [9701]~P106(f857(f857(f235(a919),f2(a919)),x97013))+~P106(f857(f857(f235(a919),x97014),x97011))+P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),x97011),f44(a919,x97012,x97013))),x97014)),f857(f857(f80(a919),x97011),x97013)))
% 15.02/14.80 [9893]~P108(x98932)+~P106(f857(f857(f234(x98932),f857(x98933,f913(x98934,x98933,x98931,x98932))),f857(x98934,f913(x98934,x98933,x98931,x98932))))+P106(f857(f857(f234(f927(x98931,x98932)),x98933),x98934))
% 15.02/14.80 [9995]~P69(x99951)+E(f857(f857(f8(a919,x99951),f857(f857(f20(a919,x99951,x99951),f857(f857(f10(x99951,f927(x99951,x99951),a919),f3(x99951)),x99952)),f857(f857(f10(a919,x99951,a919),x99952),f857(f857(f9(a919,a919,a919),f79(a919)),f77(a919))))),f302(a919,x99953,x99954)),f857(f857(f3(x99951),f857(x99952,x99953)),f857(x99952,f857(f857(f79(a919),x99954),f77(a919)))))+~P106(f857(f857(f234(a919),x99953),x99954))
% 15.02/14.80 [10071]~P39(x100713,f857(f857(f288(x100713,x100713,x100713),x100712),f306(x100713,x100712)))+~P106(f857(f857(f328(f926(x100713,x100713)),f857(f857(f251(x100713,x100713),f857(x100711,f857(a112,f836(x100712,x100711,x100713)))),f857(x100711,f836(x100712,x100711,x100713)))),f306(x100713,x100712)))+E(f857(x100711,f857(f857(f79(a919),f835(x100712,x100711,x100713)),x100714)),f857(x100711,f835(x100712,x100711,x100713)))
% 15.02/14.80 [6954]~P62(x69541)+E(f857(f857(f35(x69541),f857(f857(f80(x69541),x69542),x69543)),x69544),f857(f857(f80(x69541),x69542),f857(f857(f35(x69541),x69543),x69544)))+~P106(f857(f857(f286(x69541),x69544),x69543))
% 15.02/14.80 [7039]E(f857(f857(f134(x70391),x70392),x70393),x70394)+~E(x70393,f857(f857(f138(x70391),f857(f190(f920(x70391)),x70392)),x70394))+~E(f857(f857(f175(x70391),f857(f190(f920(x70391)),x70392)),x70394),x70392)
% 15.02/14.80 [7095]~P66(x70952)+E(x70951,f2(x70952))+E(f857(f857(f290(x70952),f857(f857(f243(x70952),x70953),x70954)),f857(f857(f243(x70952),x70951),x70954)),f857(f857(f243(x70952),f857(f857(f290(x70952),x70953),x70951)),x70954))
% 15.02/14.80 [7239]~P62(x72391)+E(f857(f857(f35(x72391),f857(f857(f80(x72391),x72392),x72393)),x72394),f857(f857(f80(x72391),f857(f857(f35(x72391),x72392),x72394)),x72393))+~P106(f857(f857(f286(x72391),x72394),x72392))
% 15.02/14.80 [7247]~P102(x72471)+~P106(f857(f857(f234(x72471),x72473),x72474))+P106(f857(f857(f234(x72471),f857(f857(f101(x72471),x72472),x72473)),x72474))
% 15.02/14.80 [7248]~P102(x72481)+~P106(f857(f857(f234(x72481),x72482),x72484))+P106(f857(f857(f234(x72481),f857(f857(f101(x72481),x72482),x72483)),x72484))
% 15.02/14.80 [7250]~P109(x72501)+~P106(f857(f857(f234(x72501),x72503),x72504))+P106(f857(f857(f234(x72501),f857(f857(f188(x72501),x72502),x72503)),x72504))
% 15.02/14.80 [7252]~P109(x72521)+~P106(f857(f857(f234(x72521),x72522),x72524))+P106(f857(f857(f234(x72521),f857(f857(f188(x72521),x72522),x72523)),x72524))
% 15.02/14.80 [7253]~P102(x72531)+~P106(f857(f857(f235(x72531),x72533),x72534))+P106(f857(f857(f235(x72531),f857(f857(f101(x72531),x72532),x72533)),x72534))
% 15.02/14.80 [7254]~P102(x72541)+~P106(f857(f857(f235(x72541),x72542),x72544))+P106(f857(f857(f235(x72541),f857(f857(f101(x72541),x72542),x72543)),x72544))
% 15.02/14.80 [7256]~P109(x72561)+~P106(f857(f857(f235(x72561),x72563),x72564))+P106(f857(f857(f235(x72561),f857(f857(f188(x72561),x72562),x72563)),x72564))
% 15.02/14.80 [7258]~P109(x72581)+~P106(f857(f857(f235(x72581),x72582),x72584))+P106(f857(f857(f235(x72581),f857(f857(f188(x72581),x72582),x72583)),x72584))
% 15.02/14.80 [7281]~P106(f857(x72813,x72814))+~P106(f857(x72812,x72814))+P106(f857(f857(f857(f101(f927(x72811,a915)),x72812),x72813),x72814))
% 15.02/14.80 [7407]P25(x74071,x74072,x74073)+~P25(x74071,x74074,x74073)+~P106(f857(f857(f234(f927(f918(x74071),a915)),x74074),x74072))
% 15.02/14.80 [7408]P25(x74081,x74082,x74083)+~P25(x74081,x74082,x74084)+~P106(f857(f857(f234(f927(f918(x74081),a915)),x74083),x74084))
% 15.02/14.80 [7773]~P72(x77731)+E(f857(f857(f79(x77731),f857(x77732,x77733)),f857(f857(f8(a919,x77731),x77732),f857(f301(a919,f857(a112,x77733)),x77734))),f857(f857(f8(a919,x77731),x77732),f857(f301(a919,x77733),x77734)))+~P106(f857(f857(f235(a919),x77733),x77734))
% 15.02/14.80 [7791]E(x77911,x77912)+P106(f857(f857(f172(x77913),x77914),x77912))+~P106(f857(f857(f172(x77913),f857(f857(f151(x77913),x77911),x77914)),x77912))
% 15.02/14.80 [7803]~P109(x78031)+P106(f857(f857(f234(x78031),x78032),x78033))+~P106(f857(f857(f234(x78031),f857(f857(f233(x78031),x78034),x78032)),x78033))
% 15.02/14.80 [7805]~P109(x78051)+P106(f857(f857(f234(x78051),x78052),x78053))+~P106(f857(f857(f234(x78051),f857(f857(f233(x78051),x78052),x78054)),x78053))
% 15.02/14.80 [7807]~P101(x78071)+P106(f857(f857(f234(x78071),x78072),x78073))+~P106(f857(f857(f234(x78071),f857(f857(f110(x78071),x78074),x78072)),x78073))
% 15.02/14.80 [7809]~P101(x78091)+P106(f857(f857(f234(x78091),x78092),x78093))+~P106(f857(f857(f234(x78091),f857(f857(f110(x78091),x78092),x78094)),x78093))
% 15.02/14.80 [7810]~P109(x78101)+P106(f857(f857(f235(x78101),x78102),x78103))+~P106(f857(f857(f235(x78101),f857(f857(f233(x78101),x78104),x78102)),x78103))
% 15.02/14.80 [7811]~P109(x78111)+P106(f857(f857(f235(x78111),x78112),x78113))+~P106(f857(f857(f235(x78111),f857(f857(f233(x78111),x78112),x78114)),x78113))
% 15.02/14.80 [7812]~P113(x78121)+P106(f857(f857(f286(x78121),x78122),x78123))+~P106(f857(f857(f286(x78121),f857(f857(f80(x78121),x78124),x78122)),x78123))
% 15.02/14.80 [7813]~P113(x78131)+P106(f857(f857(f286(x78131),x78132),x78133))+~P106(f857(f857(f286(x78131),f857(f857(f80(x78131),x78132),x78134)),x78133))
% 15.02/14.80 [7889]~P106(f857(f857(f328(x78891),x78892),x78894))+P106(f857(f857(f328(x78891),x78892),x78893))+P106(f857(f857(f328(x78891),x78892),f857(f857(f3(f927(x78891,a915)),x78894),x78893)))
% 15.02/14.80 [7972]P106(f857(x79721,x79722))+P106(f857(x79723,x79722))+~P106(f857(f857(f857(f110(f927(x79724,a915)),x79723),x79721),x79722))
% 15.02/14.80 [7983]~P106(f857(f857(f328(x79831),x79832),x79834))+~P106(f857(f857(f328(x79831),x79832),x79833))+P106(f857(f857(f328(x79831),x79832),f857(f857(f101(f927(x79831,a915)),x79833),x79834)))
% 15.02/14.80 [8030]~P101(x80301)+~P106(f857(f60(x80301),x80304))+E(f857(f857(f63(x80301,x80301,f110(x80301)),x80302),f857(f857(f308(x80301),x80303),x80304)),f857(f857(f110(x80301),x80303),f857(f857(f63(x80301,x80301,f110(x80301)),x80302),x80304)))
% 15.02/14.80 [8031]~P102(x80311)+~P106(f857(f60(x80311),x80314))+E(f857(f857(f63(x80311,x80311,f101(x80311)),x80312),f857(f857(f308(x80311),x80313),x80314)),f857(f857(f101(x80311),x80313),f857(f857(f63(x80311,x80311,f101(x80311)),x80312),x80314)))
% 15.02/14.80 [8032]~P109(x80321)+~P106(f857(f60(x80321),x80324))+E(f857(f857(f63(x80321,x80321,f188(x80321)),x80322),f857(f857(f308(x80321),x80323),x80324)),f857(f857(f188(x80321),x80323),f857(f857(f63(x80321,x80321,f188(x80321)),x80322),x80324)))
% 15.02/14.80 [8033]~P109(x80331)+~P106(f857(f60(x80331),x80334))+E(f857(f857(f63(x80331,x80331,f233(x80331)),x80332),f857(f857(f308(x80331),x80333),x80334)),f857(f857(f233(x80331),x80333),f857(f857(f63(x80331,x80331,f233(x80331)),x80332),x80334)))
% 15.02/14.80 [8035]~P111(x80351)+~P95(x80351)+E(f857(f857(f3(x80351),f857(f857(f80(x80351),f857(f103(x80351),x80352)),x80353)),f857(f857(f80(x80351),f857(f103(x80351),x80352)),x80354)),f857(f857(f80(x80351),f857(f103(x80351),x80352)),f857(f857(f3(x80351),x80353),x80354)))
% 15.02/14.80 [8036]~P141(x80361)+~P95(x80361)+E(f857(f857(f79(x80361),f857(f857(f80(x80361),f857(f103(x80361),x80362)),x80363)),f857(f857(f80(x80361),f857(f103(x80361),x80362)),x80364)),f857(f857(f80(x80361),f857(f103(x80361),x80362)),f857(f857(f79(x80361),x80363),x80364)))
% 15.02/14.80 [8151]E(x81511,x81512)+P106(f857(f857(f328(x81513),x81511),f857(f172(x81513),x81514)))+~P106(f857(f857(f328(x81513),x81511),f857(f172(x81513),f857(f857(f151(x81513),x81512),x81514))))
% 15.02/14.80 [8322]P56(x83221,x83222,x83223)+~P56(x83221,x83222,x83224)+~P106(f857(f857(f234(f927(f926(x83221,x83222),a915)),x83223),x83224))
% 15.02/14.80 [8370]P106(f857(f857(f328(x83701),x83702),x83703))+P106(f857(f857(f328(x83701),x83702),x83704))+~P106(f857(f857(f328(x83701),x83702),f857(f857(f110(f927(x83701,a915)),x83704),x83703)))
% 15.02/14.80 [8380]~P54(x83801,x83804,x83803)+~P106(f857(f857(f328(x83801),x83802),x83804))+P106(f857(f857(f328(f926(x83801,x83801)),f857(f857(f251(x83801,x83801),x83802),x83802)),x83803))
% 15.02/14.80 [8392]~P106(f857(f60(x83922),x83924))+~P106(f857(f60(x83921),x83923))+P106(f857(f60(f926(x83921,x83922)),f857(f857(f253(x83921,x83922),x83923),f857(f18(f927(x83922,a915),x83921),x83924))))
% 15.02/14.80 [8393]~P106(f857(f857(f328(x83931),x83932),x83934))+~P106(f857(f857(f234(f927(x83931,a915)),x83933),x83934))+P106(f857(f857(f234(f927(x83931,a915)),f857(f857(f308(x83931),x83932),x83933)),x83934))
% 15.02/14.80 [8400]~P77(x84002)+~P146(x84002)+E(f857(f857(f11(x84001,x84002),f857(f857(f10(a919,x84002,x84001),f100(x84002)),x84003)),x84004),f857(f100(x84002),f857(f857(f11(x84001,a919),x84003),x84004)))
% 15.02/14.80 [8401]~P77(x84012)+~P143(x84012)+E(f857(f857(f11(x84011,x84012),f857(f857(f10(a1,x84012,x84011),f102(x84012)),x84013)),x84014),f857(f102(x84012),f857(f857(f11(x84011,a1),x84013),x84014)))
% 15.02/14.80 [8425]E(f857(f857(f3(f927(x84251,a915)),x84252),f857(f857(f3(f927(x84251,a915)),x84253),x84254)),x84254)+~P106(f857(f857(f234(f927(x84251,a915)),x84252),x84253))+~P106(f857(f857(f234(f927(x84251,a915)),x84254),x84252))
% 15.02/14.80 [8521]~P106(f857(f60(x85211),x85214))+E(f857(f857(f3(a919),f857(f857(f8(x85211,a919),x85212),x85213)),f857(f857(f8(x85211,a919),x85212),x85214)),f857(f857(f8(x85211,a919),x85212),f857(f857(f3(f927(x85211,a915)),x85213),x85214)))+~P106(f857(f857(f234(f927(x85211,a915)),x85214),x85213))
% 15.02/14.80 [8671]~P9(x86711,x86714,x86713)+~P106(f857(f857(f328(x86711),x86712),x86714))+P106(f857(f857(f328(x86711),x86712),f857(f284(x86711,x86711,x86713),f857(f857(f308(x86711),x86712),f189(f927(x86711,a915))))))
% 15.02/14.80 [8732]~P106(f857(f857(f234(f927(x87321,a915)),x87322),x87323))+~P106(f857(f857(f234(f927(x87321,a915)),x87322),x87324))+P106(f857(f857(f234(f927(x87321,a915)),x87322),f857(f857(f101(f927(x87321,a915)),x87323),x87324)))
% 15.02/14.80 [8834]E(x88341,f189(f927(x88342,a915)))+P106(f857(f60(x88343),x88344))+~P106(f857(f60(f926(x88343,x88342)),f857(f857(f253(x88343,x88342),x88344),f857(f18(f927(x88342,a915),x88343),x88341))))
% 15.02/14.80 [8835]E(x88351,f189(f927(x88352,a915)))+P106(f857(f60(x88353),x88354))+~P106(f857(f60(f926(x88352,x88353)),f857(f857(f253(x88352,x88353),x88351),f857(f18(f927(x88353,a915),x88352),x88354))))
% 15.02/14.80 [8908]P106(f857(f857(f328(x89081),x89082),f315(x89081,x89083)))+~P106(f857(f857(f328(x89081),x89084),f315(x89081,x89083)))+~P106(f857(f857(f328(f926(x89081,x89081)),f857(f857(f251(x89081,x89081),x89082),x89084)),x89083))
% 15.02/14.80 [8965]~P39(x89651,x89654)+P106(f857(f857(f328(f926(x89651,x89651)),f857(f857(f251(x89651,x89651),x89653),x89652)),f306(x89651,x89654)))+P39(x89651,f857(f857(f308(f926(x89651,x89651)),f857(f857(f251(x89651,x89651),x89652),x89653)),x89654))
% 15.02/14.80 [8966]~P59(x89661,x89664)+P106(f857(f857(f328(f926(x89661,x89661)),f857(f857(f251(x89661,x89661),x89663),x89662)),f306(x89661,x89664)))+P59(x89661,f857(f857(f308(f926(x89661,x89661)),f857(f857(f251(x89661,x89661),x89662),x89663)),x89664))
% 15.02/14.80 [9048]~E(x90482,x90483)+~P106(f857(f857(f328(x90481),x90482),f857(f172(x90481),x90484)))+P106(f857(f857(f328(f926(x90481,x90481)),f857(f857(f251(x90481,x90481),x90482),x90483)),f857(f172(f926(x90481,x90481)),f857(f857(f181(x90481,x90481),x90484),x90484))))
% 15.02/14.80 [9136]~E(x91363,x91364)+P106(f857(f857(f256(x91361,x91361,a915),a324),x91362))+~P106(f857(f857(f328(f926(x91361,x91361)),x91362),f857(f172(f926(x91361,x91361)),f857(f857(f181(x91361,x91361),x91363),x91364))))
% 15.02/14.80 [9180]P106(f857(f857(f328(f926(f920(x91801),f920(x91801))),f857(f857(f251(f920(x91801),f920(x91801)),x91802),x91803)),f147(x91801,x91804)))+~E(f857(f857(f175(x91801),f857(f190(f920(x91801)),x91802)),x91803),x91802)+~P106(f857(f857(f235(a919),f857(f190(f920(x91801)),x91802)),f857(f190(f920(x91801)),x91803)))
% 15.02/14.80 [9183]~P53(x91831,x91834)+~P106(f857(f857(f328(f926(x91831,x91831)),f857(f857(f251(x91831,x91831),x91833),x91832)),x91834))+P106(f857(f857(f328(f926(x91831,x91831)),f857(f857(f251(x91831,x91831),x91832),x91833)),x91834))
% 15.02/14.80 [9274]~P106(f857(f60(x92741),x92744))+P106(f857(f857(f328(x92741),f424(x92742,x92743,x92744,x92741)),x92744))+P106(f857(f60(x92743),f857(f857(f39(x92741,f927(x92743,a915)),x92744),x92742)))
% 15.02/14.80 [9275]~P106(f857(f60(x92751),x92754))+P106(f857(f857(f328(x92751),f584(x92752,x92753,x92754,x92751)),x92754))+P106(f857(f60(x92753),f857(f857(f39(x92751,f927(x92753,a915)),x92754),x92752)))
% 15.02/14.80 [9360]P106(f857(f857(f328(f926(x93601,x93601)),x93602),f857(f857(f288(x93601,x93601,x93601),x93603),f306(x93601,x93603))))+~P106(f857(f857(f235(a919),f2(a919)),x93604))+~P106(f857(f857(f328(f926(x93601,x93601)),x93602),f857(f857(f183(f926(x93601,x93601),a915),x93604),x93603)))
% 15.02/14.80 [9368]~P39(x93681,x93682)+~P106(f857(f857(f328(f926(x93681,x93681)),f857(f857(f251(x93681,x93681),x93684),x93683)),x93682))+~P106(f857(f857(f328(f926(x93681,x93681)),f857(f857(f251(x93681,x93681),x93683),x93684)),x93682))
% 15.02/14.80 [9495]~P106(f857(f60(x94951),x94954))+E(f857(f857(f8(x94951,a919),f857(f857(f10(f927(x94952,a915),a919,x94951),f34(x94952)),x94953)),x94954),f857(f34(f926(x94951,x94952)),f857(f857(f253(x94951,x94952),x94954),x94953)))+P106(f857(f857(f328(x94951),f540(x94953,x94952,x94954,x94951)),x94954))
% 15.02/14.80 [9499]~P106(f857(f137(x94991),x94992))+P106(f857(f137(x94991),f857(f857(f159(x94991,x94992),x94993),x94994)))+P106(f857(f857(f328(x94991),x94994),f857(f857(f3(f927(x94991,a915)),f857(f172(x94991),x94992)),f857(f857(f308(x94991),f857(f857(f164(x94991),x94992),x94993)),f189(f927(x94991,a915))))))
% 15.02/14.80 [9516]~P106(f857(f60(x95162),x95163))+~P106(f857(f60(x95161),f857(x95164,f424(x95164,x95161,x95163,x95162))))+P106(f857(f60(x95161),f857(f857(f39(x95162,f927(x95161,a915)),x95163),x95164)))
% 15.02/14.80 [9517]~P106(f857(f60(x95172),x95173))+~P106(f857(f60(x95171),f857(x95174,f584(x95174,x95171,x95173,x95172))))+P106(f857(f60(x95171),f857(f857(f39(x95172,f927(x95171,a915)),x95173),x95174)))
% 15.02/14.80 [9595]~P106(f857(f857(f328(f926(x95951,x95951)),x95952),f857(f857(f288(x95951,x95951,x95951),x95954),f306(x95951,x95954))))+P106(f857(f857(f328(f926(x95951,x95951)),x95952),f857(f857(f288(x95951,x95951,x95951),x95953),f306(x95951,x95953))))+~P106(f857(f857(f234(f927(f926(x95951,x95951),a915)),x95954),x95953))
% 15.02/14.80 [9605]E(f857(f857(f175(x96051),f661(x96054,x96053,x96052,x96051)),x96053),f857(f857(f175(x96051),f661(x96054,x96053,x96052,x96051)),x96052))+~P106(f857(f857(f328(f926(f920(x96051),f920(x96051))),f857(f857(f251(f920(x96051),f920(x96051)),x96052),x96053)),f147(x96051,x96054)))+E(f857(f857(f175(x96051),f857(f190(f920(x96051)),x96052)),x96053),x96052)
% 15.02/14.80 [9621]~P106(f857(f60(x96211),x96214))+E(f857(f857(f8(x96211,a919),f857(f857(f10(f927(x96212,a915),a919,x96211),f34(x96212)),x96213)),x96214),f857(f34(f926(x96211,x96212)),f857(f857(f253(x96211,x96212),x96214),x96213)))+~P106(f857(f60(x96212),f857(x96213,f540(x96213,x96212,x96214,x96211))))
% 15.02/14.80 [9625]~E(f857(f190(f920(x96251)),x96253),f857(f190(f920(x96251)),x96252))+P106(f857(f857(f328(f926(f920(x96251),f920(x96251))),f857(f857(f251(f920(x96251),f920(x96251)),x96252),x96253)),f158(x96251,x96254)))+P106(f857(f857(f328(f926(x96251,x96251)),f666(x96254,x96253,x96252,x96251)),f857(f172(f926(x96251,x96251)),f857(f857(f181(x96251,x96251),x96252),x96253))))
% 15.02/14.80 [9713]~P106(f857(f857(f328(f926(f920(x97131),f920(x97131))),f857(f857(f251(f920(x97131),f920(x97131)),x97132),x97133)),f147(x97131,x97134)))+E(f857(f857(f175(x97131),f857(f190(f920(x97131)),x97132)),x97133),x97132)+P106(f857(f857(f235(a919),f661(x97134,x97133,x97132,x97131)),f857(f857(f188(a919),f857(f190(f920(x97131)),x97132)),f857(f190(f920(x97131)),x97133))))
% 15.02/14.80 [9737]~P106(f857(f857(f328(f926(f920(x97371),f920(x97371))),f857(f857(f251(f920(x97371),f920(x97371)),x97372),x97373)),f147(x97371,x97374)))+P106(f857(f857(f235(a919),f857(f190(f920(x97371)),x97372)),f857(f190(f920(x97371)),x97373)))+P106(f857(f857(f235(a919),f661(x97374,x97373,x97372,x97371)),f857(f857(f188(a919),f857(f190(f920(x97371)),x97372)),f857(f190(f920(x97371)),x97373))))
% 15.02/14.80 [10140]~P106(f857(f857(f328(f926(f920(x101401),f920(x101401))),f857(f857(f251(f920(x101401),f920(x101401)),x101402),x101403)),f147(x101401,x101404)))+E(f857(f857(f175(x101401),f857(f190(f920(x101401)),x101402)),x101403),x101402)+P106(f857(f857(f328(f926(x101401,x101401)),f857(f857(f251(x101401,x101401),f857(f857(f164(x101401),x101402),f661(x101404,x101403,x101402,x101401))),f857(f857(f164(x101401),x101403),f661(x101404,x101403,x101402,x101401)))),x101404))
% 15.02/14.80 [10141]~P106(f857(f857(f328(f926(f920(x101411),f920(x101411))),f857(f857(f251(f920(x101411),f920(x101411)),x101412),x101413)),f147(x101411,x101414)))+P106(f857(f857(f235(a919),f857(f190(f920(x101411)),x101412)),f857(f190(f920(x101411)),x101413)))+P106(f857(f857(f328(f926(x101411,x101411)),f857(f857(f251(x101411,x101411),f857(f857(f164(x101411),x101412),f661(x101414,x101413,x101412,x101411))),f857(f857(f164(x101411),x101413),f661(x101414,x101413,x101412,x101411)))),x101414))
% 15.02/14.80 [10208]~E(f857(f190(f920(x102081)),x102082),f857(f190(f920(x102081)),x102083))+P106(f857(f857(f328(f926(f920(x102081),f920(x102081))),f857(f857(f251(f920(x102081),f920(x102081)),x102082),x102083)),f158(x102081,x102084)))+~P106(f857(f857(f328(f926(x102081,x102081)),f857(f857(f251(x102081,x102081),f857(f857(f164(x102081),x102082),f649(x102084,x102083,x102082,x102081))),f857(f857(f164(x102081),x102083),f649(x102084,x102083,x102082,x102081)))),x102084))
% 15.02/14.80 [10358]~P72(x103581)+~P106(f857(f60(x103582),x103584))+E(f857(f165(x103581),f857(f857(f154(x103582,x103581),x103583),f89(f920(x103582),f857(f857(f20(f920(x103582),a915,a915),f857(f857(f10(a915,f927(a915,a915),f920(x103582)),a325),f857(f857(f9(f920(x103582),f927(x103582,a915),a915),f857(f857(f10(f927(x103582,a915),f927(f927(x103582,a915),a915),f920(x103582)),a324),f172(x103582))),x103584))),f137(x103582))))),f232(x103582,x103581,x103583,x103584))
% 15.02/14.80 [7623]~P65(x76232)+E(x76231,f2(x76232))+E(f857(f857(f290(x76232),f857(f857(f79(x76232),x76233),f857(f857(f80(x76232),x76234),x76231))),x76231),f857(f857(f79(x76232),x76234),f857(f857(f290(x76232),x76233),x76231)))
% 15.02/14.80 [7624]~P62(x76242)+E(x76241,f2(x76242))+E(f857(f857(f35(x76242),f857(f857(f79(x76242),x76243),f857(f857(f80(x76242),x76244),x76241))),x76241),f857(f857(f79(x76242),x76244),f857(f857(f35(x76242),x76243),x76241)))
% 15.02/14.80 [7625]~P62(x76252)+E(x76251,f2(x76252))+E(f857(f857(f35(x76252),f857(f857(f79(x76252),x76253),f857(f857(f80(x76252),x76251),x76254))),x76251),f857(f857(f79(x76252),x76254),f857(f857(f35(x76252),x76253),x76251)))
% 15.02/14.80 [7852]~P66(x78522)+E(x78521,f2(x78522))+E(f857(f857(f290(x78522),f857(f857(f3(x78522),x78523),f857(f857(f80(x78522),x78521),x78524))),x78521),f857(f857(f3(x78522),f857(f857(f290(x78522),x78523),x78521)),x78524))
% 15.02/14.80 [7853]~P65(x78532)+E(x78531,f2(x78532))+E(f857(f857(f290(x78532),f857(f857(f79(x78532),x78533),f857(f857(f80(x78532),x78534),x78531))),x78531),f857(f857(f79(x78532),f857(f857(f290(x78532),x78533),x78531)),x78534))
% 15.02/14.80 [7854]~P66(x78542)+E(x78541,f2(x78542))+E(f857(f857(f290(x78542),f857(f857(f79(x78542),x78543),f857(f857(f80(x78542),x78541),x78544))),x78541),f857(f857(f79(x78542),f857(f857(f290(x78542),x78543),x78541)),x78544))
% 15.02/14.80 [8552]~P106(f857(f160(x85521,x85523),x85524))+~P106(f857(f160(x85521,x85522),x85524))+P106(f857(f160(x85521,f857(f857(f101(f927(x85521,a915)),x85522),x85523)),x85524))
% 15.02/14.80 [8923]~E(f857(f857(f288(x89231,x89231,x89231),x89232),x89234),f189(f927(f926(x89231,x89231),a915)))+~E(f857(f857(f288(x89231,x89231,x89231),x89232),x89233),f189(f927(f926(x89231,x89231),a915)))+E(f857(f857(f288(x89231,x89231,x89231),x89232),f857(f857(f110(f927(f926(x89231,x89231),a915)),x89233),x89234)),f189(f927(f926(x89231,x89231),a915)))
% 15.02/14.80 [9049]~P106(f857(f857(f234(f927(x90491,a915)),x90493),x90494))+~P106(f857(f857(f234(f927(x90491,a915)),x90492),x90494))+P106(f857(f857(f234(f927(x90491,a915)),f857(f857(f110(f927(x90491,a915)),x90492),x90493)),x90494))
% 15.02/14.80 [9423]~P106(f857(f60(x94231),x94234))+~P106(f857(f60(x94231),x94233))+E(f857(f857(f3(a919),f857(f857(f79(a919),f857(f857(f8(x94231,a919),x94232),x94233)),f857(f857(f8(x94231,a919),x94232),x94234))),f857(f857(f8(x94231,a919),x94232),f857(f857(f101(f927(x94231,a915)),x94233),x94234))),f857(f857(f8(x94231,a919),x94232),f857(f857(f110(f927(x94231,a915)),x94233),x94234)))
% 15.02/14.80 [9513]~P106(f857(f857(f328(x95131),x95133),x95132))+~P106(f857(f857(f234(f927(x95131,a915)),x95132),f857(f857(f308(x95131),x95133),x95134)))+P106(f857(f857(f234(f927(x95131,a915)),f857(f857(f3(f927(x95131,a915)),x95132),f857(f857(f308(x95131),x95133),f189(f927(x95131,a915))))),x95134))
% 15.02/14.80 [9687]~P106(f857(f857(f328(x96871),x96873),x96872))+P106(f857(f857(f234(f927(x96871,a915)),x96872),f857(f857(f308(x96871),x96873),x96874)))+~P106(f857(f857(f234(f927(x96871,a915)),f857(f857(f3(f927(x96871,a915)),x96872),f857(f857(f308(x96871),x96873),f189(f927(x96871,a915))))),x96874))
% 15.02/14.80 [9777]~P106(f857(f857(f234(a919),x97771),x97773))+~P106(f857(f857(f235(a919),x97772),x97774))+P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),f857(f857(f251(a919,a919),x97771),x97772)),f857(f857(f251(a919,a919),x97773),x97774))),a32))
% 15.02/14.80 [9778]~P106(f857(f857(f234(a919),x97782),x97784))+~P106(f857(f857(f234(a919),x97781),x97783))+P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),f857(f857(f251(a919,a919),x97781),x97782)),f857(f857(f251(a919,a919),x97783),x97784))),a70))
% 15.02/14.80 [10069]~P106(f857(f857(f328(f920(x100691)),x100694),f161(x100691,x100693)))+~P106(f857(f857(f328(f920(x100691)),x100694),f161(x100691,x100692)))+P106(f857(f160(x100691,f857(f857(f101(f927(x100691,a915)),f857(f857(f9(x100691,f927(x100691,a915),a915),f328(x100691)),x100692)),f857(f857(f9(x100691,f927(x100691,a915),a915),f328(x100691)),x100693))),x100694))
% 15.02/14.80 [10174]~P26(x101741,f927(f927(x101741,a915),a915),f857(f857(f9(x101741,f927(f926(x101741,x101741),a915),f927(f927(x101741,a915),a915)),f857(f857(f10(f927(x101741,a915),f927(f927(f926(x101741,x101741),a915),f927(f927(x101741,a915),a915)),x101741),f59(x101741)),f857(f857(f9(x101741,f927(x101741,a915),f927(x101741,a915)),f308(x101741)),f189(f927(x101741,a915))))),x101743),x101742)+~P106(f857(f857(f328(x101741),x101744),x101742))+E(f857(f857(f3(f927(f927(x101741,a915),a915)),f857(f857(f59(x101741),x101742),x101743)),f857(f857(f59(x101741),f857(f857(f308(x101741),x101744),f189(f927(x101741,a915)))),x101743)),f857(f857(f59(x101741),f857(f857(f3(f927(x101741,a915)),x101742),f857(f857(f308(x101741),x101744),f189(f927(x101741,a915))))),x101743))
% 15.02/14.80 [10311]~P54(x103111,x103112,x103114)+~P106(f857(f857(f328(f926(x103111,x103111)),x103113),x103114))+P106(f857(f857(f256(x103111,x103111,a915),f857(f857(f9(x103111,f927(x103111,a915),f927(x103111,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x103111,a915),f927(x103111,a915)),x103111),f10(a915,a915,x103111)),f857(f857(f10(a915,f927(a915,a915),x103111),a325),f857(f857(f9(x103111,f927(x103111,a915),a915),f328(x103111)),x103112)))),f857(f857(f9(x103111,f927(x103111,a915),a915),f328(x103111)),x103112))),x103113))
% 15.02/14.80 [10326]P106(f857(f60(x103261),x103262))+~P106(f857(f60(x103263),f857(f309(x103261,x103263,x103264),x103262)))+~P106(f857(f60(x103261),f857(f261(x103261),f857(f857(f20(x103261,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103261),a325),f857(f857(f9(x103261,f927(x103261,a915),a915),f328(x103261)),x103262))),f857(f857(f9(x103261,x103263,a915),f857(f857(f10(x103263,f927(x103263,a915),x103261),a324),x103264)),f857(x103264,f576(x103264,x103263,x103262,x103261)))))))
% 15.02/14.80 [8306]~P66(x83062)+E(x83061,f2(x83062))+E(f857(f857(f290(x83062),f857(f857(f3(x83062),f857(f857(f80(x83062),x83061),x83063)),x83064)),x83061),f857(f857(f3(x83062),x83063),f857(f857(f290(x83062),x83064),x83061)))
% 15.02/14.80 [8307]~P66(x83072)+E(x83071,f2(x83072))+E(f857(f857(f290(x83072),f857(f857(f79(x83072),f857(f857(f80(x83072),x83071),x83073)),x83074)),x83071),f857(f857(f79(x83072),x83073),f857(f857(f290(x83072),x83074),x83071)))
% 15.02/14.80 [9209]~E(f857(f857(f288(x92091,x92091,x92091),x92093),x92094),f189(f927(f926(x92091,x92091),a915)))+~E(f857(f857(f288(x92091,x92091,x92091),x92092),x92094),f189(f927(f926(x92091,x92091),a915)))+E(f857(f857(f288(x92091,x92091,x92091),f857(f857(f110(f927(f926(x92091,x92091),a915)),x92092),x92093)),x92094),f189(f927(f926(x92091,x92091),a915)))
% 15.02/14.80 [9985]~P106(f857(f160(x99851,x99853),x99854))+~P106(f857(f160(x99851,x99852),x99854))+P106(f857(f160(x99851,f857(f857(f20(x99851,a915,a915),f857(f857(f10(a915,f927(a915,a915),x99851),a325),x99852)),x99853)),x99854))
% 15.02/14.80 [10247]P106(f857(x102471,f559(x102472,x102473,x102471,x102474)))+~P106(f857(f60(x102474),f857(f261(x102474),x102471)))+P106(f857(f60(x102473),f857(f261(x102473),f857(f857(f10(f927(x102474,a915),a915,x102473),f86(x102474)),f857(f857(f10(f927(x102474,a915),f927(x102474,a915),x102473),f857(f20(x102474,a915,a915),f857(f857(f10(a915,f927(a915,a915),x102474),a325),x102471))),x102472)))))
% 15.02/14.80 [10265]~P106(f857(f60(x102652),f857(f261(x102652),x102653)))+~P106(f857(f60(x102651),f857(f261(x102651),f857(f857(f9(x102651,x102652,a915),x102654),f559(x102654,x102651,x102653,x102652)))))+P106(f857(f60(x102651),f857(f261(x102651),f857(f857(f10(f927(x102652,a915),a915,x102651),f86(x102652)),f857(f857(f10(f927(x102652,a915),f927(x102652,a915),x102651),f857(f20(x102652,a915,a915),f857(f857(f10(a915,f927(a915,a915),x102652),a325),x102653))),x102654)))))
% 15.02/14.80 [10337]~P106(f857(f60(x103371),x103374))+P106(f857(f857(f328(x103371),f794(x103372,x103373,x103374,x103371)),x103374))+P106(f857(f60(x103373),f857(f261(x103373),f857(f857(f10(f927(x103371,a915),a915,x103373),f86(x103371)),f857(f857(f10(f927(x103371,a915),f927(x103371,a915),x103373),f857(f20(x103371,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103371),a325),f857(f857(f9(x103371,f927(x103371,a915),a915),f328(x103371)),x103374)))),x103372)))))
% 15.02/14.80 [10343]~P106(f857(f60(x103432),x103433))+~P106(f857(f60(x103431),f857(f261(x103431),f857(f857(f9(x103431,x103432,a915),x103434),f794(x103434,x103431,x103433,x103432)))))+P106(f857(f60(x103431),f857(f261(x103431),f857(f857(f10(f927(x103432,a915),a915,x103431),f86(x103432)),f857(f857(f10(f927(x103432,a915),f927(x103432,a915),x103431),f857(f20(x103432,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103432),a325),f857(f857(f9(x103432,f927(x103432,a915),a915),f328(x103432)),x103433)))),x103434)))))
% 15.02/14.80 [5227]~E(x52272,x52274)+E(f169(x52271,x52272,x52273),f169(x52271,x52274,x52275))+~E(x52272,f2(a919))
% 15.02/14.80 [5480]E(x54801,x54802)+~E(f169(x54804,x54803,x54801),f169(x54804,x54805,x54802))+E(x54803,f2(a919))
% 15.02/14.80 [6755]E(x67551,x67552)+~E(f857(x67553,x67551),f857(x67553,x67552))+~P26(x67554,x67555,x67553,f241(f927(x67554,a915)))
% 15.02/14.80 [7655]E(x76551,x76552)+~P26(x76553,x76554,x76555,f241(f927(x76553,a915)))+~E(f857(f309(x76553,x76554,x76555),x76551),f857(f309(x76553,x76554,x76555),x76552))
% 15.02/14.80 [7906]P26(x79062,x79063,f498(x79064,x79063,x79062,x79061),x79061)+~E(f857(f309(x79063,x79062,x79065),x79064),x79061)+E(x79061,f189(f927(x79062,a915)))
% 15.02/14.80 [8436]~P106(f857(f857(x84363,x84362),x84365))+~P106(f857(f857(x84363,x84364),x84362))+P106(f857(f857(f328(x84361),x84362),f298(x84361,x84363,x84364,x84365)))
% 15.02/14.80 [8437]~P106(f857(f857(x84373,x84372),x84375))+~P106(f857(f857(x84373,x84374),x84372))+P106(f857(f857(f328(x84371),x84372),f289(x84371,x84373,x84374,x84375)))
% 15.02/14.80 [8740]~P26(x87401,x87402,x87403,x87404)+P27(x87401,x87402,x87403,x87404,x87405)+~E(f857(f309(x87401,x87402,x87403),x87404),x87405)
% 15.02/14.80 [8873]~P27(x88731,x88733,x88734,x88732,x88735)+~P106(f857(f60(x88733),x88735))+P106(f857(f60(x88731),x88732))
% 15.02/14.80 [8874]~P27(x88743,x88741,x88744,x88745,x88742)+~P106(f857(f60(x88743),x88745))+P106(f857(f60(x88741),x88742))
% 15.02/14.80 [9006]~P26(x90061,x90063,x90065,f241(f927(x90061,a915)))+~P26(x90063,x90062,x90064,f241(f927(x90063,a915)))+P26(x90061,x90062,f857(f72(x90063,x90062,x90061,x90064),x90065),f241(f927(x90061,a915)))
% 15.02/14.80 [9572]P106(f857(f857(f328(f926(x95721,x95721)),f857(f857(f251(x95721,x95721),x95722),x95723)),f306(x95721,x95724)))+~P106(f857(f857(f328(f926(x95721,x95721)),f857(f857(f251(x95721,x95721),x95722),x95725)),f306(x95721,x95724)))+~P106(f857(f857(f328(f926(x95721,x95721)),f857(f857(f251(x95721,x95721),x95725),x95723)),f306(x95721,x95724)))
% 15.02/14.80 [9612]~P109(x96122)+~P106(f857(f137(x96121),x96125))+P106(f857(f137(x96121),f149(x96121,x96122,x96123,x96124,x96125)))
% 15.02/14.80 [5555]~E(x55552,f113(x55551))+E(f857(f857(f134(x55551),x55552),x55553),f857(f857(f151(x55551),x55554),x55555))+~E(x55553,f857(f857(f151(x55551),x55554),x55555))
% 15.02/14.80 [5556]~E(x55562,f113(x55561))+E(f857(f857(f134(x55561),x55562),x55563),f857(f857(f151(x55561),x55564),x55565))+~E(f857(f857(f151(x55561),x55564),x55565),x55563)
% 15.02/14.80 [6711]~E(f857(f190(f920(x67111)),x67115),f857(f190(f920(x67112)),x67114))+E(f857(f857(f154(f926(x67111,x67112),x67112),f255(x67111,x67112)),x67113),x67114)+~E(f857(f857(f181(x67111,x67112),x67115),x67114),x67113)
% 15.02/14.80 [6712]~E(f857(f190(f920(x67121)),x67124),f857(f190(f920(x67122)),x67125))+E(f857(f857(f154(f926(x67121,x67122),x67121),f250(x67121,x67122)),x67123),x67124)+~E(f857(f857(f181(x67121,x67122),x67124),x67125),x67123)
% 15.02/14.80 [7191]~P109(x71911)+~P14(x71911,f857(f857(f154(x71912,x71911),x71913),x71915))+P14(x71911,f857(f857(f154(x71912,x71911),x71913),f857(f136(x71912,x71914),x71915)))
% 15.02/14.80 [7234]~P106(f857(x72343,x72345))+~P106(f857(f857(x72342,x72344),x72345))+P106(f857(f857(f92(x72341,x72342,x72343),x72344),x72345))
% 15.02/14.80 [7334]~P109(x73341)+P14(x73341,f857(f857(f154(x73342,x73341),x73343),f170(x73342,x73344,x73345)))+~P14(x73341,f857(f857(f154(x73342,x73341),x73343),x73345))
% 15.02/14.80 [7357]~P56(x73573,x73572,x73575)+~P56(x73571,x73573,x73574)+P56(x73571,x73572,f857(f857(f288(x73571,x73573,x73572),x73574),x73575))
% 15.02/14.80 [7454]E(x74541,x74542)+~P26(x74543,x74544,x74545,f241(f927(x74543,a915)))+~E(f857(f857(f154(x74543,x74544),x74545),x74541),f857(f857(f154(x74543,x74544),x74545),x74542))
% 15.02/14.80 [7609]~P106(f857(f857(f234(a919),x76091),f857(x76093,x76095)))+P106(f857(f857(f234(a919),x76091),f155(x76092,x76093,x76094)))+~P106(f857(f857(f328(x76092),x76095),f857(f172(x76092),x76094)))
% 15.02/14.80 [7610]~P106(f857(f857(f235(a919),x76101),f857(x76103,x76105)))+P106(f857(f857(f235(a919),x76101),f155(x76102,x76103,x76104)))+~P106(f857(f857(f328(x76102),x76105),f857(f172(x76102),x76104)))
% 15.02/14.80 [8002]P106(f857(x80021,x80022))+~P106(f857(x80021,x80023))+~P106(f857(f857(f328(x80024),x80022),f857(f172(x80024),f169(x80024,x80025,x80023))))
% 15.02/14.80 [8003]P106(f857(x80031,x80032))+~P106(f857(x80031,x80033))+~P106(f857(f857(f328(x80034),x80033),f857(f172(x80034),f169(x80034,x80035,x80032))))
% 15.02/14.80 [8007]~P110(x80071)+P106(f857(f857(f234(f927(x80071,a915)),f302(x80071,x80072,x80073)),f302(x80071,x80074,x80075)))+P106(f857(f857(f234(x80071),x80072),x80073))
% 15.02/14.80 [8028]~P6(x80281)+P106(f857(f857(f234(x80281),f857(f857(f38(x80282,x80281),x80283),x80284)),f857(x80284,x80285)))+~P106(f857(f857(f328(x80282),x80285),x80283))
% 15.02/14.80 [8097]~P26(x80971,x80972,x80974,x80973)+E(f857(f76(x80971,x80972,x80973,x80974),f857(x80974,x80975)),x80975)+~P106(f857(f857(f328(x80971),x80975),x80973))
% 15.02/14.80 [8098]~P26(x80981,x80982,x80984,x80983)+E(f857(f91(x80981,x80982,x80983,x80984),f857(x80984,x80985)),x80985)+~P106(f857(f857(f328(x80981),x80985),x80983))
% 15.02/14.80 [8295]~P106(f857(x82951,x82955))+P106(f857(x82951,f366(x82951,x82952,x82953,x82954)))+~P106(f857(f857(f328(x82954),x82955),x82953))
% 15.02/14.80 [8296]~P106(f857(x82961,x82965))+P106(f857(x82961,f366(x82961,x82962,x82963,x82964)))+~P106(f857(f857(f328(x82964),x82965),x82962))
% 15.02/14.80 [8390]P106(f857(f60(x83901),x83902))+~P106(f857(f60(x83903),x83904))+~P106(f857(f857(f234(f927(x83901,a915)),x83902),f857(f309(x83903,x83901,x83905),x83904)))
% 15.02/14.80 [8556]E(x85561,x85562)+~P26(x85563,x85564,x85565,f857(f857(f110(f927(x85563,a915)),f857(f172(x85563),x85561)),f857(f172(x85563),x85562)))+~E(f857(f857(f154(x85563,x85564),x85565),x85561),f857(f857(f154(x85563,x85564),x85565),x85562))
% 15.02/14.80 [8609]~P110(x86091)+~P106(f857(f857(f235(f927(x86091,a915)),f302(x86091,x86094,x86095)),f302(x86091,x86092,x86093)))+P106(f857(f857(f234(x86091),x86092),x86093))
% 15.02/14.80 [8670]~P26(x86701,x86704,x86705,f241(f927(x86701,a915)))+~P106(f857(f857(f328(x86704),f857(x86705,x86702)),f857(f309(x86701,x86704,x86705),x86703)))+P106(f857(f857(f328(x86701),x86702),x86703))
% 15.02/14.80 [8746]P106(f857(x87461,x87462))+~P106(f857(x87461,f377(x87461,x87463,x87464,x87465)))+~P106(f857(f857(f328(x87465),x87462),x87464))
% 15.02/14.80 [8747]P106(f857(x87471,x87472))+~P106(f857(x87471,f377(x87471,x87473,x87474,x87475)))+~P106(f857(f857(f328(x87475),x87472),x87473))
% 15.02/14.80 [9046]~P26(x90462,x90463,x90461,x90464)+E(f857(x90461,f857(f76(x90462,x90463,x90464,x90461),x90465)),x90465)+~P106(f857(f857(f328(x90463),x90465),f857(f309(x90462,x90463,x90461),x90464)))
% 15.02/14.80 [9149]E(x91491,f113(x91492))+E(f857(f857(f151(x91492),x91493),f680(x91494,x91493,x91495,x91491,x91492)),x91491)+~E(f857(f857(f134(x91492),x91491),x91495),f857(f857(f151(x91492),x91493),x91494))
% 15.02/14.80 [9150]E(x91501,f113(x91502))+E(f857(f857(f151(x91502),x91503),f681(x91504,x91501,x91505,x91503,x91502)),x91501)+~E(f857(f857(f134(x91502),x91501),x91504),f857(f857(f151(x91502),x91503),x91505))
% 15.02/14.80 [9168]E(f857(f857(f151(x91682),x91683),f680(x91684,x91683,x91681,x91685,x91682)),x91685)+~E(f857(f857(f134(x91682),x91685),x91681),f857(f857(f151(x91682),x91683),x91684))+E(x91681,f857(f857(f151(x91682),x91683),x91684))
% 15.02/14.80 [9169]E(f857(f857(f151(x91691),x91692),f681(x91694,x91695,x91693,x91692,x91691)),x91695)+~E(f857(f857(f134(x91691),x91695),x91694),f857(f857(f151(x91691),x91692),x91693))+E(f857(f857(f151(x91691),x91692),x91693),x91694)
% 15.02/14.80 [9245]~E(f857(f309(x92453,x92452,x92454),f241(f927(x92453,a915))),f241(f927(x92452,a915)))+~E(f857(f309(x92451,x92453,x92455),f241(f927(x92451,a915))),f241(f927(x92453,a915)))+E(f857(f309(x92451,x92452,f857(f72(x92453,x92452,x92451,x92454),x92455)),f241(f927(x92451,a915))),f241(f927(x92452,a915)))
% 15.02/14.80 [9618]E(x96181,f113(x96182))+~E(f857(f857(f134(x96182),x96181),x96183),f857(f857(f151(x96182),x96185),x96184))+E(f857(f857(f134(x96182),f681(x96183,x96181,x96184,x96185,x96182)),x96183),x96184)
% 15.02/14.80 [9619]E(x96191,f113(x96192))+~E(f857(f857(f134(x96192),x96191),x96195),f857(f857(f151(x96192),x96194),x96193))+E(f857(f857(f134(x96192),f680(x96193,x96194,x96195,x96191,x96192)),x96195),x96193)
% 15.02/14.80 [9626]E(f857(f857(f134(x96262),f680(x96264,x96263,x96261,x96265,x96262)),x96261),x96264)+~E(f857(f857(f134(x96262),x96265),x96261),f857(f857(f151(x96262),x96263),x96264))+E(x96261,f857(f857(f151(x96262),x96263),x96264))
% 15.02/14.80 [9627]~E(f857(f857(f134(x96271),x96275),x96274),f857(f857(f151(x96271),x96272),x96273))+E(f857(f857(f134(x96271),f681(x96274,x96275,x96273,x96272,x96271)),x96274),x96273)+E(f857(f857(f151(x96271),x96272),x96273),x96274)
% 15.02/14.80 [9628]E(f857(f857(f134(x96281),x96285),f684(x96283,x96282,x96284,x96285,x96281)),x96282)+E(f857(f857(f134(x96281),x96282),f683(x96283,x96282,x96284,x96285,x96281)),x96285)+~E(f857(f857(f134(x96281),x96285),x96284),f857(f857(f134(x96281),x96282),x96283))
% 15.02/14.80 [9665]~P109(x96651)+P14(x96651,f857(f857(f154(x96652,x96651),x96653),f149(x96652,x96651,x96653,x96654,x96655)))+~P14(x96651,f857(f857(f154(x96652,x96651),x96653),x96655))
% 15.02/14.80 [9682]~P60(x96825,x96821,x96824,x96823)+P106(f857(f857(x96821,x96822),f531(x96823,x96824,x96821,x96825,x96822)))+~P106(f857(f857(f328(x96825),x96822),x96824))
% 15.02/14.80 [9683]~P60(x96835,x96831,x96834,x96833)+P106(f857(f857(x96831,x96832),f800(x96833,x96834,x96831,x96835,x96832)))+~P106(f857(f857(f328(x96835),x96832),x96834))
% 15.02/14.80 [9789]~P106(f857(f857(f328(f926(x97891,x97891)),f857(f857(f251(x97891,x97891),x97895),x97893)),f306(x97891,x97894)))+P106(f857(f857(f328(f926(x97891,x97891)),f857(f857(f251(x97891,x97891),x97892),x97893)),f857(f857(f288(x97891,x97891,x97891),x97894),f306(x97891,x97894))))+~P106(f857(f857(f328(f926(x97891,x97891)),f857(f857(f251(x97891,x97891),x97892),x97895)),f857(f857(f288(x97891,x97891,x97891),x97894),f306(x97891,x97894))))
% 15.02/14.80 [9790]~P106(f857(f857(f328(f926(x97901,x97901)),f857(f857(f251(x97901,x97901),x97902),x97905)),f306(x97901,x97904)))+P106(f857(f857(f328(f926(x97901,x97901)),f857(f857(f251(x97901,x97901),x97902),x97903)),f857(f857(f288(x97901,x97901,x97901),x97904),f306(x97901,x97904))))+~P106(f857(f857(f328(f926(x97901,x97901)),f857(f857(f251(x97901,x97901),x97905),x97903)),f857(f857(f288(x97901,x97901,x97901),x97904),f306(x97901,x97904))))
% 15.02/14.80 [9792]P106(f857(f857(f328(f926(f920(x97921),f920(x97921))),f857(f857(f251(f920(x97921),f920(x97921)),x97922),x97923)),f158(x97921,f306(x97921,x97924))))+~P106(f857(f857(f328(f926(f920(x97921),f920(x97921))),f857(f857(f251(f920(x97921),f920(x97921)),x97922),x97925)),f158(x97921,f306(x97921,x97924))))+~P106(f857(f857(f328(f926(f920(x97921),f920(x97921))),f857(f857(f251(f920(x97921),f920(x97921)),x97925),x97923)),f158(x97921,f306(x97921,x97924))))
% 15.02/14.80 [9796]E(f857(f857(f134(x97961),x97962),f683(x97963,x97962,x97964,x97965,x97961)),x97965)+E(f857(f857(f134(x97961),f684(x97963,x97962,x97964,x97965,x97961)),x97963),x97964)+~E(f857(f857(f134(x97961),x97962),x97963),f857(f857(f134(x97961),x97965),x97964))
% 15.02/14.80 [9797]E(f857(f857(f134(x97971),x97972),f684(x97973,x97974,x97975,x97972,x97971)),x97974)+E(f857(f857(f134(x97971),f683(x97973,x97974,x97975,x97972,x97971)),x97975),x97973)+~E(f857(f857(f134(x97971),x97972),x97975),f857(f857(f134(x97971),x97974),x97973))
% 15.02/14.80 [9851]P106(f857(f857(f328(f926(x98511,x98511)),f857(f857(f251(x98511,x98511),x98512),x98513)),f857(f857(f288(x98511,x98511,x98511),x98514),f306(x98511,x98514))))+~P106(f857(f857(f328(f926(x98511,x98511)),f857(f857(f251(x98511,x98511),x98512),x98515)),f857(f857(f288(x98511,x98511,x98511),x98514),f306(x98511,x98514))))+~P106(f857(f857(f328(f926(x98511,x98511)),f857(f857(f251(x98511,x98511),x98515),x98513)),f857(f857(f288(x98511,x98511,x98511),x98514),f306(x98511,x98514))))
% 15.02/14.80 [9878]P36(x98781,x98782,x98783,x98784,x98785)+~E(f857(f190(f920(x98781)),x98784),f857(f190(f920(x98782)),x98785))+~P106(f857(f857(f256(x98781,x98782,a915),x98783),f696(x98785,x98784,x98783,x98782,x98781)))
% 15.02/14.80 [9879]P36(x98791,x98792,x98793,x98794,x98795)+~E(f857(f190(f920(x98791)),x98794),f857(f190(f920(x98792)),x98795))+~P106(f857(f857(f256(x98791,x98792,a915),x98793),f702(x98793,x98795,x98794,x98792,x98791)))
% 15.02/14.80 [9884]E(f857(f857(f134(x98841),f683(x98842,x98843,x98844,x98845,x98841)),x98844),x98842)+~E(f857(f857(f134(x98841),x98843),x98842),f857(f857(f134(x98841),x98845),x98844))+E(f857(f857(f134(x98841),f684(x98842,x98843,x98844,x98845,x98841)),x98842),x98844)
% 15.02/14.80 [9899]~P109(x98992)+E(f857(f857(f148(x98991,x98992,x98993),x98994),x98995),f857(f857(f151(x98991),x98994),x98995))+P106(f857(f857(f328(x98991),f744(x98994,x98993,x98995,x98991,x98992)),f857(f172(x98991),x98995)))
% 15.02/14.80 [9903]~P60(x99031,x99034,x99033,x99032)+~P106(f857(f857(f328(x99031),x99035),x99033))+P106(f857(f857(f328(x99031),f531(x99032,x99033,x99034,x99031,x99035)),x99032))
% 15.02/14.80 [9904]~P60(x99041,x99044,x99043,x99042)+~P106(f857(f857(f328(x99041),x99045),x99043))+P106(f857(f857(f328(x99041),f800(x99042,x99043,x99044,x99041,x99045)),x99042))
% 15.02/14.80 [10018]~P106(f857(f857(f328(f926(f927(x100181,a915),f927(x100181,a915))),f857(f857(f251(f927(x100181,a915),f927(x100181,a915)),x100184),x100183)),f317(x100181,x100182)))+~P106(f857(f857(f328(x100181),x100185),x100184))+P106(f857(f857(f328(x100181),f607(x100182,x100183,x100184,x100181,x100185)),x100183))
% 15.02/14.80 [10029]~P109(x100292)+E(f857(f857(f148(x100291,x100292,x100293),x100294),x100295),f857(f857(f151(x100291),x100294),x100295))+~P106(f857(f857(f234(x100292),f857(x100293,x100294)),f857(x100293,f744(x100294,x100293,x100295,x100291,x100292))))
% 15.02/14.80 [10078]~P26(x100783,x100784,x100785,f241(f927(x100783,a915)))+P106(f857(x100781,x100782))+~P106(f857(x100781,f857(f91(x100783,x100784,f241(f927(x100783,a915)),x100785),f813(x100782,x100781,x100785,x100784,x100783))))
% 15.02/14.80 [10225]P36(x102251,x102252,x102253,x102254,x102255)+~E(f857(f190(f920(x102251)),x102254),f857(f190(f920(x102252)),x102255))+~P106(f857(f857(x102253,f857(f857(f164(x102251),x102254),f703(x102255,x102254,x102253,x102252,x102251))),f857(f857(f164(x102252),x102255),f703(x102255,x102254,x102253,x102252,x102251))))
% 15.02/14.80 [10226]P36(x102261,x102262,x102263,x102264,x102265)+~E(f857(f190(f920(x102261)),x102264),f857(f190(f920(x102262)),x102265))+~P106(f857(f857(x102263,f857(f857(f164(x102261),x102264),f737(x102263,x102265,x102262,x102264,x102261))),f857(f857(f164(x102262),x102265),f737(x102263,x102265,x102262,x102264,x102261))))
% 15.02/14.80 [6786]~P18(x67862,x67865,x67861)+~P106(f857(f60(x67862),x67864))+E(f857(x67861,f857(f857(f308(x67862),x67863),x67864)),f857(f857(f63(x67862,x67862,x67865),x67863),x67864))
% 15.02/14.80 [6787]~E(x67873,x67874)+~E(x67872,x67875)+E(f857(f857(f308(x67871),x67872),f857(f857(f308(x67871),x67873),f189(f927(x67871,a915)))),f857(f857(f308(x67871),x67874),f857(f857(f308(x67871),x67875),f189(f927(x67871,a915)))))
% 15.02/14.80 [6797]P106(f857(x67972,x67975))+E(f177(x67971,x67972,f857(f857(f134(x67971),x67973),x67974)),f177(x67971,x67972,x67973))+~P106(f857(f857(f328(x67971),x67975),f857(f172(x67971),x67973)))
% 15.02/14.80 [6835]E(f857(x68351,x68352),f189(f927(x68353,a915)))+~E(f857(f857(f39(x68354,f927(x68353,a915)),x68355),x68351),f189(f927(x68353,a915)))+~P106(f857(f857(f328(x68354),x68352),x68355))
% 15.02/14.80 [6836]E(f857(x68361,x68362),f241(f927(x68363,a915)))+~E(f857(f857(f38(x68364,f927(x68363,a915)),x68365),x68361),f241(f927(x68363,a915)))+~P106(f857(f857(f328(x68364),x68362),x68365))
% 15.02/14.80 [7344]~E(x73442,x73444)+~P140(x73441)+E(f857(f857(f79(x73441),f857(f857(f80(x73441),x73442),x73443)),f857(f857(f80(x73441),x73444),x73445)),f857(f857(f79(x73441),f857(f857(f80(x73441),x73442),x73445)),f857(f857(f80(x73441),x73444),x73443)))
% 15.02/14.80 [7406]~P6(x74061)+~P106(f857(f857(f328(x74064),x74063),x74065))+P106(f857(f857(f234(x74061),f857(x74062,x74063)),f857(f857(f39(x74064,x74061),x74065),x74062)))
% 15.02/14.80 [7459]~P108(x74591)+P106(f857(f857(f234(x74591),f857(x74592,x74593)),f857(x74594,x74593)))+~P106(f857(f857(f234(f927(x74595,x74591)),x74592),x74594))
% 15.02/14.80 [7579]E(x75791,x75792)+E(x75793,x75791)+~E(f857(f857(f308(x75794),x75791),f857(f857(f308(x75794),x75795),f189(f927(x75794,a915)))),f857(f857(f308(x75794),x75792),f857(f857(f308(x75794),x75793),f189(f927(x75794,a915)))))
% 15.02/14.80 [7580]E(x75801,x75802)+E(x75803,x75801)+~E(f857(f857(f308(x75804),x75803),f857(f857(f308(x75804),x75802),f189(f927(x75804,a915)))),f857(f857(f308(x75804),x75805),f857(f857(f308(x75804),x75801),f189(f927(x75804,a915)))))
% 15.02/14.80 [7581]E(x75811,x75812)+E(x75811,x75813)+~E(f857(f857(f308(x75814),x75813),f857(f857(f308(x75814),x75812),f189(f927(x75814,a915)))),f857(f857(f308(x75814),x75815),f857(f857(f308(x75814),x75811),f189(f927(x75814,a915)))))
% 15.02/14.80 [7582]E(x75821,x75822)+E(x75821,x75823)+~E(f857(f857(f308(x75824),x75821),f857(f857(f308(x75824),x75825),f189(f927(x75824,a915)))),f857(f857(f308(x75824),x75822),f857(f857(f308(x75824),x75823),f189(f927(x75824,a915)))))
% 15.02/14.80 [8107]P26(x81071,x81072,x81073,x81074)+~P26(x81071,x81072,x81073,x81075)+~P106(f857(f857(f234(f927(x81071,a915)),x81074),x81075))
% 15.02/14.80 [8137]~E(f857(x81373,x81375),x81374)+~P26(x81371,x81372,x81373,f241(f927(x81371,a915)))+E(f857(f91(x81371,x81372,f241(f927(x81371,a915)),x81373),x81374),x81375)
% 15.02/14.80 [8284]E(x82841,x82842)+~E(f857(f309(x82843,x82844,x82845),x82841),f857(f309(x82843,x82844,x82845),x82842))+~P26(x82843,x82844,x82845,f857(f857(f110(f927(x82843,a915)),x82841),x82842))
% 15.02/14.80 [8360]P106(f857(x83602,x83604))+E(f857(f857(f138(x83601),f857(f190(f920(x83601)),f177(x83601,x83602,x83603))),x83603),f857(f857(f151(x83601),x83604),x83605))+~E(f857(f857(f134(x83601),f177(x83601,x83602,x83603)),f857(f857(f151(x83601),x83604),x83605)),x83603)
% 15.02/14.80 [8388]~P26(x83881,x83882,x83883,x83885)+~P26(x83881,x83882,x83883,x83884)+P26(x83881,x83882,x83883,f857(f857(f101(f927(x83881,a915)),x83884),x83885))
% 15.02/14.80 [8495]~P72(x84951)+E(f857(f857(f79(x84951),f857(x84952,x84953)),f857(f165(x84951),f857(f857(f154(x84954,x84951),x84952),f170(x84954,x84953,x84955)))),f857(f165(x84951),f857(f857(f154(x84954,x84951),x84952),x84955)))+~P106(f857(f857(f328(x84954),x84953),f857(f172(x84954),x84955)))
% 15.02/14.80 [8582]~P109(x85821)+~P14(x85821,f857(f857(f154(x85822,x85821),x85823),x85825))+P14(x85821,f857(f857(f154(x85822,x85821),x85823),f857(f857(f148(x85822,x85821,x85823),x85824),x85825)))
% 15.02/14.80 [8666]~P6(x86661)+P106(f857(f857(f234(x86661),f857(f857(f38(x86662,x86661),x86663),x86664)),f857(f857(f38(x86662,x86661),x86665),x86664)))+~P106(f857(f857(f234(f927(x86662,a915)),x86665),x86663))
% 15.02/14.80 [8667]~P6(x86671)+P106(f857(f857(f234(x86671),f857(f857(f39(x86672,x86671),x86673),x86674)),f857(f857(f39(x86672,x86671),x86675),x86674)))+~P106(f857(f857(f234(f927(x86672,a915)),x86673),x86675))
% 15.02/14.80 [8700]~P109(x87003)+P106(f857(f137(x87001),x87002))+~P106(f857(f137(x87001),f857(f857(f148(x87001,x87003,x87004),x87005),x87002)))
% 15.02/14.80 [8845]~P109(x88451)+~P106(f857(f857(f328(x88452),x88453),f857(f172(x88452),x88454)))+~P106(f857(f137(x88452),f857(f857(f148(x88452,x88451,x88455),x88453),x88454)))
% 15.02/14.80 [8935]~P109(x89351)+P14(x89351,f857(f857(f154(x89352,x89351),x89353),x89354))+~P14(x89351,f857(f857(f154(x89352,x89351),x89353),f857(f857(f148(x89352,x89351,x89353),x89355),x89354)))
% 15.02/14.80 [8981]~P26(x89812,x89811,x89814,x89813)+E(f857(f309(x89811,x89812,f91(x89812,x89811,x89813,x89814)),f857(f309(x89812,x89811,x89814),x89815)),x89815)+~P106(f857(f857(f234(f927(x89812,a915)),x89815),x89813))
% 15.02/14.80 [9034]~P109(x90342)+E(f857(f857(f148(x90341,x90342,x90343),x90344),x90345),f149(x90341,x90342,x90343,x90344,x90345))+P106(f857(f857(f328(x90342),f857(x90343,x90344)),f857(f309(x90341,x90342,x90343),f857(f172(x90341),x90345))))
% 15.02/14.80 [9115]~P109(x91152)+E(f149(x91151,x91152,x91153,x91154,x91155),x91155)+~P106(f857(f857(f328(x91152),f857(x91153,x91154)),f857(f309(x91151,x91152,x91153),f857(f172(x91151),x91155))))
% 15.02/14.80 [9129]~P26(x91292,x91291,x91293,x91295)+P106(f857(f857(f235(f927(x91291,a915)),f857(f309(x91292,x91291,x91293),x91294)),f857(f309(x91292,x91291,x91293),x91295)))+~P106(f857(f857(f235(f927(x91292,a915)),x91294),x91295))
% 15.02/14.80 [9286]~P26(x92861,x92862,x92863,f241(f927(x92861,a915)))+~P106(f857(f857(f234(f927(x92862,a915)),x92864),f857(f309(x92861,x92862,x92863),x92865)))+P106(f857(f857(f234(f927(x92861,a915)),f857(f310(x92861,x92862,x92863),x92864)),x92865))
% 15.02/14.80 [9309]~E(f857(f309(x93093,x93091,x93094),f241(f927(x93093,a915))),f241(f927(x93091,a915)))+P106(f857(f857(f234(f927(x93091,a915)),x93092),f857(f309(x93093,x93091,x93094),x93095)))+~P106(f857(f857(f234(f927(x93093,a915)),f857(f310(x93093,x93091,x93094),x93092)),x93095))
% 15.02/14.80 [9415]~P26(x94151,x94154,x94155,f241(f927(x94151,a915)))+~P106(f857(f857(f234(f927(x94154,a915)),f857(f309(x94151,x94154,x94155),x94152)),f857(f309(x94151,x94154,x94155),x94153)))+P106(f857(f857(f234(f927(x94151,a915)),x94152),x94153))
% 15.02/14.80 [9540]~P83(x95401)+~E(f857(x95403,f721(x95403,x95404,x95405,x95402,x95401)),f2(x95401))+E(f857(f165(x95401),f857(f857(f154(x95402,x95401),x95403),f857(f136(x95402,x95404),x95405))),f857(f165(x95401),f857(f857(f154(x95402,x95401),x95403),x95405)))
% 15.02/14.80 [9567]~P27(x95671,x95672,x95673,f241(f927(x95671,a915)),f241(f927(x95672,a915)))+~P106(f857(f857(f234(f927(x95672,a915)),x95674),f857(f309(x95671,x95672,x95673),x95675)))+P106(f857(f857(f234(f927(x95671,a915)),f857(f310(x95671,x95672,x95673),x95674)),x95675))
% 15.02/14.80 [9596]~P27(x95963,x95961,x95964,f241(f927(x95963,a915)),f241(f927(x95961,a915)))+P106(f857(f857(f234(f927(x95961,a915)),x95962),f857(f309(x95963,x95961,x95964),x95965)))+~P106(f857(f857(f234(f927(x95963,a915)),f857(f310(x95963,x95961,x95964),x95962)),x95965))
% 15.02/14.80 [9730]~P17(x97301,x97302,x97303)+~P106(f857(f60(x97301),x97305))+P106(f857(f65(x97301,x97302,x97303,x97304,x97305),f857(f857(f63(x97301,x97302,x97303),x97304),x97305)))
% 15.02/14.80 [9809]~P27(x98092,x98091,x98094,f241(f927(x98092,a915)),f241(f927(x98091,a915)))+~P27(x98091,x98093,x98095,f241(f927(x98091,a915)),f241(f927(x98093,a915)))+E(f857(f72(x98091,x98092,x98093,f91(x98092,x98091,f241(f927(x98092,a915)),x98094)),f91(x98091,x98093,f241(f927(x98091,a915)),x98095)),f91(x98092,x98093,f241(f927(x98092,a915)),f857(f72(x98091,x98093,x98092,x98095),x98094)))
% 15.02/14.80 [9810]P106(f857(x98101,f645(x98102,x98101,x98103,x98104,x98105)))+~P106(f857(f857(f234(f927(x98105,a915)),x98104),x98103))+P106(f857(f857(f234(f927(x98105,a915)),f857(f857(f101(f927(x98105,a915)),x98104),f857(f261(x98105),x98101))),f857(f857(f101(f927(x98105,a915)),x98103),f857(f261(x98105),x98102))))
% 15.02/14.80 [9824]~P83(x98241)+~P106(f857(x98244,f721(x98243,x98244,x98245,x98242,x98241)))+E(f857(f165(x98241),f857(f857(f154(x98242,x98241),x98243),f857(f136(x98242,x98244),x98245))),f857(f165(x98241),f857(f857(f154(x98242,x98241),x98243),x98245)))
% 15.02/14.80 [9901]~P6(x99015)+P106(f857(f857(f328(x99011),f434(x99012,x99013,x99011,x99014,x99015)),x99013))+P106(f857(f857(f234(x99015),x99014),f857(f857(f38(x99011,x99015),x99013),x99012)))
% 15.02/14.80 [9905]~P83(x99051)+E(f857(f165(x99051),f857(f857(f154(x99052,x99051),x99053),f857(f136(x99052,x99054),x99055))),f857(f165(x99051),f857(f857(f154(x99052,x99051),x99053),x99055)))+P106(f857(f857(f328(x99052),f721(x99053,x99054,x99055,x99052,x99051)),f857(f172(x99052),x99055)))
% 15.02/14.80 [9915]~P106(f857(x99155,f645(x99155,x99153,x99154,x99152,x99151)))+~P106(f857(f857(f234(f927(x99151,a915)),x99152),x99154))+P106(f857(f857(f234(f927(x99151,a915)),f857(f857(f101(f927(x99151,a915)),x99152),f857(f261(x99151),x99153))),f857(f857(f101(f927(x99151,a915)),x99154),f857(f261(x99151),x99155))))
% 15.02/14.80 [9931]~P26(x99315,x99313,x99314,f241(f927(x99315,a915)))+P106(f857(x99311,x99312))+P106(f857(f857(f328(x99313),f813(x99312,x99311,x99314,x99313,x99315)),f857(f309(x99315,x99313,x99314),f241(f927(x99315,a915)))))
% 15.02/14.80 [9954]P36(x99541,x99542,x99543,x99544,x99545)+~E(f857(f190(f920(x99542)),x99545),f857(f190(f920(x99541)),x99544))+P106(f857(f857(f235(a919),f703(x99545,x99544,x99543,x99542,x99541)),f857(f190(f920(x99541)),x99544)))
% 15.02/14.80 [9955]P36(x99551,x99552,x99553,x99554,x99555)+~E(f857(f190(f920(x99552)),x99555),f857(f190(f920(x99551)),x99554))+P106(f857(f857(f235(a919),f737(x99553,x99555,x99552,x99554,x99551)),f857(f190(f920(x99551)),x99554)))
% 15.02/14.80 [9986]P106(f857(f857(f328(x99861),f645(x99862,x99863,x99864,x99865,x99861)),x99865))+~P106(f857(f857(f234(f927(x99861,a915)),x99865),x99864))+P106(f857(f857(f234(f927(x99861,a915)),f857(f857(f101(f927(x99861,a915)),x99865),f857(f261(x99861),x99863))),f857(f857(f101(f927(x99861,a915)),x99864),f857(f261(x99861),x99862))))
% 15.02/14.80 [10030]~P6(x100301)+~P106(f857(f857(f234(x100301),x100302),f857(x100305,f434(x100305,x100304,x100303,x100302,x100301))))+P106(f857(f857(f234(x100301),x100302),f857(f857(f38(x100303,x100301),x100304),x100305)))
% 15.02/14.80 [10067]~P77(x100671)+~P106(f857(f60(x100672),x100675))+E(f857(f857(f857(f64(x100671,x100672,f80(x100671)),f857(f857(f20(x100672,x100671,x100671),f857(f857(f10(x100671,f927(x100671,x100671),x100672),f80(x100671)),x100673)),x100674)),f77(x100671)),x100675),f857(f857(f80(x100671),f857(f857(f857(f64(x100671,x100672,f80(x100671)),x100673),f77(x100671)),x100675)),f857(f857(f857(f64(x100671,x100672,f80(x100671)),x100674),f77(x100671)),x100675)))
% 15.02/14.80 [10122]~P106(f857(f857(f328(f926(f927(x101221,a915),f927(x101221,a915))),f857(f857(f251(f927(x101221,a915),f927(x101221,a915)),x101225),x101224)),f317(x101221,x101223)))+~P106(f857(f857(f328(x101221),x101222),x101225))+P106(f857(f857(f328(f926(x101221,x101221)),f857(f857(f251(x101221,x101221),x101222),f607(x101223,x101224,x101225,x101221,x101222))),x101223))
% 15.02/14.80 [10262]~P106(f857(f857(f328(f926(f920(x102621),f920(x102621))),f857(f857(f251(f920(x102621),f920(x102621)),f857(f857(f134(x102621),x102625),x102622)),f857(f857(f134(x102621),x102625),x102623))),f147(x102621,x102624)))+P106(f857(f857(f328(f926(f920(x102621),f920(x102621))),f857(f857(f251(f920(x102621),f920(x102621)),x102622),x102623)),f147(x102621,x102624)))+P106(f857(f857(f328(f926(x102621,x102621)),f857(f857(f251(x102621,x102621),f689(x102624,x102623,x102622,x102625,x102621)),f689(x102624,x102623,x102622,x102625,x102621))),x102624))
% 15.02/14.80 [7462]~E(x74623,x74625)+E(f857(f857(f164(x74621),f857(f857(f159(x74621,x74622),x74623),x74624)),x74625),x74624)+~P106(f857(f857(f235(a919),x74623),f857(f190(f920(x74621)),x74622)))
% 15.02/14.80 [7575]~E(f857(f857(f134(x75751),x75752),x75754),f857(f857(f134(x75751),x75753),x75755))+E(f857(f857(f175(x75751),f857(f190(f920(x75751)),x75752)),x75753),x75752)+P106(f857(f857(f234(a919),f857(f190(f920(x75751)),x75753)),f857(f190(f920(x75751)),x75752)))
% 15.02/14.80 [8068]~E(f857(f857(f134(x80681),x80682),x80684),f857(f857(f134(x80681),x80683),x80685))+E(f857(f857(f175(x80681),f857(f190(f920(x80681)),x80682)),x80683),x80682)+~P106(f857(f857(f234(a919),f857(f190(f920(x80681)),x80682)),f857(f190(f920(x80681)),x80683)))
% 15.02/14.80 [8092]~P106(f857(f60(x80921),f857(x80924,x80925)))+~P106(f857(f857(f328(x80922),x80925),x80923))+P106(f857(f60(x80921),f857(f857(f38(x80922,f927(x80921,a915)),x80923),x80924)))
% 15.02/14.80 [8268]~P54(x82681,x82683,x82685)+~P54(x82681,x82682,x82684)+P54(x82681,f857(f857(f110(f927(x82681,a915)),x82682),x82683),f857(f857(f110(f927(f926(x82681,x82681),a915)),x82684),x82685))
% 15.02/14.80 [8269]~P54(x82691,x82693,x82695)+~P54(x82691,x82692,x82694)+P54(x82691,f857(f857(f101(f927(x82691,a915)),x82692),x82693),f857(f857(f101(f927(f926(x82691,x82691),a915)),x82694),x82695))
% 15.02/14.80 [8621]E(f857(f857(f251(x86211,x86212),f857(f857(f164(x86211),x86213),x86214)),f857(f857(f164(x86212),x86215),x86214)),f857(f857(f164(f926(x86211,x86212)),f857(f857(f181(x86211,x86212),x86213),x86215)),x86214))+~P106(f857(f857(f235(a919),x86214),f857(f190(f920(x86211)),x86213)))+~P106(f857(f857(f235(a919),x86214),f857(f190(f920(x86212)),x86215)))
% 15.02/14.80 [8774]~P54(x87741,x87743,x87744)+P106(f857(f857(f328(x87741),x87742),x87743))+~P106(f857(f857(f328(f926(x87741,x87741)),f857(f857(f251(x87741,x87741),x87745),x87742)),x87744))
% 15.02/14.80 [8775]~P54(x87751,x87753,x87754)+P106(f857(f857(f328(x87751),x87752),x87753))+~P106(f857(f857(f328(f926(x87751,x87751)),f857(f857(f251(x87751,x87751),x87752),x87755)),x87754))
% 15.02/14.80 [8776]~P9(x87761,x87763,x87764)+P106(f857(f857(f328(x87761),x87762),x87763))+~P106(f857(f857(f328(f926(x87761,x87761)),f857(f857(f251(x87761,x87761),x87765),x87762)),x87764))
% 15.02/14.80 [8777]~P9(x87771,x87773,x87774)+P106(f857(f857(f328(x87771),x87772),x87773))+~P106(f857(f857(f328(f926(x87771,x87771)),f857(f857(f251(x87771,x87771),x87772),x87775)),x87774))
% 15.02/14.80 [9058]~P9(x90581,x90585,x90582)+E(f857(f284(x90581,x90581,x90582),f857(f857(f308(x90581),x90583),f189(f927(x90581,a915)))),f857(f284(x90581,x90581,x90582),f857(f857(f308(x90581),x90584),f189(f927(x90581,a915)))))+~P106(f857(f857(f328(f926(x90581,x90581)),f857(f857(f251(x90581,x90581),x90583),x90584)),x90582))
% 15.02/14.80 [9242]P106(f857(x92421,x92422))+~P106(f857(f857(f328(x92423),x92422),x92425))+P106(f857(f857(f328(x92423),f377(x92421,x92424,x92425,x92423)),f857(f857(f110(f927(x92423,a915)),x92425),x92424)))
% 15.02/14.80 [9243]P106(f857(x92431,x92432))+~P106(f857(f857(f328(x92433),x92432),x92434))+P106(f857(f857(f328(x92433),f377(x92431,x92434,x92435,x92433)),f857(f857(f110(f927(x92433,a915)),x92435),x92434)))
% 15.02/14.80 [9251]~P106(f857(x92512,x92515))+~P106(f857(f857(f328(x92511),x92515),x92514))+P106(f857(f857(f328(x92511),f366(x92512,x92513,x92514,x92511)),f857(f857(f110(f927(x92511,a915)),x92514),x92513)))
% 15.02/14.80 [9252]~P106(f857(x92522,x92525))+~P106(f857(f857(f328(x92521),x92525),x92523))+P106(f857(f857(f328(x92521),f366(x92522,x92523,x92524,x92521)),f857(f857(f110(f927(x92521,a915)),x92524),x92523)))
% 15.02/14.80 [9267]~P106(f857(f857(f234(f927(x92671,a915)),x92673),x92675))+~P106(f857(f857(f234(f927(x92671,a915)),x92672),x92674))+P106(f857(f857(f234(f927(x92671,a915)),f857(f857(f110(f927(x92671,a915)),x92672),x92673)),f857(f857(f110(f927(x92671,a915)),x92674),x92675)))
% 15.02/14.80 [9268]~P106(f857(f857(f234(f927(x92681,a915)),x92685),x92683))+~P106(f857(f857(f234(f927(x92681,a915)),x92682),x92684))+P106(f857(f857(f234(f927(x92681,a915)),f857(f857(f3(f927(x92681,a915)),x92682),x92683)),f857(f857(f3(f927(x92681,a915)),x92684),x92685)))
% 15.02/14.80 [9269]~P106(f857(f857(f234(f927(x92691,a915)),x92693),x92695))+~P106(f857(f857(f234(f927(x92691,a915)),x92692),x92694))+P106(f857(f857(f234(f927(x92691,a915)),f857(f857(f101(f927(x92691,a915)),x92692),x92693)),f857(f857(f101(f927(x92691,a915)),x92694),x92695)))
% 15.02/14.80 [9363]P106(f857(f857(f328(f926(x93631,x93631)),f857(f857(f251(x93631,x93631),x93632),x93633)),f320(x93631,x93634,x93635)))+~P106(f857(f857(f234(a919),f857(x93634,x93632)),f857(x93634,x93633)))+~P106(f857(f857(f328(f926(x93631,x93631)),f857(f857(f251(x93631,x93631),x93632),x93633)),x93635))
% 15.02/14.80 [9550]P106(f857(f857(f328(f926(x95501,x95501)),f857(f857(f251(x95501,x95501),x95502),x95503)),f306(x95501,x95504)))+~P106(f857(f857(f328(f926(x95501,x95501)),f857(f857(f251(x95501,x95501),x95502),x95505)),f306(x95501,x95504)))+~P106(f857(f857(f328(f926(x95501,x95501)),f857(f857(f251(x95501,x95501),x95505),x95503)),x95504))
% 15.02/14.80 [9551]P106(f857(f857(f328(f926(x95511,x95511)),f857(f857(f251(x95511,x95511),x95512),x95513)),f306(x95511,x95514)))+~P106(f857(f857(f328(f926(x95511,x95511)),f857(f857(f251(x95511,x95511),x95515),x95513)),f306(x95511,x95514)))+~P106(f857(f857(f328(f926(x95511,x95511)),f857(f857(f251(x95511,x95511),x95512),x95515)),x95514))
% 15.02/14.80 [9652]E(x96521,x96522)+E(f857(a112,f624(x96523,x96524,x96521,x96522,x96525)),x96524)+~P106(f857(f857(f328(f926(x96525,x96525)),f857(f857(f251(x96525,x96525),x96522),x96521)),f857(f857(f183(f926(x96525,x96525),a915),x96524),x96523)))
% 15.02/14.80 [9653]E(x96531,x96532)+E(f857(a112,f626(x96533,x96534,x96531,x96532,x96535)),x96534)+~P106(f857(f857(f328(f926(x96535,x96535)),f857(f857(f251(x96535,x96535),x96532),x96531)),f857(f857(f183(f926(x96535,x96535),a915),x96534),x96533)))
% 15.02/14.80 [9654]E(x96541,f2(a919))+E(f857(a112,f624(x96542,x96541,x96543,x96544,x96545)),x96541)+~P106(f857(f857(f328(f926(x96545,x96545)),f857(f857(f251(x96545,x96545),x96544),x96543)),f857(f857(f183(f926(x96545,x96545),a915),x96541),x96542)))
% 15.02/14.80 [9655]E(x96551,f2(a919))+E(f857(a112,f626(x96552,x96551,x96553,x96554,x96555)),x96551)+~P106(f857(f857(f328(f926(x96555,x96555)),f857(f857(f251(x96555,x96555),x96554),x96553)),f857(f857(f183(f926(x96555,x96555),a915),x96551),x96552)))
% 15.02/14.80 [9678]P106(f857(f857(f328(f926(x96781,x96781)),f857(f857(f251(x96781,x96781),x96782),x96783)),f857(f857(f288(x96781,x96781,x96781),x96784),f306(x96781,x96784))))+~P106(f857(f857(f328(f926(x96781,x96781)),f857(f857(f251(x96781,x96781),x96782),x96785)),x96784))+~P106(f857(f857(f328(f926(x96781,x96781)),f857(f857(f251(x96781,x96781),x96785),x96783)),x96784))
% 15.02/14.80 [9688]~P106(f857(f857(f328(f926(x96881,x96881)),f857(f857(f251(x96881,x96881),x96882),x96885)),f306(x96881,x96884)))+P106(f857(f857(f328(f926(x96881,x96881)),f857(f857(f251(x96881,x96881),x96882),x96883)),f857(f857(f288(x96881,x96881,x96881),x96884),f306(x96881,x96884))))+~P106(f857(f857(f328(f926(x96881,x96881)),f857(f857(f251(x96881,x96881),x96885),x96883)),x96884))
% 15.02/14.80 [9724]~P9(x97241,x97245,x97242)+~P106(f857(f857(f328(f926(x97241,x97241)),f857(f857(f251(x97241,x97241),x97243),x97244)),x97242))+P106(f857(f857(f234(f927(x97241,a915)),f857(f284(x97241,x97241,x97242),f857(f857(f308(x97241),x97243),f189(f927(x97241,a915))))),f857(f284(x97241,x97241,x97242),f857(f857(f308(x97241),x97244),f189(f927(x97241,a915))))))
% 15.02/14.80 [9782]P106(f857(f857(f328(f926(x97821,x97821)),f857(f857(f251(x97821,x97821),x97822),x97823)),f857(f857(f288(x97821,x97821,x97821),x97824),f306(x97821,x97824))))+~P106(f857(f857(f328(f926(x97821,x97821)),f857(f857(f251(x97821,x97821),x97822),x97825)),f857(f857(f288(x97821,x97821,x97821),x97824),f306(x97821,x97824))))+~P106(f857(f857(f328(f926(x97821,x97821)),f857(f857(f251(x97821,x97821),x97825),x97823)),x97824))
% 15.02/14.80 [9783]P106(f857(f857(f328(f926(x97831,x97831)),f857(f857(f251(x97831,x97831),x97832),x97833)),f857(f857(f288(x97831,x97831,x97831),x97834),f306(x97831,x97834))))+~P106(f857(f857(f328(f926(x97831,x97831)),f857(f857(f251(x97831,x97831),x97835),x97833)),f857(f857(f288(x97831,x97831,x97831),x97834),f306(x97831,x97834))))+~P106(f857(f857(f328(f926(x97831,x97831)),f857(f857(f251(x97831,x97831),x97832),x97835)),x97834))
% 15.02/14.80 [9833]~P106(f857(f65(x98331,x98331,x98334,x98332,x98333),x98335))+P106(f857(f857(f328(x98331),x98332),x98333))+P106(f857(f61(x98331,x98334,f857(f857(f308(x98331),x98332),x98333)),x98335))
% 15.02/14.80 [9871]~E(f857(f309(x98713,x98712,x98715),x98714),x98711)+E(x98711,f189(f927(x98712,a915)))+P106(f857(f857(f234(f927(x98713,a915)),f857(f309(x98712,x98713,f498(x98714,x98713,x98712,x98711)),x98711)),x98714))
% 15.02/14.80 [9918]~P6(x99185)+P106(f857(f857(f328(x99181),f431(x99182,x99183,x99184,x99181,x99185)),x99184))+P106(f857(f857(f234(x99185),f857(f857(f39(x99181,x99185),x99184),x99183)),x99182))
% 15.02/14.80 [9973]P36(x99731,x99732,x99733,x99734,x99735)+~E(f857(f190(f920(x99731)),x99734),f857(f190(f920(x99732)),x99735))+P106(f857(f857(f328(f926(x99731,x99732)),f696(x99735,x99734,x99733,x99732,x99731)),f857(f172(f926(x99731,x99732)),f857(f857(f181(x99731,x99732),x99734),x99735))))
% 15.02/14.80 [9974]P36(x99741,x99742,x99743,x99744,x99745)+~E(f857(f190(f920(x99741)),x99744),f857(f190(f920(x99742)),x99745))+P106(f857(f857(f328(f926(x99741,x99742)),f702(x99743,x99745,x99744,x99742,x99741)),f857(f172(f926(x99741,x99742)),f857(f857(f181(x99741,x99742),x99744),x99745))))
% 15.02/14.80 [10101]E(x101011,x101012)+P106(f857(f857(f328(f926(x101013,x101013)),f857(f857(f251(x101013,x101013),x101011),f627(x101014,x101015,x101012,x101011,x101013))),x101014))+~P106(f857(f857(f328(f926(x101013,x101013)),f857(f857(f251(x101013,x101013),x101011),x101012)),f857(f857(f183(f926(x101013,x101013),a915),x101015),x101014)))
% 15.02/14.80 [10102]E(x101021,f2(a919))+P106(f857(f857(f328(f926(x101022,x101022)),f857(f857(f251(x101022,x101022),x101023),f627(x101024,x101021,x101025,x101023,x101022))),x101024))+~P106(f857(f857(f328(f926(x101022,x101022)),f857(f857(f251(x101022,x101022),x101023),x101025)),f857(f857(f183(f926(x101022,x101022),a915),x101021),x101024)))
% 15.02/14.80 [10143]~P6(x101431)+~P106(f857(f857(f234(x101431),f857(x101434,f431(x101435,x101434,x101433,x101432,x101431))),x101435))+P106(f857(f857(f234(x101431),f857(f857(f39(x101432,x101431),x101433),x101434)),x101435))
% 15.02/14.80 [10195]E(x101951,x101952)+P106(f857(f857(f328(f926(x101953,x101953)),f857(f857(f251(x101953,x101953),f625(x101954,x101955,x101951,x101952,x101953)),x101951)),x101954))+~P106(f857(f857(f328(f926(x101953,x101953)),f857(f857(f251(x101953,x101953),x101952),x101951)),f857(f857(f183(f926(x101953,x101953),a915),x101955),x101954)))
% 15.02/14.80 [10196]E(x101961,f2(a919))+P106(f857(f857(f328(f926(x101962,x101962)),f857(f857(f251(x101962,x101962),f625(x101963,x101961,x101964,x101965,x101962)),x101964)),x101963))+~P106(f857(f857(f328(f926(x101962,x101962)),f857(f857(f251(x101962,x101962),x101965),x101964)),f857(f857(f183(f926(x101962,x101962),a915),x101961),x101963)))
% 15.02/14.80 [10200]E(x102001,x102002)+P106(f857(f857(f328(f926(x102003,x102003)),f857(f857(f251(x102003,x102003),x102001),f625(x102004,x102005,x102002,x102001,x102003))),f857(f857(f183(f926(x102003,x102003),a915),f624(x102004,x102005,x102002,x102001,x102003)),x102004)))+~P106(f857(f857(f328(f926(x102003,x102003)),f857(f857(f251(x102003,x102003),x102001),x102002)),f857(f857(f183(f926(x102003,x102003),a915),x102005),x102004)))
% 15.02/14.80 [10201]E(x102011,f2(a919))+P106(f857(f857(f328(f926(x102012,x102012)),f857(f857(f251(x102012,x102012),x102013),f625(x102014,x102011,x102015,x102013,x102012))),f857(f857(f183(f926(x102012,x102012),a915),f624(x102014,x102011,x102015,x102013,x102012)),x102014)))+~P106(f857(f857(f328(f926(x102012,x102012)),f857(f857(f251(x102012,x102012),x102013),x102015)),f857(f857(f183(f926(x102012,x102012),a915),x102011),x102014)))
% 15.02/14.80 [10253]E(x102531,x102532)+P106(f857(f857(f328(f926(x102533,x102533)),f857(f857(f251(x102533,x102533),f627(x102534,x102535,x102531,x102532,x102533)),x102531)),f857(f857(f183(f926(x102533,x102533),a915),f626(x102534,x102535,x102531,x102532,x102533)),x102534)))+~P106(f857(f857(f328(f926(x102533,x102533)),f857(f857(f251(x102533,x102533),x102532),x102531)),f857(f857(f183(f926(x102533,x102533),a915),x102535),x102534)))
% 15.02/14.80 [10254]E(x102541,f2(a919))+P106(f857(f857(f328(f926(x102542,x102542)),f857(f857(f251(x102542,x102542),f627(x102543,x102541,x102544,x102545,x102542)),x102544)),f857(f857(f183(f926(x102542,x102542),a915),f626(x102543,x102541,x102544,x102545,x102542)),x102543)))+~P106(f857(f857(f328(f926(x102542,x102542)),f857(f857(f251(x102542,x102542),x102545),x102544)),f857(f857(f183(f926(x102542,x102542),a915),x102541),x102543)))
% 15.02/14.80 [10289]~P72(x102892)+~P106(f857(f60(x102891),x102895))+E(f857(f857(f8(x102891,x102892),f857(f857(f9(x102891,x102892,x102892),f857(f857(f20(x102891,x102892,f927(x102892,x102892)),f857(f857(f10(a915,f927(x102892,f927(x102892,x102892)),x102891),f96(x102892)),f857(f857(f9(x102891,f927(x102891,a915),a915),f328(x102891)),x102893))),x102894)),f2(x102892))),x102895),f857(f857(f8(x102891,x102892),x102894),f857(f857(f101(f927(x102891,a915)),x102895),x102893)))
% 15.02/14.80 [8842]~P72(x88421)+~P106(f857(f60(x88424),x88425))+E(f857(f857(f79(x88421),f857(x88422,x88423)),f857(f857(f8(x88424,x88421),x88422),f857(f857(f3(f927(x88424,a915)),x88425),f857(f857(f308(x88424),x88423),f189(f927(x88424,a915)))))),f857(f857(f8(x88424,x88421),x88422),f857(f857(f308(x88424),x88423),x88425)))
% 15.02/14.80 [8843]~P77(x88431)+~P106(f857(f60(x88434),x88435))+E(f857(f857(f80(x88431),f857(x88432,x88433)),f857(f857(f11(x88434,x88431),x88432),f857(f857(f3(f927(x88434,a915)),x88435),f857(f857(f308(x88434),x88433),f189(f927(x88434,a915)))))),f857(f857(f11(x88434,x88431),x88432),f857(f857(f308(x88434),x88433),x88435)))
% 15.02/14.80 [9175]~P109(x91752)+~P14(x91752,f857(f168(x91752),f857(f857(f154(x91751,x91752),x91754),x91755)))+E(f857(f136(x91751,f857(f857(f10(x91752,a915,x91751),f857(f235(x91752),x91753)),x91754)),x91755),f177(x91751,f857(f857(f10(x91752,a915,x91751),f857(f235(x91752),x91753)),x91754),x91755))
% 15.02/14.80 [9199]~P72(x91991)+E(f857(f857(f79(x91991),f857(f857(f8(a919,x91991),x91992),f302(a919,x91993,x91994))),f857(f857(f8(a919,x91991),x91992),f302(a919,f857(f857(f79(a919),x91994),f77(a919)),f857(f857(f79(a919),x91994),x91995)))),f857(f857(f8(a919,x91991),x91992),f302(a919,x91993,f857(f857(f79(a919),x91994),x91995))))+~P106(f857(f857(f234(a919),x91993),f857(f857(f79(a919),x91994),f77(a919))))
% 15.02/14.80 [9200]~P106(f857(f857(f328(x92001),x92004),x92005))+~P106(f857(f857(f234(f927(x92001,a915)),f857(f172(x92001),x92002)),x92005))+P106(f857(f857(f234(f927(x92001,a915)),f857(f172(x92001),f857(f857(f159(x92001,x92002),x92003),x92004))),x92005))
% 15.02/14.80 [9424]~P6(x94242)+~P106(f857(f60(x94241),x94245))+E(f857(f857(f63(x94241,x94242,f857(f857(f10(x94242,f927(x94242,x94242),x94241),f110(x94242)),x94243)),x94244),x94245),f857(f857(f110(x94242),x94244),f857(f857(f39(x94241,x94242),x94245),x94243)))
% 15.02/14.80 [9425]~P6(x94252)+~P106(f857(f60(x94251),x94255))+E(f857(f857(f63(x94251,x94252,f857(f857(f10(x94252,f927(x94252,x94252),x94251),f101(x94252)),x94253)),x94254),x94255),f857(f857(f101(x94252),x94254),f857(f857(f38(x94251,x94252),x94255),x94253)))
% 15.02/14.80 [9475]E(f857(x94751,x94752),f857(x94751,x94753))+P106(f857(f857(f235(a919),f857(x94751,x94752)),f857(x94751,x94753)))+~P106(f857(f857(f328(f926(x94754,x94754)),f857(f857(f251(x94754,x94754),x94752),x94753)),f153(x94754,f857(f857(f151(f927(x94754,a919)),x94751),x94755))))
% 15.02/14.80 [9508]~E(f857(x95084,x95082),f857(x95084,x95083))+~P106(f857(f857(f328(f926(x95081,x95081)),f857(f857(f251(x95081,x95081),x95082),x95083)),f153(x95081,x95085)))+P106(f857(f857(f328(f926(x95081,x95081)),f857(f857(f251(x95081,x95081),x95082),x95083)),f153(x95081,f857(f857(f151(f927(x95081,a919)),x95084),x95085))))
% 15.02/14.80 [9528]~P26(x95281,x95282,x95283,x95285)+P26(x95281,x95282,x95283,f857(f857(f308(x95281),x95284),x95285))+P106(f857(f857(f328(x95282),f857(x95283,x95284)),f857(f309(x95281,x95282,x95283),f857(f857(f3(f927(x95281,a915)),x95285),f857(f857(f308(x95281),x95284),f189(f927(x95281,a915)))))))
% 15.02/14.80 [9531]P106(f857(x95312,x95315))+~P106(f857(f857(f328(x95311),x95315),f857(f172(x95311),x95313)))+E(f857(f857(f138(x95311),f857(f190(f920(x95311)),f177(x95311,x95312,f857(f857(f134(x95311),x95313),x95314)))),f857(f857(f134(x95311),x95313),x95314)),f857(f857(f134(x95311),f857(f857(f138(x95311),f857(f190(f920(x95311)),f177(x95311,x95312,x95313))),x95313)),x95314))
% 15.02/14.80 [9536]~P106(f857(f857(f328(f926(x95361,x95361)),f857(f857(f251(x95361,x95361),x95362),x95363)),f153(x95361,x95365)))+~P106(f857(f857(f234(a919),f857(x95364,x95362)),f857(x95364,x95363)))+P106(f857(f857(f328(f926(x95361,x95361)),f857(f857(f251(x95361,x95361),x95362),x95363)),f153(x95361,f857(f857(f151(f927(x95361,a919)),x95364),x95365))))
% 15.02/14.80 [9603]P106(f857(f857(f328(f926(x96034,x96034)),f857(f857(f251(x96034,x96034),x96032),x96033)),f153(x96034,x96035)))+P106(f857(f857(f235(a919),f857(x96031,x96032)),f857(x96031,x96033)))+~P106(f857(f857(f328(f926(x96034,x96034)),f857(f857(f251(x96034,x96034),x96032),x96033)),f153(x96034,f857(f857(f151(f927(x96034,a919)),x96031),x96035))))
% 15.02/14.80 [9754]~P106(f857(f857(f328(f926(f920(x97541),f920(x97541))),f857(f857(f251(f920(x97541),f920(x97541)),x97542),x97544)),f158(x97541,x97545)))+~P106(f857(f857(f235(a919),x97543),f857(f190(f920(x97541)),x97542)))+P106(f857(f857(f328(f926(x97541,x97541)),f857(f857(f251(x97541,x97541),f857(f857(f164(x97541),x97542),x97543)),f857(f857(f164(x97541),x97544),x97543))),x97545))
% 15.02/14.80 [9996]E(x99961,f2(a1))+~P106(f857(f48(x99963,x99961),f857(f857(f251(a1,a1),x99964),x99965)))+P106(f857(f48(f857(f857(f80(a1),x99962),x99963),x99961),f857(f857(f251(a1,a1),f857(f857(f79(a1),f857(f857(f80(a1),x99962),x99964)),f857(f857(f35(a1),f857(f857(f80(a1),x99962),x99965)),x99961))),f44(a1,f857(f857(f80(a1),x99962),x99965),x99961))))
% 15.02/14.80 [9997]~P106(f857(f857(f235(a919),f2(a919)),x99973))+~P106(f857(f47(x99972,x99973),f857(f857(f251(a919,a919),x99974),x99975)))+P106(f857(f47(f857(f857(f80(a919),x99971),x99972),x99973),f857(f857(f251(a919,a919),f857(f857(f79(a919),f857(f857(f80(a919),x99971),x99974)),f857(f857(f35(a919),f857(f857(f80(a919),x99971),x99975)),x99973))),f44(a919,f857(f857(f80(a919),x99971),x99975),x99973))))
% 15.02/14.80 [10312]~P72(x103122)+~P106(f857(f60(x103121),x103124))+E(f857(f857(f8(x103121,x103122),x103123),f857(f261(x103121),f857(f857(f20(x103121,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103121),a325),f857(f857(f9(x103121,f927(x103121,a915),a915),f328(x103121)),x103124))),f857(f857(f9(x103121,f927(x103121,a915),a915),f328(x103121)),x103125)))),f857(f857(f8(x103121,x103122),f857(f857(f9(x103121,x103122,x103122),f857(f857(f20(x103121,x103122,f927(x103122,x103122)),f857(f857(f10(a915,f927(x103122,f927(x103122,x103122)),x103121),f96(x103122)),f857(f857(f9(x103121,f927(x103121,a915),a915),f328(x103121)),x103125))),x103123)),f2(x103122))),x103124))
% 15.02/14.80 [8474]~E(f857(f857(f134(x84741),x84742),x84745),f857(f857(f134(x84741),x84743),x84744))+E(f857(f857(f134(x84741),f857(f857(f138(x84741),f857(f190(f920(x84741)),x84742)),x84743)),x84744),x84745)+P106(f857(f857(f234(a919),f857(f190(f920(x84741)),x84743)),f857(f190(f920(x84741)),x84742)))
% 15.02/14.80 [8669]~E(f857(f857(f134(x86692),x86693),x86691),f857(f857(f134(x86692),x86694),x86695))+E(x86691,f857(f857(f134(x86692),f857(f857(f138(x86692),f857(f190(f920(x86692)),x86693)),x86694)),x86695))+~P106(f857(f857(f234(a919),f857(f190(f920(x86692)),x86693)),f857(f190(f920(x86692)),x86694)))
% 15.02/14.80 [8757]~E(f857(f857(f79(a919),f857(f857(f80(a919),x87573),x87574)),x87571),f857(f857(f79(a919),f857(f857(f80(a919),x87572),x87574)),x87575))+~P106(f857(f857(f234(a919),x87573),x87572))+E(x87571,f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x87572),x87573)),x87574)),x87575))
% 15.02/14.80 [8758]~E(f857(f857(f79(a919),f857(f857(f80(a919),x87581),x87583)),x87584),f857(f857(f79(a919),f857(f857(f80(a919),x87582),x87583)),x87585))+~P106(f857(f857(f234(a919),x87582),x87581))+E(f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x87581),x87582)),x87583)),x87584),x87585)
% 15.02/14.80 [8926]E(f857(f857(f79(a919),f857(f857(f80(a919),x89261),x89262)),x89263),f857(f857(f79(a919),f857(f857(f80(a919),x89264),x89262)),x89265))+~P106(f857(f857(f234(a919),x89264),x89261))+~E(x89265,f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x89261),x89264)),x89262)),x89263))
% 15.02/14.80 [8927]E(f857(f857(f79(a919),f857(f857(f80(a919),x89271),x89272)),x89273),f857(f857(f79(a919),f857(f857(f80(a919),x89274),x89272)),x89275))+~P106(f857(f857(f234(a919),x89274),x89271))+~E(f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x89271),x89274)),x89272)),x89273),x89275)
% 15.02/14.80 [9808]~P65(x98082)+~P106(f857(f60(x98081),x98085))+E(f857(f857(f11(x98081,x98082),f857(f857(f20(x98081,x98082,x98082),f857(f857(f10(x98082,f927(x98082,x98082),x98081),f290(x98082)),x98083)),x98084)),x98085),f857(f857(f290(x98082),f857(f857(f11(x98081,x98082),x98083),x98085)),f857(f857(f11(x98081,x98082),x98084),x98085)))
% 15.02/14.80 [9937]~E(f629(x99375,x99374,x99373,x99372,x99371),f630(x99375,x99374,x99373,x99372,x99371))+P106(f857(f857(f328(f926(x99371,x99371)),f857(f857(f251(x99371,x99371),x99372),x99373)),f306(x99371,x99374)))+~P106(f857(f857(f328(f926(x99371,x99371)),f857(f857(f251(x99371,x99371),x99372),x99373)),f306(x99371,f857(f857(f110(f927(f926(x99371,x99371),a915)),x99374),x99375))))
% 15.02/14.80 [9938]~E(f631(x99385,x99384,x99383,x99382,x99381),f632(x99385,x99384,x99383,x99382,x99381))+P106(f857(f857(f328(f926(x99381,x99381)),f857(f857(f251(x99381,x99381),x99382),x99383)),f306(x99381,x99384)))+~P106(f857(f857(f328(f926(x99381,x99381)),f857(f857(f251(x99381,x99381),x99382),x99383)),f306(x99381,f857(f857(f110(f927(f926(x99381,x99381),a915)),x99384),x99385))))
% 15.02/14.80 [10133]P106(f857(f857(f328(f926(x101331,x101331)),f857(f857(f251(x101331,x101331),x101332),f630(x101335,x101334,x101333,x101332,x101331))),f306(x101331,x101334)))+P106(f857(f857(f328(f926(x101331,x101331)),f857(f857(f251(x101331,x101331),x101332),x101333)),f306(x101331,x101334)))+~P106(f857(f857(f328(f926(x101331,x101331)),f857(f857(f251(x101331,x101331),x101332),x101333)),f306(x101331,f857(f857(f110(f927(f926(x101331,x101331),a915)),x101334),x101335))))
% 15.02/14.80 [10222]P106(f857(f857(f328(f926(x102221,x102221)),f857(f857(f251(x102221,x102221),f632(x102225,x102224,x102223,x102222,x102221)),x102223)),f306(x102221,x102224)))+P106(f857(f857(f328(f926(x102221,x102221)),f857(f857(f251(x102221,x102221),x102222),x102223)),f306(x102221,x102224)))+~P106(f857(f857(f328(f926(x102221,x102221)),f857(f857(f251(x102221,x102221),x102222),x102223)),f306(x102221,f857(f857(f110(f927(f926(x102221,x102221),a915)),x102224),x102225))))
% 15.02/14.80 [10260]P106(f857(f857(f328(f926(x102601,x102601)),f857(f857(f251(x102601,x102601),x102602),x102603)),f306(x102601,x102604)))+P106(f857(f857(f328(f926(x102601,x102601)),f857(f857(f251(x102601,x102601),f630(x102605,x102604,x102603,x102602,x102601)),f629(x102605,x102604,x102603,x102602,x102601))),x102605))+~P106(f857(f857(f328(f926(x102601,x102601)),f857(f857(f251(x102601,x102601),x102602),x102603)),f306(x102601,f857(f857(f110(f927(f926(x102601,x102601),a915)),x102604),x102605))))
% 15.02/14.80 [10261]P106(f857(f857(f328(f926(x102611,x102611)),f857(f857(f251(x102611,x102611),x102612),x102613)),f306(x102611,x102614)))+P106(f857(f857(f328(f926(x102611,x102611)),f857(f857(f251(x102611,x102611),f631(x102615,x102614,x102613,x102612,x102611)),f632(x102615,x102614,x102613,x102612,x102611))),x102615))+~P106(f857(f857(f328(f926(x102611,x102611)),f857(f857(f251(x102611,x102611),x102612),x102613)),f306(x102611,f857(f857(f110(f927(f926(x102611,x102611),a915)),x102614),x102615))))
% 15.02/14.80 [10409]~P106(f857(f857(f328(f926(f920(x104091),f920(x104091))),f857(f857(f251(f920(x104091),f920(x104091)),x104094),x104095)),f158(x104091,x104092)))+~P106(f857(f857(f328(f926(x104091,x104091)),x104093),f857(f172(f926(x104091,x104091)),f857(f857(f181(x104091,x104091),x104094),x104095))))+P106(f857(f857(f256(x104091,x104091,a915),f857(f857(f9(x104091,f927(f926(x104091,x104091),a915),f927(x104091,a915)),f857(f857(f10(f927(x104091,f927(f927(f926(x104091,x104091),a915),a915)),f927(f927(f926(x104091,x104091),a915),f927(x104091,a915)),x104091),f9(x104091,f927(f926(x104091,x104091),a915),a915)),f857(f857(f10(f927(x104091,f926(x104091,x104091)),f927(x104091,f927(f927(f926(x104091,x104091),a915),a915)),x104091),f857(f10(f926(x104091,x104091),f927(f927(f926(x104091,x104091),a915),a915),x104091),f328(f926(x104091,x104091)))),f251(x104091,x104091)))),x104092)),x104093))
% 15.02/14.80 [9837]~P106(f857(f857(f234(a919),x98373),x98372))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),f857(f857(f80(a919),x98373),x98374)),x98371)),f857(f857(f79(a919),f857(f857(f80(a919),x98372),x98374)),x98375)))+P106(f857(f857(f234(a919),x98371),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x98372),x98373)),x98374)),x98375)))
% 15.02/14.80 [9838]~P106(f857(f857(f234(a919),x98383),x98382))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),x98383),x98384)),x98381)),f857(f857(f79(a919),f857(f857(f80(a919),x98382),x98384)),x98385)))+P106(f857(f857(f235(a919),x98381),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x98382),x98383)),x98384)),x98385)))
% 15.02/14.80 [9855]~P106(f857(f857(f234(a919),x98551),x98554))+P106(f857(f857(f234(a919),f857(f857(f79(a919),f857(f857(f80(a919),x98551),x98552)),x98553)),f857(f857(f79(a919),f857(f857(f80(a919),x98554),x98552)),x98555)))+~P106(f857(f857(f234(a919),x98553),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x98554),x98551)),x98552)),x98555)))
% 15.02/14.80 [9856]~P106(f857(f857(f234(a919),x98561),x98564))+P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),x98561),x98562)),x98563)),f857(f857(f79(a919),f857(f857(f80(a919),x98564),x98562)),x98565)))+~P106(f857(f857(f235(a919),x98563),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x98564),x98561)),x98562)),x98565)))
% 15.02/14.80 [9971]~P106(f857(f857(f234(a919),x99712),x99711))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),f857(f857(f80(a919),x99711),x99713)),x99714)),f857(f857(f79(a919),f857(f857(f80(a919),x99712),x99713)),x99715)))+P106(f857(f857(f234(a919),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x99711),x99712)),x99713)),x99714)),x99715))
% 15.02/14.80 [9972]~P106(f857(f857(f234(a919),x99722),x99721))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),x99721),x99723)),x99724)),f857(f857(f79(a919),f857(f857(f80(a919),x99722),x99723)),x99725)))+P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x99721),x99722)),x99723)),x99724)),x99725))
% 15.02/14.80 [10015]~P106(f857(f857(f234(a919),x100154),x100151))+P106(f857(f857(f234(a919),f857(f857(f79(a919),f857(f857(f80(a919),x100151),x100152)),x100153)),f857(f857(f79(a919),f857(f857(f80(a919),x100154),x100152)),x100155)))+~P106(f857(f857(f234(a919),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x100151),x100154)),x100152)),x100153)),x100155))
% 15.02/14.80 [10016]~P106(f857(f857(f234(a919),x100164),x100161))+P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),x100161),x100162)),x100163)),f857(f857(f79(a919),f857(f857(f80(a919),x100164),x100162)),x100165)))+~P106(f857(f857(f235(a919),f857(f857(f79(a919),f857(f857(f80(a919),f857(f857(f3(a919),x100161),x100164)),x100162)),x100163)),x100165))
% 15.02/14.80 [10248]~P12(x102481,x102482,x102485,x102483)+~P106(f857(f857(f328(f926(x102481,x102481)),x102484),x102485))+P106(f857(f857(f256(x102481,x102481,a915),f857(f857(f9(x102481,f927(x102481,x102482),f927(x102481,a915)),f857(f857(f10(f927(x102482,a915),f927(f927(x102481,x102482),f927(x102481,a915)),x102481),f10(x102482,a915,x102481)),f857(f857(f10(x102482,f927(x102482,a915),x102481),a324),x102483))),x102483)),x102484))
% 15.02/14.80 [8633]~P20(x86336,x86331,x86332,x86334)+E(f857(f72(x86331,x86331,x86331,f857(x86332,x86333)),f857(x86334,x86335)),f857(f72(x86331,x86331,x86331,f857(x86334,x86335)),f857(x86332,x86333)))+~P106(f857(f60(x86336),x86335))
% 15.02/14.80 [9070]~P26(x90701,x90703,x90705,x90706)+~P26(x90703,x90702,x90704,f857(f309(x90701,x90703,x90705),x90706))+P26(x90701,x90702,f857(f72(x90703,x90702,x90701,x90704),x90705),x90706)
% 15.02/14.80 [9635]~P106(f857(f857(x96353,x96352),x96356))+~P106(f857(f857(x96354,x96355),x96352))+P106(f857(f857(f328(x96351),x96352),f299(x96351,x96353,x96354,x96355,x96356)))
% 15.02/14.80 [9636]~P106(f857(f857(x96364,x96362),x96366))+~P106(f857(f857(x96363,x96365),x96362))+P106(f857(f857(f328(x96361),x96362),f296(x96361,x96363,x96364,x96365,x96366)))
% 15.02/14.80 [9755]E(x97551,x97552)+E(x97553,x97554)+~P106(f857(f857(f328(f926(f920(x97555),f920(x97555))),f857(f857(f251(f920(x97555),f920(x97555)),f857(f857(f151(x97555),x97553),x97551)),f857(f857(f151(x97555),x97554),x97552))),f157(x97555,x97556)))
% 15.02/14.80 [9764]~E(x97642,x97644)+P106(f857(f857(f328(f926(f920(x97641),f920(x97641))),f857(f857(f251(f920(x97641),f920(x97641)),f857(f857(f151(x97641),x97642),x97643)),f857(f857(f151(x97641),x97644),x97645))),f145(x97641,x97646)))+~P106(f857(f857(f328(f926(f920(x97641),f920(x97641))),f857(f857(f251(f920(x97641),f920(x97641)),x97643),x97645)),f145(x97641,x97646)))
% 15.02/14.80 [9765]~E(x97652,x97654)+P106(f857(f857(f328(f926(f920(x97651),f920(x97651))),f857(f857(f251(f920(x97651),f920(x97651)),f857(f857(f151(x97651),x97652),x97653)),f857(f857(f151(x97651),x97654),x97655))),f147(x97651,x97656)))+~P106(f857(f857(f328(f926(f920(x97651),f920(x97651))),f857(f857(f251(f920(x97651),f920(x97651)),x97653),x97655)),f147(x97651,x97656)))
% 15.02/14.80 [9766]~E(x97662,x97664)+P106(f857(f857(f328(f926(f920(x97661),f920(x97661))),f857(f857(f251(f920(x97661),f920(x97661)),f857(f857(f151(x97661),x97662),x97663)),f857(f857(f151(x97661),x97664),x97665))),f157(x97661,x97666)))+~P106(f857(f857(f328(f926(f920(x97661),f920(x97661))),f857(f857(f251(f920(x97661),f920(x97661)),x97663),x97665)),f157(x97661,x97666)))
% 15.02/14.80 [9767]~E(x97672,x97674)+P106(f857(f857(f328(f926(f920(x97671),f920(x97671))),f857(f857(f251(f920(x97671),f920(x97671)),f857(f857(f134(x97671),x97672),x97673)),f857(f857(f134(x97671),x97674),x97675))),f157(x97671,x97676)))+~P106(f857(f857(f328(f926(f920(x97671),f920(x97671))),f857(f857(f251(f920(x97671),f920(x97671)),x97673),x97675)),f157(x97671,x97676)))
% 15.02/14.80 [9768]~E(x97683,x97685)+P106(f857(f857(f328(f926(f920(x97681),f920(x97681))),f857(f857(f251(f920(x97681),f920(x97681)),f857(f857(f134(x97681),x97682),x97683)),f857(f857(f134(x97681),x97684),x97685))),f157(x97681,x97686)))+~P106(f857(f857(f328(f926(f920(x97681),f920(x97681))),f857(f857(f251(f920(x97681),f920(x97681)),x97682),x97684)),f157(x97681,x97686)))
% 15.02/14.80 [9825]E(x98251,x98252)+P106(f857(f857(f328(f926(f920(x98253),f920(x98253))),f857(f857(f251(f920(x98253),f920(x98253)),x98251),x98252)),f157(x98253,x98254)))+~P106(f857(f857(f328(f926(f920(x98253),f920(x98253))),f857(f857(f251(f920(x98253),f920(x98253)),f857(f857(f151(x98253),x98255),x98251)),f857(f857(f151(x98253),x98256),x98252))),f157(x98253,x98254)))
% 15.02/14.80 [9975]~E(x99753,x99755)+P106(f857(f857(f328(f926(f920(x99751),f920(x99751))),f857(f857(f251(f920(x99751),f920(x99751)),f857(f857(f134(x99751),x99752),f857(f857(f151(x99751),x99753),f113(x99751)))),f857(f857(f134(x99751),x99754),f857(f857(f151(x99751),x99755),f113(x99751))))),f157(x99751,x99756)))+~P106(f857(f857(f328(f926(f920(x99751),f920(x99751))),f857(f857(f251(f920(x99751),f920(x99751)),x99752),x99754)),f157(x99751,x99756)))
% 15.02/14.80 [10019]E(x100191,x100192)+E(x100193,x100194)+~P106(f857(f857(f328(f926(f920(x100195),f920(x100195))),f857(f857(f251(f920(x100195),f920(x100195)),f857(f857(f134(x100195),x100193),f857(f857(f151(x100195),x100191),f113(x100195)))),f857(f857(f134(x100195),x100194),f857(f857(f151(x100195),x100192),f113(x100195))))),f157(x100195,x100196)))
% 15.02/14.80 [10046]E(x100461,x100462)+~P106(f857(f857(f328(f926(f920(x100463),f920(x100463))),f857(f857(f251(f920(x100463),f920(x100463)),f857(f857(f134(x100463),x100461),f857(f857(f151(x100463),x100465),f113(x100463)))),f857(f857(f134(x100463),x100462),f857(f857(f151(x100463),x100466),f113(x100463))))),f157(x100463,x100464)))+P106(f857(f857(f328(f926(f920(x100463),f920(x100463))),f857(f857(f251(f920(x100463),f920(x100463)),x100461),x100462)),f157(x100463,x100464)))
% 15.02/14.80 [10084]~P106(f857(f857(f328(f926(f927(x100841,a915),f927(x100841,a915))),f857(f857(f251(f927(x100841,a915),f927(x100841,a915)),x100842),x100844)),f317(x100841,x100846)))+~P106(f857(f857(f328(f926(f927(x100841,a915),f927(x100841,a915))),f857(f857(f251(f927(x100841,a915),f927(x100841,a915)),x100843),x100845)),f317(x100841,x100846)))+P106(f857(f857(f328(f926(f927(x100841,a915),f927(x100841,a915))),f857(f857(f251(f927(x100841,a915),f927(x100841,a915)),f857(f857(f110(f927(x100841,a915)),x100842),x100843)),f857(f857(f110(f927(x100841,a915)),x100844),x100845))),f317(x100841,x100846)))
% 15.02/14.80 [5862]~E(f857(f857(f134(x58621),x58626),x58623),x58625)+E(f857(f857(f134(x58621),x58622),x58623),f857(f857(f151(x58621),x58624),x58625))+~E(x58622,f857(f857(f151(x58621),x58624),x58626))
% 15.02/14.80 [5863]~E(f857(f857(f134(x58631),x58636),x58633),x58635)+E(f857(f857(f134(x58631),x58632),x58633),f857(f857(f134(x58631),x58634),x58635))+~E(x58632,f857(f857(f134(x58631),x58634),x58636))
% 15.02/14.80 [5865]E(f857(f857(f134(x58651),x58652),x58653),f857(f857(f151(x58651),x58654),x58655))+~E(f857(f857(f151(x58651),x58654),x58656),x58652)+~E(x58655,f857(f857(f134(x58651),x58656),x58653))
% 15.02/14.80 [5867]~E(f857(f857(f134(x58671),x58672),x58676),x58674)+E(f857(f857(f134(x58671),x58672),x58673),f857(f857(f134(x58671),x58674),x58675))+~E(x58673,f857(f857(f134(x58671),x58676),x58675))
% 15.02/14.80 [7021]E(f857(x70211,x70212),f857(x70213,x70212))+~E(f857(f857(f154(x70214,x70215),x70211),x70216),f857(f857(f154(x70214,x70215),x70213),x70216))+~P106(f857(f857(f328(x70214),x70212),f857(f172(x70214),x70216)))
% 15.02/14.80 [7409]~P20(x74094,x74095,x74096,x74091)+E(f857(f857(x74091,x74092),x74093),f857(f857(f63(x74094,x74095,x74096),x74093),x74092))+~P106(f857(f60(x74094),x74092))
% 15.02/14.80 [7480]~E(x74802,f857(x74804,x74806))+~P106(f857(f857(f328(x74803),x74806),x74805))+P106(f857(f857(f328(x74801),x74802),f857(f309(x74803,x74801,x74804),x74805)))
% 15.02/14.80 [7481]~E(f857(x74814,x74812),x74816)+~P106(f857(f857(f328(x74813),x74816),x74815))+P106(f857(f857(f328(x74811),x74812),f857(f310(x74811,x74813,x74814),x74815)))
% 15.02/14.80 [7927]~P34(x79271,x79272,x79274,x79276)+P34(x79271,x79272,f857(f857(f151(x79271),x79273),x79274),f857(f857(f151(x79271),x79275),x79276))+~P106(f857(f857(x79272,x79273),x79275))
% 15.02/14.80 [8936]~P58(x89364,x89365,x89361,x89362,x89366)+E(f857(x89361,f857(x89362,x89363)),x89363)+~P106(f857(f857(f328(x89365),x89363),x89366))
% 15.02/14.80 [9433]~P27(x94332,x94331,x94335,x94334,x94333)+E(f857(f91(x94331,x94332,x94333,f91(x94332,x94331,x94334,x94335)),x94336),f857(x94335,x94336))+~P106(f857(f857(f328(x94332),x94336),x94334))
% 15.02/14.80 [9444]~P26(x94441,x94442,x94443,x94446)+P26(x94441,x94442,f74(x94441,x94442,x94443,x94444,x94445),x94446)+P106(f857(f857(f328(x94442),x94445),f857(f309(x94441,x94442,x94443),x94446)))
% 15.02/14.80 [9757]E(x97571,x97572)+E(f857(f190(f920(x97573)),x97574),f857(f190(f920(x97573)),x97575))+~P106(f857(f857(f328(f926(f920(x97573),f920(x97573))),f857(f857(f251(f920(x97573),f920(x97573)),f857(f857(f151(x97573),x97571),x97574)),f857(f857(f151(x97573),x97572),x97575))),f145(x97573,x97576)))
% 15.02/14.80 [9820]~P17(x98201,x98202,x98203)+E(f857(f857(f63(x98201,x98202,x98203),x98204),x98205),x98206)+~P106(f857(f65(x98201,x98202,x98203,x98204,x98205),x98206))
% 15.02/14.80 [9828]E(f857(f190(f920(x98281)),x98282),f857(f190(f920(x98281)),x98283))+P106(f857(f857(f328(f926(f920(x98281),f920(x98281))),f857(f857(f251(f920(x98281),f920(x98281)),x98282),x98283)),f145(x98281,x98284)))+~P106(f857(f857(f328(f926(f920(x98281),f920(x98281))),f857(f857(f251(f920(x98281),f920(x98281)),f857(f857(f151(x98281),x98285),x98282)),f857(f857(f151(x98281),x98286),x98283))),f145(x98281,x98284)))
% 15.02/14.80 [9849]~P106(f857(f857(f328(f926(x98491,x98491)),f857(f857(f251(x98491,x98491),x98492),x98494)),f306(x98491,x98496)))+P106(f857(f857(f328(f926(f920(x98491),f920(x98491))),f857(f857(f251(f920(x98491),f920(x98491)),f857(f857(f151(x98491),x98492),x98493)),f857(f857(f151(x98491),x98494),x98495))),f306(f920(x98491),f157(x98491,x98496))))+~P106(f857(f857(f328(f926(f920(x98491),f920(x98491))),f857(f857(f251(f920(x98491),f920(x98491)),x98493),x98495)),f306(f920(x98491),f157(x98491,x98496))))
% 15.02/14.80 [10025]~P106(f857(x100252,x100256))+~E(f857(f136(x100251,x100252),x100253),f857(f857(f151(x100251),x100254),x100255))+~P106(f857(f857(f328(x100251),x100256),f857(f172(x100251),f747(x100255,x100254,x100253,x100252,x100251))))
% 15.02/14.80 [10026]~P106(f857(x100264,x100266))+~E(f857(f857(f151(x100261),x100262),x100263),f857(f136(x100261,x100264),x100265))+~P106(f857(f857(f328(x100261),x100266),f857(f172(x100261),f743(x100265,x100264,x100263,x100262,x100261))))
% 15.02/14.80 [10348]~P72(x103482)+E(f857(f857(f8(x103481,x103482),f857(f857(f10(f927(x103483,a915),x103482,x103481),f857(f8(x103483,x103482),x103484)),f857(f857(f10(f927(x103483,a915),f927(x103483,a915),x103481),f261(x103483)),f857(f857(f10(f927(x103483,a915),f927(x103483,a915),x103481),f857(f20(x103483,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103483),a325),f857(f857(f9(x103483,f927(x103483,a915),a915),f328(x103483)),x103485)))),f857(f9(x103483,x103481,a915),f857(f857(f10(x103481,f927(x103481,a915),x103483),a324),x103486)))))),f857(f309(x103483,x103481,x103486),x103485)),f857(f857(f8(x103483,x103482),x103484),x103485))+~P106(f857(f60(x103483),x103485))
% 15.02/14.80 [7079]~P109(x70793)+P106(f857(x70792,x70795))+E(f857(f136(x70791,x70792),f857(f857(f148(x70791,x70793,x70794),x70795),x70796)),f857(f136(x70791,x70792),x70796))
% 15.02/14.80 [7081]P106(f857(x70811,x70812))+~E(f166(x70813,x70811,x70814),f857(f857(f251(f920(x70813),f920(x70813)),x70815),x70816))+~P106(f857(f857(f328(x70813),x70812),f857(f172(x70813),x70815)))
% 15.02/14.80 [7126]~P106(f857(x71262,x71266))+~E(f166(x71261,x71262,x71263),f857(f857(f251(f920(x71261),f920(x71261)),x71264),x71265))+~P106(f857(f857(f328(x71261),x71266),f857(f172(x71261),x71265)))
% 15.02/14.80 [7790]~P15(x77901,x77902,x77903)+~P106(f857(f60(x77901),x77906))+E(f857(f857(f63(x77901,x77902,x77903),x77904),f857(f857(f308(x77901),x77905),x77906)),f857(f857(f63(x77901,x77902,x77903),f857(f857(x77903,x77905),x77904)),x77906))
% 15.02/14.80 [7843]~P109(x78432)+~P106(f857(f857(f234(x78432),f857(x78433,x78434)),f857(x78433,x78435)))+E(f857(f857(f148(x78431,x78432,x78433),x78434),f857(f857(f151(x78431),x78435),x78436)),f857(f857(f151(x78431),x78434),f857(f857(f151(x78431),x78435),x78436)))
% 15.02/14.80 [7955]E(x79551,x79552)+~E(f857(f857(f253(x79553,x79554),x79551),f857(f18(f927(x79554,a915),x79553),x79555)),f857(f857(f253(x79553,x79554),x79552),f857(f18(f927(x79554,a915),x79553),x79555)))+~P106(f857(f857(f328(x79554),x79556),x79555))
% 15.02/14.80 [8020]~P15(x80201,x80202,x80203)+~P106(f857(f60(x80201),x80206))+E(f857(f857(f63(x80201,x80202,x80203),x80204),f857(f857(f308(x80201),x80205),x80206)),f857(f857(x80203,x80205),f857(f857(f63(x80201,x80202,x80203),x80204),x80206)))
% 15.02/14.80 [8138]~P17(x81381,x81382,x81383)+~P106(f857(f60(x81381),x81386))+E(f857(f857(f63(x81381,x81382,x81383),f857(f857(x81383,x81384),x81385)),x81386),f857(f857(x81383,x81384),f857(f857(f63(x81381,x81382,x81383),x81385),x81386)))
% 15.02/14.80 [8207]~P21(x82072,x82075,x82076,x82071)+~P106(f857(f60(x82072),x82074))+E(f857(x82071,f857(f857(f308(x82072),x82073),x82074)),f857(f72(x82075,x82075,x82075,f857(x82071,x82074)),f857(x82076,x82073)))
% 15.02/14.80 [8239]~P109(x82392)+P106(f857(f857(f234(x82392),f857(x82393,x82394)),f857(x82393,x82395)))+E(f857(f857(f148(x82391,x82392,x82393),x82394),f857(f857(f151(x82391),x82395),x82396)),f857(f857(f151(x82391),x82395),f857(f857(f148(x82391,x82392,x82393),x82394),x82396)))
% 15.02/14.80 [8381]~E(f857(f190(f920(x83811)),x83815),f857(f190(f920(x83812)),x83816))+~E(f857(f190(f920(x83811)),x83813),f857(f190(f920(x83812)),x83814))+E(f857(f857(f134(f926(x83811,x83812)),f857(f857(f181(x83811,x83812),x83813),x83814)),f857(f857(f181(x83811,x83812),x83815),x83816)),f857(f857(f181(x83811,x83812),f857(f857(f134(x83811),x83813),x83815)),f857(f857(f134(x83812),x83814),x83816)))
% 15.02/14.80 [8492]~E(x84922,f857(f309(x84923,x84921,x84924),x84926))+P106(f857(f857(f234(f927(x84921,a915)),x84922),f857(f309(x84923,x84921,x84924),x84925)))+~P106(f857(f857(f234(f927(x84923,a915)),x84926),x84925))
% 15.02/14.80 [8593]~P109(x85935)+E(f857(x85931,x85932),f857(x85931,x85933))+E(f857(f857(f148(x85934,x85935,x85931),x85932),f857(f857(f148(x85934,x85935,x85931),x85933),x85936)),f857(f857(f148(x85934,x85935,x85931),x85933),f857(f857(f148(x85934,x85935,x85931),x85932),x85936)))
% 15.02/14.80 [8766]~P106(f857(f857(f328(x87662),x87664),f857(x87666,x87663)))+~P106(f857(f857(f328(x87661),x87663),x87665))+P106(f857(f857(f328(f926(x87661,x87662)),f857(f857(f251(x87661,x87662),x87663),x87664)),f857(f857(f253(x87661,x87662),x87665),x87666)))
% 15.02/14.80 [9240]~P72(x92402)+~P26(x92404,x92401,x92405,x92406)+E(f857(f857(f8(x92401,x92402),x92403),f857(f309(x92404,x92401,x92405),x92406)),f857(f857(f8(x92404,x92402),f857(f72(x92401,x92402,x92404,x92403),x92405)),x92406))
% 15.02/14.80 [9241]~P77(x92412)+~P26(x92414,x92411,x92415,x92416)+E(f857(f857(f11(x92411,x92412),x92413),f857(f309(x92414,x92411,x92415),x92416)),f857(f857(f11(x92414,x92412),f857(f72(x92411,x92412,x92414,x92413),x92415)),x92416))
% 15.02/14.80 [9288]~P36(x92882,x92885,x92881,x92883,x92886)+P106(f857(f857(x92881,f857(f857(f164(x92882),x92883),x92884)),f857(f857(f164(x92885),x92886),x92884)))+~P106(f857(f857(f235(a919),x92884),f857(f190(f920(x92885)),x92886)))
% 15.02/14.80 [9289]~P36(x92892,x92895,x92891,x92893,x92896)+P106(f857(f857(x92891,f857(f857(f164(x92892),x92893),x92894)),f857(f857(f164(x92895),x92896),x92894)))+~P106(f857(f857(f235(a919),x92894),f857(f190(f920(x92892)),x92893)))
% 15.02/14.80 [9300]~E(f857(f309(x93001,x93002,x93003),x93004),x93006)+E(f857(f309(x93001,x93002,x93003),f857(f309(x93002,x93001,f91(x93001,x93002,x93004,x93003)),x93005)),x93005)+~P106(f857(f857(f234(f927(x93002,a915)),x93005),x93006))
% 15.02/14.80 [9503]~P20(x95033,x95031,x95036,x95032)+~P106(f857(f60(x95033),x95034))+E(f857(f72(x95031,x95031,x95031,f857(x95032,f857(f857(f3(f927(x95033,a915)),x95034),f857(f857(f308(x95033),x95035),f189(f927(x95033,a915)))))),f857(x95036,x95035)),f857(x95032,f857(f857(f308(x95033),x95035),x95034)))
% 15.02/14.80 [10113]~E(f857(f309(x101132,x101134,x101136),f241(f927(x101132,a915))),f241(f927(x101134,a915)))+~E(f857(f309(x101131,x101133,x101135),f241(f927(x101131,a915))),f241(f927(x101133,a915)))+E(f857(f309(f926(x101131,x101132),f926(x101133,x101134),f257(x101131,x101133,x101132,x101134,x101135,x101136)),f241(f927(f926(x101131,x101132),a915))),f241(f927(f926(x101133,x101134),a915)))
% 15.02/14.80 [10172]~P26(x101723,x101724,x101725,f857(x101726,f551(x101726,x101725,x101724,x101723,x101722,x101721)))+P26(x101723,x101724,x101725,f857(f857(f38(x101722,f927(x101723,a915)),x101721),x101726))+E(x101721,f189(f927(x101722,a915)))
% 15.02/14.80 [10229]P26(x102296,x102295,x102294,f857(f857(f38(x102292,f927(x102296,a915)),x102291),x102293))+E(x102291,f189(f927(x102292,a915)))+P106(f857(f857(f328(x102292),f551(x102293,x102294,x102295,x102296,x102292,x102291)),x102291))
% 15.02/14.80 [10234]P106(f857(f857(f328(x102341),f603(x102342,x102343,x102344,x102345,x102346,x102341)),x102346))+P106(f857(f857(f234(f927(f926(x102341,x102344),a915)),f857(f857(f253(x102341,x102344),x102346),x102343)),f857(f857(f253(x102341,x102344),x102345),x102342)))+~P106(f857(f857(f234(f927(x102341,a915)),x102346),x102345))
% 15.02/14.80 [10274]P25(x102746,x102745,f857(f857(f308(f918(x102746)),f857(f857(f857(f90(x102746),x102744),x102743),x102742)),f189(f927(f918(x102746),a915))))+~P25(x102746,x102745,f857(f857(f308(f918(x102746)),f857(f857(f857(f90(x102746),x102744),x102743),x102741)),f189(f927(f918(x102746),a915))))+P106(f857(f857(x102741,f552(x102742,x102741,x102743,x102744,x102745,x102746)),f664(x102742,x102741,x102743,x102744,x102745,x102746)))
% 15.02/14.80 [10275]P25(x102756,x102755,f857(f857(f308(f918(x102756)),f857(f857(f857(f90(x102756),x102751),x102753),x102752)),f189(f927(f918(x102756),a915))))+~P25(x102756,x102755,f857(f857(f308(f918(x102756)),f857(f857(f857(f90(x102756),x102754),x102753),x102752)),f189(f927(f918(x102756),a915))))+P106(f857(f857(x102751,f780(x102751,x102752,x102753,x102754,x102755,x102756)),f874(x102751,x102752,x102753,x102754,x102755,x102756)))
% 15.02/14.80 [10317]~P25(x103171,x103172,f857(f857(f308(f918(x103171)),f857(f857(f857(f90(x103171),x103173),x103174),x103176)),f189(f927(f918(x103171),a915))))+P25(x103171,x103172,f857(f857(f308(f918(x103171)),f857(f857(f857(f90(x103171),x103173),x103174),x103175)),f189(f927(f918(x103171),a915))))+~P106(f857(f857(x103175,f552(x103175,x103176,x103174,x103173,x103172,x103171)),f664(x103175,x103176,x103174,x103173,x103172,x103171)))
% 15.02/14.80 [10318]~P25(x103181,x103182,f857(f857(f308(f918(x103181)),f857(f857(f857(f90(x103181),x103186),x103184),x103185)),f189(f927(f918(x103181),a915))))+P25(x103181,x103182,f857(f857(f308(f918(x103181)),f857(f857(f857(f90(x103181),x103183),x103184),x103185)),f189(f927(f918(x103181),a915))))+~P106(f857(f857(x103186,f780(x103183,x103185,x103184,x103186,x103182,x103181)),f874(x103183,x103185,x103184,x103186,x103182,x103181)))
% 15.02/14.80 [10362]~P106(f857(f857(f234(f927(x103622,a915)),f857(x103624,f603(x103626,x103624,x103622,x103625,x103623,x103621))),f857(x103626,f603(x103626,x103624,x103622,x103625,x103623,x103621))))+~P106(f857(f857(f234(f927(x103621,a915)),x103623),x103625))+P106(f857(f857(f234(f927(f926(x103621,x103622),a915)),f857(f857(f253(x103621,x103622),x103623),x103624)),f857(f857(f253(x103621,x103622),x103625),x103626)))
% 15.02/14.80 [7977]~P106(f857(x79771,x79775))+~P106(f857(x79776,x79774))+P106(f857(x79771,f857(f255(x79772,x79773),f857(f857(f251(x79772,x79773),x79774),x79775))))
% 15.02/14.80 [7978]~P106(f857(x79781,x79784))+~P106(f857(x79786,x79785))+P106(f857(x79781,f857(f250(x79782,x79783),f857(f857(f251(x79782,x79783),x79784),x79785))))
% 15.02/14.80 [8025]~P106(f857(f857(x80254,x80256),x80255))+~P106(f857(f857(f328(x80251),x80256),x80253))+P106(f857(f857(f857(f39(x80251,f927(x80252,a915)),x80253),x80254),x80255))
% 15.02/14.80 [8331]~P106(f857(f857(f328(x83311),x83312),f857(x83315,x83316)))+~P106(f857(f857(f328(x83313),x83316),x83314))+P106(f857(f857(f328(x83311),x83312),f857(f857(f39(x83313,f927(x83311,a915)),x83314),x83315)))
% 15.02/14.80 [8375]P106(f857(f857(x83751,x83752),x83753))+~P106(f857(f857(x83754,x83752),x83753))+~P106(f857(f857(f234(f927(x83755,f927(x83756,a915))),x83754),x83751))
% 15.02/14.80 [8515]P106(f857(f857(x85151,x85152),x85153))+~P106(f857(f857(f328(x85154),x85152),x85155))+~P106(f857(f857(f857(f38(x85154,f927(x85156,a915)),x85155),x85151),x85153))
% 15.02/14.80 [8648]P106(f857(f857(f328(x86481),x86482),f857(x86483,x86484)))+~P106(f857(f857(f328(x86485),x86484),x86486))+~P106(f857(f857(f328(x86481),x86482),f857(f857(f38(x86485,f927(x86481,a915)),x86486),x86483)))
% 15.02/14.80 [8915]~P12(x89154,x89155,x89156,x89151)+E(f857(x89151,x89152),f857(x89151,x89153))+~P106(f857(f857(f328(f926(x89154,x89154)),f857(f857(f251(x89154,x89154),x89152),x89153)),x89156))
% 15.02/14.80 [8950]P106(f857(f857(f234(f927(x89501,a915)),x89502),f857(x89503,x89504)))+~P106(f857(f857(f328(x89505),x89504),x89506))+~P106(f857(f857(f234(f927(x89501,a915)),x89502),f857(f857(f38(x89505,f927(x89501,a915)),x89506),x89503)))
% 15.02/14.80 [8983]~P56(x89833,x89834,f857(f285(x89834,x89833),x89835))+E(x89831,f189(f927(x89832,a915)))+E(f857(f857(f38(x89832,f927(x89833,a915)),x89831),f857(f857(f10(f927(x89834,a915),f927(x89833,a915),x89832),f284(x89834,x89833,x89835)),x89836)),f857(f284(x89834,x89833,x89835),f857(f857(f38(x89832,f927(x89834,a915)),x89831),x89836)))
% 15.02/14.80 [9061]P106(f857(f857(f328(x90611),x90612),f857(f284(x90613,x90611,x90614),x90615)))+~P106(f857(f857(f328(x90613),x90616),x90615))+~P106(f857(f857(f328(f926(x90613,x90611)),f857(f857(f251(x90613,x90611),x90616),x90612)),x90614))
% 15.02/14.80 [9365]P106(f857(f857(f234(f927(x93651,a915)),f857(f284(x93652,x93651,x93653),x93654)),f857(f284(x93652,x93651,x93655),x93656)))+~P106(f857(f857(f234(f927(x93652,a915)),x93654),x93656))+~P106(f857(f857(f234(f927(f926(x93652,x93651),a915)),x93653),x93655))
% 15.02/14.80 [9552]~P106(f857(f857(f328(x95522),x95526),x95524))+~P106(f857(f857(f234(f927(x95521,a915)),x95523),x95525))+P106(f857(f857(f234(f927(f926(x95521,x95522),a915)),f857(f857(f253(x95521,x95522),x95523),f857(f18(f927(x95522,a915),x95521),x95524))),f857(f857(f253(x95521,x95522),x95525),f857(f18(f927(x95522,a915),x95521),x95524))))
% 15.02/14.80 [9564]~P36(x95641,x95642,x95643,x95645,x95646)+P106(f857(f857(f256(x95641,x95642,a915),x95643),x95644))+~P106(f857(f857(f328(f926(x95641,x95642)),x95644),f857(f172(f926(x95641,x95642)),f857(f857(f181(x95641,x95642),x95645),x95646))))
% 15.02/14.80 [9711]~E(x97113,x97115)+P106(f857(f857(f328(f926(f920(x97111),f920(x97111))),f857(f857(f251(f920(x97111),f920(x97111)),f857(f857(f151(x97111),x97112),x97113)),f857(f857(f151(x97111),x97114),x97115))),f157(x97111,x97116)))+~P106(f857(f857(f328(f926(x97111,x97111)),f857(f857(f251(x97111,x97111),x97112),x97114)),x97116))
% 15.02/14.80 [9717]~E(f857(f190(f920(x97171)),x97173),f857(f190(f920(x97171)),x97175))+P106(f857(f857(f328(f926(f920(x97171),f920(x97171))),f857(f857(f251(f920(x97171),f920(x97171)),f857(f857(f151(x97171),x97172),x97173)),f857(f857(f151(x97171),x97174),x97175))),f145(x97171,x97176)))+~P106(f857(f857(f328(f926(x97171,x97171)),f857(f857(f251(x97171,x97171),x97172),x97174)),x97176))
% 15.02/14.80 [9749]P106(f857(f857(f328(f926(x97491,x97491)),f857(f857(f251(x97491,x97491),x97492),x97493)),f857(f857(f183(f926(x97491,x97491),a915),f857(a112,x97494)),x97495)))+~P106(f857(f857(f328(f926(x97491,x97491)),f857(f857(f251(x97491,x97491),x97496),x97493)),x97495))+~P106(f857(f857(f328(f926(x97491,x97491)),f857(f857(f251(x97491,x97491),x97492),x97496)),f857(f857(f183(f926(x97491,x97491),a915),x97494),x97495)))
% 15.02/14.80 [9750]P106(f857(f857(f328(f926(x97501,x97501)),f857(f857(f251(x97501,x97501),x97502),x97503)),f857(f857(f183(f926(x97501,x97501),a915),f857(a112,x97504)),x97505)))+~P106(f857(f857(f328(f926(x97501,x97501)),f857(f857(f251(x97501,x97501),x97502),x97506)),x97505))+~P106(f857(f857(f328(f926(x97501,x97501)),f857(f857(f251(x97501,x97501),x97506),x97503)),f857(f857(f183(f926(x97501,x97501),a915),x97504),x97505)))
% 15.02/14.80 [9753]~P106(f857(f857(f328(x97534),x97535),x97536))+P106(f857(f857(f234(f927(x97531,a915)),x97532),x97533))+~P106(f857(f857(f234(f927(f926(x97531,x97534),a915)),f857(f857(f253(x97531,x97534),x97532),f857(f18(f927(x97534,a915),x97531),x97536))),f857(f857(f253(x97531,x97534),x97533),f857(f18(f927(x97534,a915),x97531),x97536))))
% 15.02/14.80 [9798]E(x97981,x97982)+~P106(f857(f857(f328(f926(f920(x97983),f920(x97983))),f857(f857(f251(f920(x97983),f920(x97983)),f857(f857(f151(x97983),x97981),x97985)),f857(f857(f151(x97983),x97982),x97986))),f145(x97983,x97984)))+P106(f857(f857(f328(f926(x97983,x97983)),f857(f857(f251(x97983,x97983),x97981),x97982)),x97984))
% 15.02/14.80 [9799]E(x97991,x97992)+~P106(f857(f857(f328(f926(f920(x97993),f920(x97993))),f857(f857(f251(f920(x97993),f920(x97993)),f857(f857(f151(x97993),x97991),x97995)),f857(f857(f151(x97993),x97992),x97996))),f147(x97993,x97994)))+P106(f857(f857(f328(f926(x97993,x97993)),f857(f857(f251(x97993,x97993),x97991),x97992)),x97994))
% 15.02/14.80 [9800]E(x98001,x98002)+~P106(f857(f857(f328(f926(f920(x98003),f920(x98003))),f857(f857(f251(f920(x98003),f920(x98003)),f857(f857(f151(x98003),x98001),x98005)),f857(f857(f151(x98003),x98002),x98006))),f157(x98003,x98004)))+P106(f857(f857(f328(f926(x98003,x98003)),f857(f857(f251(x98003,x98003),x98001),x98002)),x98004))
% 15.02/14.80 [9836]P106(f857(f857(f328(f926(f920(x98361),f920(x98361))),f857(f857(f251(f920(x98361),f920(x98361)),f857(f857(f151(x98361),x98362),x98363)),f857(f857(f151(x98361),x98364),x98365))),f158(x98361,x98366)))+~P106(f857(f857(f328(f926(f920(x98361),f920(x98361))),f857(f857(f251(f920(x98361),f920(x98361)),x98363),x98365)),f158(x98361,x98366)))+~P106(f857(f857(f328(f926(x98361,x98361)),f857(f857(f251(x98361,x98361),x98362),x98364)),x98366))
% 15.02/14.80 [9853]P106(f857(x98531,x98532))+~P106(f857(x98531,f453(x98531,x98533,x98534,x98535,x98536)))+~P106(f857(f857(f328(x98536),x98532),f857(f857(f39(x98535,f927(x98536,a915)),x98534),x98533)))
% 15.02/14.80 [9858]~P106(f857(f857(f328(f926(f920(x98581),f920(x98581))),f857(f857(f251(f920(x98581),f920(x98581)),f857(f857(f151(x98581),x98582),x98585)),f857(f857(f151(x98581),x98583),x98586))),f145(x98581,x98584)))+P106(f857(f857(f328(f926(f920(x98581),f920(x98581))),f857(f857(f251(f920(x98581),f920(x98581)),x98585),x98586)),f145(x98581,x98584)))+P106(f857(f857(f328(f926(x98581,x98581)),f857(f857(f251(x98581,x98581),x98582),x98583)),x98584))
% 15.02/14.80 [9859]~P106(f857(f857(f328(f926(f920(x98591),f920(x98591))),f857(f857(f251(f920(x98591),f920(x98591)),f857(f857(f151(x98591),x98592),x98595)),f857(f857(f151(x98591),x98593),x98596))),f147(x98591,x98594)))+P106(f857(f857(f328(f926(f920(x98591),f920(x98591))),f857(f857(f251(f920(x98591),f920(x98591)),x98595),x98596)),f147(x98591,x98594)))+P106(f857(f857(f328(f926(x98591,x98591)),f857(f857(f251(x98591,x98591),x98592),x98593)),x98594))
% 15.02/14.80 [9860]~P106(f857(f857(f328(f926(f920(x98601),f920(x98601))),f857(f857(f251(f920(x98601),f920(x98601)),f857(f857(f151(x98601),x98602),x98605)),f857(f857(f151(x98601),x98603),x98606))),f157(x98601,x98604)))+P106(f857(f857(f328(f926(f920(x98601),f920(x98601))),f857(f857(f251(f920(x98601),f920(x98601)),x98605),x98606)),f157(x98601,x98604)))+P106(f857(f857(f328(f926(x98601,x98601)),f857(f857(f251(x98601,x98601),x98602),x98603)),x98604))
% 15.02/14.80 [9948]P106(f857(x99481,x99482))+P106(f857(f857(f328(x99483),f454(x99481,x99484,x99485,x99483,x99486)),x99485))+~P106(f857(f857(f328(x99486),x99482),f857(f857(f39(x99483,f927(x99486,a915)),x99485),x99484)))
% 15.02/14.80 [9959]~E(x99592,x99594)+P106(f857(f857(f328(f926(f920(x99591),f920(x99591))),f857(f857(f251(f920(x99591),f920(x99591)),f857(f857(f134(x99591),x99592),f857(f857(f151(x99591),x99593),f113(x99591)))),f857(f857(f134(x99591),x99594),f857(f857(f151(x99591),x99595),f113(x99591))))),f157(x99591,x99596)))+~P106(f857(f857(f328(f926(x99591,x99591)),f857(f857(f251(x99591,x99591),x99593),x99595)),x99596))
% 15.02/14.80 [10034]E(x100341,x100342)+~P106(f857(f857(f328(f926(f920(x100343),f920(x100343))),f857(f857(f251(f920(x100343),f920(x100343)),f857(f857(f134(x100343),x100345),f857(f857(f151(x100343),x100341),f113(x100343)))),f857(f857(f134(x100343),x100346),f857(f857(f151(x100343),x100342),f113(x100343))))),f157(x100343,x100344)))+P106(f857(f857(f328(f926(x100343,x100343)),f857(f857(f251(x100343,x100343),x100341),x100342)),x100344))
% 15.02/14.80 [10065]~P106(f857(f857(f328(f926(f920(x100651),f920(x100651))),f857(f857(f251(f920(x100651),f920(x100651)),f857(f857(f134(x100651),x100655),f857(f857(f151(x100651),x100652),f113(x100651)))),f857(f857(f134(x100651),x100656),f857(f857(f151(x100651),x100653),f113(x100651))))),f157(x100651,x100654)))+P106(f857(f857(f328(f926(f920(x100651),f920(x100651))),f857(f857(f251(f920(x100651),f920(x100651)),x100655),x100656)),f157(x100651,x100654)))+P106(f857(f857(f328(f926(x100651,x100651)),f857(f857(f251(x100651,x100651),x100652),x100653)),x100654))
% 15.02/14.80 [10085]P106(f857(x100851,x100852))+P106(f857(f857(f328(x100853),f453(x100851,x100854,x100855,x100856,x100853)),f857(x100854,f454(x100851,x100854,x100855,x100856,x100853))))+~P106(f857(f857(f328(x100853),x100852),f857(f857(f39(x100856,f927(x100853,a915)),x100855),x100854)))
% 15.02/14.80 [10238]P106(f857(f857(f328(x102381),f837(x102382,x102383,x102384,x102385,x102386,x102381)),x102385))+~P106(f857(f857(f234(f927(x102381,a915)),x102386),x102385))+P106(f857(f857(f234(f927(x102384,a915)),f857(f857(f38(x102381,f927(x102384,a915)),x102385),x102383)),f857(f857(f38(x102381,f927(x102384,a915)),x102385),x102382)))
% 15.02/14.80 [10363]~P106(f857(f857(f234(f927(x103631,a915)),f857(x103634,f837(x103635,x103634,x103631,x103633,x103636,x103632))),f857(x103635,f837(x103635,x103634,x103631,x103633,x103636,x103632))))+~P106(f857(f857(f234(f927(x103632,a915)),x103636),x103633))+P106(f857(f857(f234(f927(x103631,a915)),f857(f857(f38(x103632,f927(x103631,a915)),x103633),x103634)),f857(f857(f38(x103632,f927(x103631,a915)),x103633),x103635)))
% 15.02/14.80 [9081]~P17(x90813,x90814,x90811)+~P106(f857(f60(x90813),x90816))+E(f857(f857(x90811,x90812),f857(f857(f63(x90813,x90814,x90811),x90815),f857(f857(f3(f927(x90813,a915)),x90816),f857(f857(f308(x90813),x90812),f189(f927(x90813,a915)))))),f857(f857(f63(x90813,x90814,x90811),x90815),f857(f857(f308(x90813),x90812),x90816)))
% 15.02/14.80 [9374]~P106(f857(f857(f328(x93745),x93743),x93746))+P106(f857(f857(f234(f927(x93741,a915)),f857(x93742,x93743)),x93744))+~P106(f857(f857(f234(f927(x93741,a915)),f857(f857(f39(x93745,f927(x93741,a915)),x93746),x93742)),x93744))
% 15.02/14.80 [10008]~P9(x100081,x100085,x100084)+P106(f857(f857(f328(f926(x100081,x100081)),f857(f857(f251(x100081,x100081),x100082),x100083)),x100084))+~P106(f857(f857(f328(x100081),x100086),f857(f857(f101(f927(x100081,a915)),f857(f284(x100081,x100081,x100084),f857(f857(f308(x100081),x100082),f189(f927(x100081,a915))))),f857(f284(x100081,x100081,x100084),f857(f857(f308(x100081),x100083),f189(f927(x100081,a915)))))))
% 15.02/14.80 [8803]~P111(x88032)+~E(f857(f857(f79(x88032),f857(f857(f80(x88032),x88034),x88035)),x88031),f857(f857(f79(x88032),f857(f857(f80(x88032),x88033),x88035)),x88036))+E(x88031,f857(f857(f79(x88032),f857(f857(f80(x88032),f857(f857(f3(x88032),x88033),x88034)),x88035)),x88036))
% 15.02/14.80 [8804]~P111(x88041)+~E(f857(f857(f79(x88041),f857(f857(f80(x88041),x88042),x88044)),x88045),f857(f857(f79(x88041),f857(f857(f80(x88041),x88043),x88044)),x88046))+E(f857(f857(f79(x88041),f857(f857(f80(x88041),f857(f857(f3(x88041),x88042),x88043)),x88044)),x88045),x88046)
% 15.02/14.80 [8986]~P111(x89861)+E(f857(f857(f79(x89861),f857(f857(f80(x89861),x89862),x89863)),x89864),f857(f857(f79(x89861),f857(f857(f80(x89861),x89865),x89863)),x89866))+~E(x89866,f857(f857(f79(x89861),f857(f857(f80(x89861),f857(f857(f3(x89861),x89862),x89865)),x89863)),x89864))
% 15.02/14.80 [8987]~P111(x89871)+E(f857(f857(f79(x89871),f857(f857(f80(x89871),x89872),x89873)),x89874),f857(f857(f79(x89871),f857(f857(f80(x89871),x89875),x89873)),x89876))+~E(f857(f857(f79(x89871),f857(f857(f80(x89871),f857(f857(f3(x89871),x89872),x89875)),x89873)),x89874),x89876)
% 15.02/14.80 [9311]~P106(f857(f857(x93114,x93115),x93116))+~P106(f857(f857(x93113,x93115),x93116))+P106(f857(f857(f857(f857(f101(f927(x93111,f927(x93112,a915))),x93113),x93114),x93115),x93116))
% 15.02/14.80 [9573]P106(f857(f857(x95731,x95732),x95733))+P106(f857(f857(x95734,x95732),x95733))+~P106(f857(f857(f857(f857(f110(f927(x95735,f927(x95736,a915))),x95734),x95731),x95732),x95733))
% 15.02/14.80 [9873]~P112(x98731)+~P106(f857(f857(f234(x98731),f857(f857(f79(x98731),f857(f857(f80(x98731),x98734),x98735)),x98732)),f857(f857(f79(x98731),f857(f857(f80(x98731),x98733),x98735)),x98736)))+P106(f857(f857(f234(x98731),x98732),f857(f857(f79(x98731),f857(f857(f80(x98731),f857(f857(f3(x98731),x98733),x98734)),x98735)),x98736)))
% 15.02/14.80 [9874]~P112(x98741)+~P106(f857(f857(f235(x98741),f857(f857(f79(x98741),f857(f857(f80(x98741),x98744),x98745)),x98742)),f857(f857(f79(x98741),f857(f857(f80(x98741),x98743),x98745)),x98746)))+P106(f857(f857(f235(x98741),x98742),f857(f857(f79(x98741),f857(f857(f80(x98741),f857(f857(f3(x98741),x98743),x98744)),x98745)),x98746)))
% 15.02/14.80 [9897]~P112(x98971)+P106(f857(f857(f234(x98971),f857(f857(f79(x98971),f857(f857(f80(x98971),x98972),x98973)),x98974)),f857(f857(f79(x98971),f857(f857(f80(x98971),x98975),x98973)),x98976)))+~P106(f857(f857(f234(x98971),x98974),f857(f857(f79(x98971),f857(f857(f80(x98971),f857(f857(f3(x98971),x98975),x98972)),x98973)),x98976)))
% 15.02/14.80 [9898]~P112(x98981)+P106(f857(f857(f235(x98981),f857(f857(f79(x98981),f857(f857(f80(x98981),x98982),x98983)),x98984)),f857(f857(f79(x98981),f857(f857(f80(x98981),x98985),x98983)),x98986)))+~P106(f857(f857(f235(x98981),x98984),f857(f857(f79(x98981),f857(f857(f80(x98981),f857(f857(f3(x98981),x98985),x98982)),x98983)),x98986)))
% 15.02/14.80 [10000]~P112(x100001)+~P106(f857(f857(f234(x100001),f857(f857(f79(x100001),f857(f857(f80(x100001),x100002),x100004)),x100005)),f857(f857(f79(x100001),f857(f857(f80(x100001),x100003),x100004)),x100006)))+P106(f857(f857(f234(x100001),f857(f857(f79(x100001),f857(f857(f80(x100001),f857(f857(f3(x100001),x100002),x100003)),x100004)),x100005)),x100006))
% 15.02/14.80 [10001]~P112(x100011)+~P106(f857(f857(f235(x100011),f857(f857(f79(x100011),f857(f857(f80(x100011),x100012),x100014)),x100015)),f857(f857(f79(x100011),f857(f857(f80(x100011),x100013),x100014)),x100016)))+P106(f857(f857(f235(x100011),f857(f857(f79(x100011),f857(f857(f80(x100011),f857(f857(f3(x100011),x100012),x100013)),x100014)),x100015)),x100016))
% 15.02/14.80 [10048]~P112(x100481)+P106(f857(f857(f234(x100481),f857(f857(f79(x100481),f857(f857(f80(x100481),x100482),x100483)),x100484)),f857(f857(f79(x100481),f857(f857(f80(x100481),x100485),x100483)),x100486)))+~P106(f857(f857(f234(x100481),f857(f857(f79(x100481),f857(f857(f80(x100481),f857(f857(f3(x100481),x100482),x100485)),x100483)),x100484)),x100486))
% 15.02/14.80 [10049]~P112(x100491)+P106(f857(f857(f235(x100491),f857(f857(f79(x100491),f857(f857(f80(x100491),x100492),x100493)),x100494)),f857(f857(f79(x100491),f857(f857(f80(x100491),x100495),x100493)),x100496)))+~P106(f857(f857(f235(x100491),f857(f857(f79(x100491),f857(f857(f80(x100491),f857(f857(f3(x100491),x100492),x100495)),x100493)),x100494)),x100496))
% 15.02/14.80 [10223]~P72(x102232)+~P106(f857(f60(x102231),x102236))+E(f857(f857(f8(x102231,x102232),f857(f857(f20(x102231,x102232,x102232),f857(f857(f20(x102231,x102232,f927(x102232,x102232)),f857(f857(f10(a915,f927(x102232,f927(x102232,x102232)),x102231),f96(x102232)),x102233)),x102234)),x102235)),x102236),f857(f857(f79(x102232),f857(f857(f8(x102231,x102232),x102234),f857(f857(f101(f927(x102231,a915)),x102236),f857(f261(x102231),x102233)))),f857(f857(f8(x102231,x102232),x102235),f857(f857(f101(f927(x102231,a915)),x102236),f857(f78(f927(x102231,a915)),f857(f261(x102231),x102233))))))
% 15.02/14.80 [10285]P106(f857(f857(f328(x102852),x102854),x102856))+P106(f857(f857(f328(x102852),x102855),x102856))+E(f857(f310(x102851,x102852,f857(f857(f9(x102851,x102852,x102852),f857(f857(f9(x102851,x102852,f927(x102852,x102852)),f857(f857(f10(a915,f927(x102852,f927(x102852,x102852)),x102851),f96(x102852)),f857(f857(f9(x102851,f927(x102851,a915),a915),f328(x102851)),x102853))),x102854)),x102855)),x102856),f189(f927(x102851,a915)))
% 15.02/14.80 [10286]P106(f857(f857(f328(x102862),x102865),x102866))+~P106(f857(f857(f328(x102862),x102864),x102866))+E(f857(f310(x102861,x102862,f857(f857(f9(x102861,x102862,x102862),f857(f857(f9(x102861,x102862,f927(x102862,x102862)),f857(f857(f10(a915,f927(x102862,f927(x102862,x102862)),x102861),f96(x102862)),f857(f857(f9(x102861,f927(x102861,a915),a915),f328(x102861)),x102863))),x102864)),x102865)),x102866),x102863)
% 15.02/14.80 [10287]P106(f857(f857(f328(x102872),x102874),x102876))+~P106(f857(f857(f328(x102872),x102875),x102876))+E(f857(f310(x102871,x102872,f857(f857(f9(x102871,x102872,x102872),f857(f857(f9(x102871,x102872,f927(x102872,x102872)),f857(f857(f10(a915,f927(x102872,f927(x102872,x102872)),x102871),f96(x102872)),f857(f857(f9(x102871,f927(x102871,a915),a915),f328(x102871)),x102873))),x102874)),x102875)),x102876),f857(f78(f927(x102871,a915)),x102873))
% 15.02/14.80 [10288]~P106(f857(f857(f328(x102882),x102884),x102886))+~P106(f857(f857(f328(x102882),x102885),x102886))+E(f857(f310(x102881,x102882,f857(f857(f9(x102881,x102882,x102882),f857(f857(f9(x102881,x102882,f927(x102882,x102882)),f857(f857(f10(a915,f927(x102882,f927(x102882,x102882)),x102881),f96(x102882)),f857(f857(f9(x102881,f927(x102881,a915),a915),f328(x102881)),x102883))),x102884)),x102885)),x102886),f241(f927(x102881,a915)))
% 15.02/14.80 [8836]E(x88361,x88362)+~P58(x88364,x88365,x88363,x88366,x88367)+~E(f857(x88363,x88361),f857(x88363,x88362))
% 15.02/14.80 [8865]~P11(x88656,x88655,x88657,x88654,x88651)+E(f857(f857(x88651,x88652),x88653),x88654)+P106(f857(f60(x88655),x88653))
% 15.02/14.80 [9740]P44(x97401,x97402,x97403,x97404,x97405,f857(f857(x97403,x97406),x97407))+~E(f857(f857(x97403,x97406),x97407),x97404)+~E(x97405,f189(f927(x97401,a915)))
% 15.02/14.80 [9919]~P106(f857(x99196,x99193))+~P106(f857(f857(f328(f926(x99192,x99192)),f857(f857(f251(x99192,x99192),x99194),x99195)),f857(x99197,x99193)))+P106(f857(f857(f328(f926(f926(x99191,x99192),f926(x99191,x99192))),f857(f857(f251(f926(x99191,x99192),f926(x99191,x99192)),f857(f857(f251(x99191,x99192),x99193),x99194)),f857(f857(f251(x99191,x99192),x99193),x99195))),f279(x99191,x99192,x99196,x99197)))
% 15.02/14.80 [10351]~P44(x103512,x103517,x103513,x103516,x103511,f857(f857(x103513,x103515),x103514))+E(f857(f857(x103513,f781(x103514,x103515,x103511,x103516,x103513,x103517,x103512)),f789(x103514,x103515,x103511,x103516,x103513,x103517,x103512)),f857(f857(x103513,x103515),x103514))+E(x103511,f189(f927(x103512,a915)))
% 15.02/14.80 [10352]~P44(x103527,x103526,x103521,x103524,x103525,f857(f857(x103521,x103522),x103523))+E(f857(f857(x103521,f781(x103523,x103522,x103525,x103524,x103521,x103526,x103527)),f789(x103523,x103522,x103525,x103524,x103521,x103526,x103527)),f857(f857(x103521,x103522),x103523))+E(f857(f857(x103521,x103522),x103523),x103524)
% 15.02/14.80 [9407]~P36(x94071,x94072,x94073,x94075,x94077)+P36(x94071,x94072,x94073,f857(f857(f151(x94071),x94074),x94075),f857(f857(f151(x94072),x94076),x94077))+~P106(f857(f857(x94073,x94074),x94076))
% 15.02/14.80 [9426]P36(x94261,x94262,x94263,x94264,x94265)+~P36(x94261,x94262,x94263,f857(f857(f134(x94261),x94266),x94264),f857(f857(f134(x94262),x94267),x94265))+~E(f857(f190(f920(x94261)),x94266),f857(f190(f920(x94262)),x94267))
% 15.02/14.80 [9427]P36(x94271,x94272,x94273,x94274,x94275)+~P36(x94271,x94272,x94273,f857(f857(f134(x94271),x94274),x94276),f857(f857(f134(x94272),x94275),x94277))+~E(f857(f190(f920(x94271)),x94274),f857(f190(f920(x94272)),x94275))
% 15.02/14.80 [9640]~P36(x96401,x96402,x96403,x96405,x96407)+~P36(x96401,x96402,x96403,x96404,x96406)+P36(x96401,x96402,x96403,f857(f857(f134(x96401),x96404),x96405),f857(f857(f134(x96402),x96406),x96407))
% 15.02/14.80 [9993]~P106(f857(f65(x99931,x99934,x99935,x99936,x99933),x99937))+P106(f857(f65(x99931,x99934,x99935,x99936,f857(f857(f308(x99931),x99932),x99933)),f857(f857(x99935,x99932),x99937)))+P106(f857(f857(f328(x99931),x99932),x99933))
% 15.02/14.80 [10379]~P44(x103792,x103797,x103796,x103795,x103791,f857(f857(x103796,x103794),x103793))+E(x103791,f189(f927(x103792,a915)))+P106(f857(f857(f328(x103792),f781(x103793,x103794,x103791,x103795,x103796,x103797,x103792)),x103791))
% 15.02/14.80 [10380]~P44(x103805,x103807,x103801,x103804,x103806,f857(f857(x103801,x103802),x103803))+E(f857(f857(x103801,x103802),x103803),x103804)+P106(f857(f857(f328(x103805),f781(x103803,x103802,x103806,x103804,x103801,x103807,x103805)),x103806))
% 15.02/14.80 [10471]E(f857(f857(f251(x104711,x104712),x104713),x104714),f857(f857(f251(x104711,x104712),x104715),x104716))+P106(f857(f857(f328(f926(f926(x104711,x104712),f926(x104711,x104712))),f857(f857(f251(f926(x104711,x104712),f926(x104711,x104712)),f857(f857(f251(x104711,x104712),f847(x104717,x104714,x104713,x104716,x104715,x104712,x104711)),f848(x104717,x104714,x104713,x104716,x104715,x104712,x104711))),f857(f857(f251(x104711,x104712),x104713),x104714))),f306(f926(x104711,x104712),x104717)))+~P106(f857(f857(f328(f926(f926(x104711,x104712),f926(x104711,x104712))),f857(f857(f251(f926(x104711,x104712),f926(x104711,x104712)),f857(f857(f251(x104711,x104712),x104715),x104716)),f857(f857(f251(x104711,x104712),x104713),x104714))),f306(f926(x104711,x104712),x104717)))
% 15.02/14.80 [9106]~P22(x91064,x91065,x91066,x91067,x91061)+~P106(f857(f60(x91065),x91063))+E(f857(f857(x91061,x91062),x91063),f857(f857(f857(f64(x91064,x91065,x91066),x91062),x91067),x91063))
% 15.02/14.80 [9107]~P11(x91074,x91075,x91076,x91077,x91071)+~P106(f857(f60(x91075),x91073))+E(f857(f857(x91071,x91072),x91073),f857(f857(f857(f64(x91074,x91075,x91076),x91072),x91077),x91073))
% 15.02/14.80 [9704]~P25(x97041,x97042,f857(f857(f308(f918(x97041)),f857(f857(f857(f90(x97041),x97043),x97044),x97047)),f189(f927(f918(x97041),a915))))+P25(x97041,x97042,f857(f857(f308(f918(x97041)),f857(f857(f857(f90(x97041),x97043),f30(x97044,x97045)),x97046)),f189(f927(f918(x97041),a915))))+~P25(x97041,x97042,f857(f857(f308(f918(x97041)),f857(f857(f857(f90(x97041),x97047),x97045),x97046)),f189(f927(f918(x97041),a915))))
% 15.02/14.80 [9892]~P24(x98923,x98924,x98925,x98927,x98926,x98921)+~P106(f857(f60(x98924),x98922))+E(f857(x98921,x98922),f857(f857(f857(f64(x98923,x98924,x98925),x98926),x98927),x98922))
% 15.02/14.80 [10043]P44(x100431,x100432,x100433,x100434,x100435,f857(f857(x100433,x100436),x100437))+~P44(x100431,x100432,x100433,x100434,f857(f857(f3(f927(x100431,a915)),x100435),f857(f857(f308(x100431),x100436),f189(f927(x100431,a915)))),x100437)+~P106(f857(f857(f328(x100431),x100436),x100435))
% 15.02/14.80 [10319]~P25(x103191,x103192,f857(f857(f308(f918(x103191)),f857(f857(f857(f90(x103191),f92(x103191,x103193,x103194)),x103195),x103197)),f189(f927(f918(x103191),a915))))+P25(x103191,x103192,f857(f857(f308(f918(x103191)),f857(f857(f857(f90(x103191),x103193),f27(x103194,x103195,x103196)),x103197)),f189(f927(f918(x103191),a915))))+~P25(x103191,x103192,f857(f857(f308(f918(x103191)),f857(f857(f857(f90(x103191),f92(x103191,x103193,f857(f72(a915,a915,a917,a321),x103194))),x103196),x103197)),f189(f927(f918(x103191),a915))))
% 15.02/14.80 [10404]P106(f857(f857(x104047,f790(x104044,x104045,x104041,x104046,x104043,x104042,x104047)),f791(x104044,x104045,x104041,x104046,x104043,x104042,x104047)))+~P106(f857(f857(x104047,f857(f255(x104042,x104043),x104046)),f857(f250(x104042,x104043),x104046)))+P106(f857(x104041,f857(f857(f256(x104042,x104043,x104044),x104045),x104046)))
% 15.02/14.80 [10405]P25(x104057,x104056,f857(f857(f308(f918(x104057)),f857(f857(f857(f90(x104057),x104051),x104054),x104052)),f189(f927(f918(x104057),a915))))+~P25(x104057,x104056,f857(f857(f308(f918(x104057)),f857(f857(f857(f90(x104057),x104055),x104054),x104053)),f189(f927(f918(x104057),a915))))+P106(f857(f857(x104051,f887(x104052,x104051,x104053,x104054,x104055,x104056,x104057)),f894(x104052,x104051,x104053,x104054,x104055,x104056,x104057)))
% 15.02/14.80 [10415]~P44(x104152,x104153,x104154,x104155,x104151,f857(f857(x104154,x104157),x104156))+P44(x104152,x104153,x104154,x104155,f857(f857(f3(f927(x104152,a915)),x104151),f857(f857(f308(x104152),f781(x104156,x104157,x104151,x104155,x104154,x104153,x104152)),f189(f927(x104152,a915)))),f789(x104156,x104157,x104151,x104155,x104154,x104153,x104152))+E(x104151,f189(f927(x104152,a915)))
% 15.02/14.80 [10416]~P44(x104165,x104166,x104161,x104164,x104167,f857(f857(x104161,x104162),x104163))+P44(x104165,x104166,x104161,x104164,f857(f857(f3(f927(x104165,a915)),x104167),f857(f857(f308(x104165),f781(x104163,x104162,x104167,x104164,x104161,x104166,x104165)),f189(f927(x104165,a915)))),f789(x104163,x104162,x104167,x104164,x104161,x104166,x104165))+E(f857(f857(x104161,x104162),x104163),x104164)
% 15.02/14.80 [10417]~P25(x104171,x104172,f857(f857(f308(f918(x104171)),f857(f857(f857(f90(x104171),x104177),x104174),x104176)),f189(f927(f918(x104171),a915))))+P25(x104171,x104172,f857(f857(f308(f918(x104171)),f857(f857(f857(f90(x104171),x104173),x104174),x104175)),f189(f927(f918(x104171),a915))))+~P106(f857(f857(x104175,f887(x104175,x104173,x104176,x104174,x104177,x104172,x104171)),f904(x104175,x104173,x104176,x104174,x104177,x104172,x104171)))
% 15.02/14.80 [10438]~P106(f857(x104381,f857(f857(x104385,f791(x104384,x104385,x104381,x104386,x104383,x104382,x104387)),f790(x104384,x104385,x104381,x104386,x104383,x104382,x104387))))+~P106(f857(f857(x104387,f857(f255(x104382,x104383),x104386)),f857(f250(x104382,x104383),x104386)))+P106(f857(x104381,f857(f857(f256(x104382,x104383,x104384),x104385),x104386)))
% 15.02/14.80 [9725]P106(f857(f857(f234(f927(f926(x97251,x97252),a915)),f857(f857(f288(x97251,x97253,x97252),x97254),x97255)),f857(f857(f288(x97251,x97253,x97252),x97256),x97257)))+~P106(f857(f857(f234(f927(f926(x97253,x97252),a915)),x97255),x97257))+~P106(f857(f857(f234(f927(f926(x97251,x97253),a915)),x97254),x97256))
% 15.02/14.80 [10465]E(f857(f857(f251(x104651,x104652),x104653),x104654),f857(f857(f251(x104651,x104652),x104655),x104656))+~P106(f857(f857(f328(f926(f926(x104651,x104652),f926(x104651,x104652))),f857(f857(f251(f926(x104651,x104652),f926(x104651,x104652)),f857(f857(f251(x104651,x104652),x104653),x104654)),f857(f857(f251(x104651,x104652),x104655),x104656))),f306(f926(x104651,x104652),x104657)))+P106(f857(f857(f328(f926(f926(x104651,x104652),f926(x104651,x104652))),f857(f857(f251(f926(x104651,x104652),f926(x104651,x104652)),f857(f857(f251(x104651,x104652),x104653),x104654)),f857(f857(f251(x104651,x104652),f847(x104657,x104656,x104655,x104654,x104653,x104652,x104651)),f848(x104657,x104656,x104655,x104654,x104653,x104652,x104651)))),x104657))
% 15.02/14.80 [10054]~P106(f857(f857(f328(x100541),x100546),x100545))+P106(f857(f65(x100541,x100542,x100543,x100544,x100545),f857(f857(x100543,x100546),x100547)))+~P106(f857(f65(x100541,x100542,x100543,x100544,f857(f857(f3(f927(x100541,a915)),x100545),f857(f857(f308(x100541),x100546),f189(f927(x100541,a915))))),x100547))
% 15.02/14.80 [10478]~P147(x104781)+~P26(f926(x104782,x104783),x104781,f857(f256(x104782,x104783,x104781),f857(f857(f9(x104782,f927(x104783,x104781),f927(x104783,x104781)),f857(f857(f10(f927(x104781,x104781),f927(f927(x104783,x104781),f927(x104783,x104781)),x104782),f10(x104781,x104781,x104783)),f857(f857(f10(x104781,f927(x104781,x104781),x104782),f80(x104781)),x104784))),x104785)),f857(f857(f253(x104782,x104783),x104786),f857(f18(f927(x104783,a915),x104782),x104787)))+E(f857(f857(f8(x104781,x104781),f31(x104781)),f857(f261(x104781),f857(f857(f10(f927(x104782,a915),a915,x104781),f86(x104782)),f857(f857(f10(f927(x104782,f927(x104783,a915)),f927(x104782,a915),x104781),f857(f10(f927(x104783,a915),a915,x104782),f86(x104783))),f857(f857(f9(x104781,f927(x104782,f927(x104783,a915)),f927(x104782,f927(x104783,a915))),f857(f857(f10(f927(x104782,f927(f927(x104783,a915),f927(x104783,a915))),f927(f927(x104782,f927(x104783,a915)),f927(x104782,f927(x104783,a915))),x104781),f20(x104782,f927(x104783,a915),f927(x104783,a915))),f857(f857(f10(f927(x104782,f927(x104783,f927(a915,a915))),f927(x104782,f927(f927(x104783,a915),f927(x104783,a915))),x104781),f857(f10(f927(x104783,f927(a915,a915)),f927(f927(x104783,a915),f927(x104783,a915)),x104782),f20(x104783,a915,a915))),f857(f857(f10(f927(x104782,f927(x104783,a915)),f927(x104782,f927(x104783,f927(a915,a915))),x104781),f857(f10(f927(x104783,a915),f927(x104783,f927(a915,a915)),x104782),f857(f10(a915,f927(a915,a915),x104783),a325))),f857(f857(f9(x104781,f927(x104782,f927(x104783,x104781)),f927(x104782,f927(x104783,a915))),f857(f857(f10(f927(f927(x104783,x104781),f927(x104783,a915)),f927(f927(x104782,f927(x104783,x104781)),f927(x104782,f927(x104783,a915))),x104781),f10(f927(x104783,x104781),f927(x104783,a915),x104782)),f857(f857(f10(f927(x104781,a915),f927(f927(x104783,x104781),f927(x104783,a915)),x104781),f10(x104781,a915,x104783)),a324))),f857(f857(f9(x104782,f927(x104783,x104781),f927(x104783,x104781)),f857(f857(f10(f927(x104781,x104781),f927(f927(x104783,x104781),f927(x104783,x104781)),x104782),f10(x104781,x104781,x104783)),f857(f857(f10(x104781,f927(x104781,x104781),x104782),f80(x104781)),x104784))),x104785)))))),f857(f857(f9(x104782,f927(x104783,a915),f927(x104783,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x104783,a915),f927(x104783,a915)),x104782),f10(a915,a915,x104783)),f857(f857(f10(a915,f927(a915,a915),x104782),a325),f857(f857(f9(x104782,f927(x104782,a915),a915),f328(x104782)),x104786)))),f857(f857(f9(x104783,f927(x104783,a915),a915),f328(x104783)),x104787))))))),f857(f857(f80(x104781),f857(f857(f8(x104782,x104781),x104784),x104786)),f857(f857(f8(x104783,x104781),x104785),x104787)))
% 15.02/14.80 [9729]~P27(x97291,x97293,x97295,x97296,x97298)+~P27(x97293,x97292,x97294,x97298,x97297)+P27(x97291,x97292,f857(f72(x97293,x97292,x97291,x97294),x97295),x97296,x97297)
% 15.02/14.80 [9758]P27(x97581,x97582,x97583,x97584,x97585)+~P27(x97586,x97581,x97587,x97588,x97584)+~P27(x97586,x97582,f857(f72(x97581,x97582,x97586,x97583),x97587),x97588,x97585)
% 15.02/14.80 [9890]~P106(f857(f857(x98904,x98906),x98908))+~P106(f857(f857(x98905,x98908),x98907))+P106(f857(f857(f252(x98901,x98902,x98903,x98904,x98905),x98906),x98907))
% 15.02/14.80 [9480]~P20(x94808,x94801,x94803,x94805)+~P106(f857(f60(x94808),x94806))+E(f857(f72(x94801,x94801,x94802,f857(x94803,x94804)),f857(f72(x94801,x94801,x94802,f857(x94805,x94806)),x94807)),f857(f72(x94801,x94801,x94802,f857(x94805,x94806)),f857(f72(x94801,x94801,x94802,f857(x94803,x94804)),x94807)))
% 15.02/14.80 [9880]~P23(x98807,x98802,x98805,x98808,x98806,x98801)+~P106(f857(f60(x98802),x98804))+E(f857(x98801,f857(f857(f308(x98802),x98803),x98804)),f857(f857(x98805,f857(x98806,x98803)),f857(x98801,x98804)))
% 15.02/14.80 [9998]~P26(x99982,x99984,x99986,x99988)+~P26(x99981,x99983,x99985,x99987)+P26(f926(x99981,x99982),f926(x99983,x99984),f257(x99981,x99983,x99982,x99984,x99985,x99986),f857(f857(f253(x99981,x99982),x99987),f857(f18(f927(x99982,a915),x99981),x99988)))
% 15.02/14.80 [9666]P106(f857(f857(f328(f926(x96661,x96662)),f857(f857(f251(x96661,x96662),x96663),x96664)),f857(f857(f288(x96661,x96665,x96662),x96666),x96667)))+~P106(f857(f857(f328(f926(x96661,x96665)),f857(f857(f251(x96661,x96665),x96663),x96668)),x96666))+~P106(f857(f857(f328(f926(x96665,x96662)),f857(f857(f251(x96665,x96662),x96668),x96664)),x96667))
% 15.02/14.80 [9861]~P106(f857(f857(f234(f927(f926(x98613,x98612),a915)),x98615),f857(f857(f253(x98613,x98612),x98618),f857(f18(f927(x98612,a915),x98613),x98617))))+~P106(f857(f857(f234(f927(f926(x98611,x98613),a915)),x98614),f857(f857(f253(x98611,x98613),x98616),f857(f18(f927(x98613,a915),x98611),x98618))))+P106(f857(f857(f234(f927(f926(x98611,x98612),a915)),f857(f857(f288(x98611,x98613,x98612),x98614),x98615)),f857(f857(f253(x98611,x98612),x98616),f857(f18(f927(x98612,a915),x98611),x98617))))
% 15.02/14.80 [9914]~E(x99143,x99145)+P106(f857(f857(f328(f926(f926(x99141,x99142),f926(x99141,x99142))),f857(f857(f251(f926(x99141,x99142),f926(x99141,x99142)),f857(f857(f251(x99141,x99142),x99143),x99144)),f857(f857(f251(x99141,x99142),x99145),x99146))),f318(x99141,x99142,x99147,x99148)))+~P106(f857(f857(f328(f926(x99142,x99142)),f857(f857(f251(x99142,x99142),x99144),x99146)),x99148))
% 15.02/14.80 [10017]E(x100171,x100172)+~P106(f857(f857(f328(f926(f926(x100173,x100175),f926(x100173,x100175))),f857(f857(f251(f926(x100173,x100175),f926(x100173,x100175)),f857(f857(f251(x100173,x100175),x100171),x100176)),f857(f857(f251(x100173,x100175),x100172),x100177))),f318(x100173,x100175,x100174,x100178)))+P106(f857(f857(f328(f926(x100173,x100173)),f857(f857(f251(x100173,x100173),x100171),x100172)),x100174))
% 15.02/14.80 [10033]~P106(f857(f857(f328(f926(f926(x100331,x100335),f926(x100331,x100335))),f857(f857(f251(f926(x100331,x100335),f926(x100331,x100335)),f857(f857(f251(x100331,x100335),x100332),x100336)),f857(f857(f251(x100331,x100335),x100333),x100337))),f318(x100331,x100335,x100334,x100338)))+P106(f857(f857(f328(f926(x100331,x100331)),f857(f857(f251(x100331,x100331),x100332),x100333)),x100334))+P106(f857(f857(f328(f926(x100335,x100335)),f857(f857(f251(x100335,x100335),x100336),x100337)),x100338))
% 15.02/14.80 [9949]~P24(x99497,x99495,x99491,x99498,x99492,x99494)+~P106(f857(f60(x99495),x99496))+E(f857(f857(x99491,f857(x99492,x99493)),f857(x99494,f857(f857(f3(f927(x99495,a915)),x99496),f857(f857(f308(x99495),x99493),f189(f927(x99495,a915)))))),f857(x99494,f857(f857(f308(x99495),x99493),x99496)))
% 15.02/14.80 [9432]~P106(f857(f857(f857(x94325,x94328),x94326),x94327))+~P106(f857(f857(f328(x94321),x94328),x94324))+P106(f857(f857(f857(f857(f39(x94321,f927(x94322,f927(x94323,a915))),x94324),x94325),x94326),x94327))
% 15.02/14.80 [9651]P106(f857(f857(f857(x96511,x96512),x96513),x96514))+~P106(f857(f857(f328(x96515),x96512),x96516))+~P106(f857(f857(f857(f857(f38(x96515,f927(x96517,f927(x96518,a915))),x96516),x96511),x96513),x96514))
% 15.02/14.80 [9854]~P22(x98543,x98542,x98544,x98548,x98541)+~P106(f857(f60(x98542),x98547))+E(f857(f857(x98541,f857(f857(f20(x98542,x98543,x98543),f857(f857(f10(x98543,f927(x98543,x98543),x98542),x98544),x98545)),x98546)),x98547),f857(f857(x98544,f857(f857(x98541,x98545),x98547)),f857(f857(x98541,x98546),x98547)))
% 15.02/14.80 [10119]~E(f857(f309(x101192,x101194,x101196),x101198),x1011910)+~E(f857(f309(x101191,x101193,x101195),x101197),x101199)+E(f857(f309(f926(x101191,x101192),f926(x101193,x101194),f257(x101191,x101193,x101192,x101194,x101195,x101196)),f857(f857(f253(x101191,x101192),x101197),f857(f18(f927(x101192,a915),x101191),x101198))),f857(f857(f253(x101193,x101194),x101199),f857(f18(f927(x101194,a915),x101193),x1011910)))
% 15.02/14.80 [5072]~P45(x50721,x50722)+~P51(x50721,x50722)+~P52(x50721,x50722)+P8(x50721,x50722)
% 15.02/14.80 [5028]~P109(x50282)+~P14(x50282,x50281)+P14(x50282,f114(x50282,x50281))+E(x50281,f113(x50282))
% 15.02/14.80 [5029]~P109(x50292)+~P14(x50292,x50291)+P14(x50292,f708(x50291,x50292))+E(x50291,f113(x50292))
% 15.02/14.80 [5271]~P6(x52712)+E(f12(x52712,x52711),f36(x52712,x52711))+E(x52711,f189(f927(x52712,a915)))+~P106(f857(f60(x52712),x52711))
% 15.02/14.80 [5272]~P6(x52722)+E(f13(x52722,x52721),f37(x52722,x52721))+E(x52721,f189(f927(x52722,a915)))+~P106(f857(f60(x52722),x52721))
% 15.02/14.80 [5429]~P109(x54292)+~P14(x54292,x54291)+E(x54291,f113(x54292))+E(f857(f857(f151(x54292),f728(x54291,x54292)),f708(x54291,x54292)),x54291)
% 15.02/14.80 [6246]~P2(x62462)+E(x62461,f189(f927(x62462,a915)))+P106(f857(f857(f234(x62462),f13(x62462,x62461)),f12(x62462,x62461)))+~P106(f857(f60(x62462),x62461))
% 15.02/14.80 [6260]~P42(x62602)+~P42(x62601)+E(x62601,x62602)+~E(f857(f309(a1,a919,a104),x62601),f857(f309(a1,a919,a104),x62602))
% 15.02/14.80 [9290]~P120(x92901)+~P106(f857(f857(f328(x92901),x92902),f109(x92901)))+P106(f857(f857(f235(x92901),f857(f857(f79(x92901),f857(f857(f79(x92901),f77(x92901)),x92902)),x92902)),f2(x92901)))+~P106(f857(f857(f235(x92901),x92902),f2(x92901)))
% 15.02/14.80 [9533]~P120(x95331)+~P106(f857(f857(f328(x95331),x95332),f109(x95331)))+~P106(f857(f857(f235(x95331),f857(f857(f79(x95331),f857(f857(f79(x95331),f77(x95331)),x95332)),x95332)),f2(x95331)))+P106(f857(f857(f235(x95331),x95332),f2(x95331)))
% 15.02/14.80 [5087]~P116(x50872)+~P147(x50872)+E(x50871,f2(a919))+E(f857(f857(f243(x50872),f2(x50872)),x50871),f2(x50872))
% 15.02/14.80 [5090]~P116(x50901)+~P147(x50901)+~E(x50902,f2(a919))+E(f857(f857(f243(x50901),f2(x50901)),x50902),f77(x50901))
% 15.02/14.80 [5257]~P144(x52572)+E(x52571,f77(x52572))+E(x52571,f857(f78(x52572),f77(x52572)))+~E(f857(f857(f80(x52572),x52571),x52571),f77(x52572))
% 15.02/14.80 [5510]~P91(x55102)+E(x55101,f2(x55102))+E(f81(x55102,x55101),f857(f78(x55102),f77(x55102)))+P106(f857(f857(f235(x55102),f2(x55102)),x55101))
% 15.02/14.80 [5753]~P91(x57532)+E(f81(x57532,x57531),f77(x57532))+E(x57531,f2(x57532))+~P106(f857(f857(f235(x57532),f2(x57532)),x57531))
% 15.02/14.80 [5762]E(x57621,x57622)+~E(f857(f103(a919),x57621),f857(f103(a919),x57622))+P106(f857(a194,f857(f103(a1),x57622)))+P106(f857(a194,f857(f103(a1),x57621)))
% 15.02/14.80 [5812]~P93(x58121)+~E(x58122,f2(x58121))+E(f857(f857(f79(x58121),x58122),x58122),f2(x58121))+~P106(f857(f857(f328(x58121),x58122),f109(x58121)))
% 15.02/14.80 [5851]E(x58511,f2(a1))+~E(f857(f857(f35(a1),x58512),x58511),f2(a1))+P106(f857(f857(f235(a1),x58511),x58512))+P106(f857(f857(f235(a1),x58512),x58511))
% 15.02/14.80 [5881]E(x58811,f2(a1))+~E(f857(f857(f35(a1),x58812),x58811),f2(a1))+P106(f857(f857(f234(a1),x58812),f2(a1)))+P106(f857(f857(f235(a1),x58812),x58811))
% 15.02/14.80 [5915]E(x59151,f2(a1))+~E(f857(f857(f35(a1),x59152),x59151),f2(a1))+P106(f857(f857(f234(a1),f2(a1)),x59152))+P106(f857(f857(f235(a1),x59151),x59152))
% 15.02/14.80 [5950]~P93(x59502)+E(x59501,f2(x59502))+~E(f857(f857(f79(x59502),x59501),x59501),f2(x59502))+~P106(f857(f857(f328(x59502),x59501),f109(x59502)))
% 15.02/14.80 [6012]E(f857(f103(a919),x60121),f857(f103(a919),x60122))+~E(f857(f103(a1),x60122),f2(a1))+P106(f857(a194,f857(f103(a1),x60122)))+~P106(f857(a194,f857(f103(a1),x60121)))
% 15.02/14.80 [6041]~E(f857(f103(a919),x60412),f857(f103(a919),x60411))+E(f857(f103(a1),x60411),f2(a1))+P106(f857(a194,f857(f103(a1),x60411)))+~P106(f857(a194,f857(f103(a1),x60412)))
% 15.02/14.80 [6051]~P109(x60512)+E(x60511,f189(f927(x60512,a915)))+~P106(f857(f60(x60512),x60511))+P106(f857(f857(f328(x60512),f16(x60512,x60511)),x60511))
% 15.02/14.80 [6052]~P109(x60522)+E(x60521,f189(f927(x60522,a915)))+~P106(f857(f60(x60522),x60521))+P106(f857(f857(f328(x60522),f17(x60522,x60521)),x60521))
% 15.02/14.80 [6223]~P120(x62231)+~P94(x62231)+P106(f857(f857(f234(x62231),f2(x62231)),f857(f103(x62231),x62232)))+~P106(f857(f857(f234(a1),a82),x62232))
% 15.02/14.80 [6224]~P120(x62241)+~P94(x62241)+P106(f857(f857(f235(x62241),f2(x62241)),f857(f103(x62241),x62242)))+~P106(f857(f857(f235(a1),a82),x62242))
% 15.02/14.80 [6245]~P120(x62451)+~P94(x62451)+E(f857(f75(x62451),f857(f103(x62451),x62452)),f857(f103(x62451),x62452))+P106(f857(f857(f235(x62451),f857(f103(x62451),x62452)),f2(x62451)))
% 15.02/14.80 [6284]E(x62841,x62842)+~E(f857(a104,x62841),f857(a104,x62842))+~P106(f857(f857(f234(a1),f2(a1)),x62842))+~P106(f857(f857(f234(a1),f2(a1)),x62841))
% 15.02/14.80 [6481]~P94(x64812)+~P120(x64812)+~P106(f857(f857(f234(x64812),f2(x64812)),f857(f103(x64812),x64811)))+P106(f857(f857(f234(a1),a82),x64811))
% 15.02/14.80 [6482]~P94(x64822)+~P120(x64822)+~P106(f857(f857(f235(x64822),f2(x64822)),f857(f103(x64822),x64821)))+P106(f857(f857(f235(a1),a82),x64821))
% 15.02/14.80 [6487]~P120(x64871)+~P94(x64871)+P106(f857(f857(f234(x64871),f857(f103(x64871),x64872)),f2(x64871)))+~P106(f857(f857(f234(a1),x64872),a82))
% 15.02/14.80 [6488]~P120(x64881)+~P94(x64881)+P106(f857(f857(f235(x64881),f857(f103(x64881),x64882)),f2(x64881)))+~P106(f857(f857(f235(a1),x64882),a82))
% 15.02/14.80 [6807]~P94(x68072)+~P120(x68072)+~P106(f857(f857(f234(x68072),f857(f103(x68072),x68071)),f2(x68072)))+P106(f857(f857(f234(a1),x68071),a82))
% 15.02/14.80 [6808]~P94(x68082)+~P120(x68082)+~P106(f857(f857(f235(x68082),f857(f103(x68082),x68081)),f2(x68082)))+P106(f857(f857(f235(a1),x68081),a82))
% 15.02/14.80 [6899]~P120(x68991)+~P94(x68991)+E(f857(f75(x68991),f857(f103(x68991),x68992)),f857(f78(x68991),f857(f103(x68991),x68992)))+~P106(f857(f857(f235(x68991),f857(f103(x68991),x68992)),f2(x68991)))
% 15.02/14.80 [6917]E(f857(f103(a919),x69171),f857(f103(a919),x69172))+~E(f857(f103(a1),x69172),f2(a1))+~P106(f857(f857(f234(a1),f857(f103(a1),x69171)),f2(a1)))+~P106(f857(a194,f857(f103(a1),x69171)))
% 15.02/14.80 [7797]~P109(x77972)+E(x77971,f189(f927(x77972,a915)))+~P106(f857(f60(x77972),x77971))+P106(f857(f857(f234(x77972),f14(x77972,f188(x77972),x77971)),f15(x77972,f233(x77972),x77971)))
% 15.02/14.80 [8114]~P7(x81141)+~P42(x81142)+P106(f857(f857(f328(a1),x81141),x81142))+~P106(f857(f857(f328(a919),f857(a104,x81141)),f857(f309(a1,a919,a104),x81142)))
% 15.02/14.80 [6047]~P143(x60472)+E(x60471,f2(a1))+E(f857(f78(x60472),f857(f102(x60472),f857(f78(a1),x60471))),f857(f102(x60472),x60471))+~P106(f857(f857(f235(a1),x60471),f2(a1)))
% 15.02/14.80 [6125]~P93(x61251)+~P94(x61251)+~P29(x61251,f857(f103(x61251),x61252))+P29(x61251,f857(f103(x61251),f857(f857(f79(a1),x61252),x61252)))
% 15.02/14.80 [6470]~P78(x64702)+E(x64701,f189(f927(x64702,a915)))+E(f17(x64702,f857(f309(x64702,x64702,f78(x64702)),x64701)),f857(f78(x64702),f16(x64702,x64701)))+~P106(f857(f60(x64702),x64701))
% 15.02/14.80 [6471]~P78(x64712)+E(x64711,f189(f927(x64712,a915)))+E(f16(x64712,f857(f309(x64712,x64712,f78(x64712)),x64711)),f857(f78(x64712),f17(x64712,x64711)))+~P106(f857(f60(x64712),x64711))
% 15.02/14.80 [6504]~P93(x65041)+~P94(x65041)+P29(x65041,f857(f103(x65041),x65042))+~P29(x65041,f857(f103(x65041),f857(f857(f79(a1),x65042),x65042)))
% 15.02/14.80 [6599]E(x65991,f2(a1))+E(f857(a50,f49(f857(f78(a1),x65991),f857(f78(a1),x65992))),f45(x65991,x65992))+P106(f857(f857(f234(a1),f2(a1)),x65992))+~P106(f857(f857(f234(a1),f2(a1)),x65991))
% 15.02/14.80 [8893]~P42(x88932)+~P42(x88931)+P106(f857(f857(f235(f927(a919,a915)),f857(f309(a1,a919,a104),x88931)),f857(f309(a1,a919,a104),x88932)))+~P106(f857(f857(f235(f927(a1,a915)),x88931),x88932))
% 15.02/14.80 [9124]~E(f733(x91242,x91241),f731(x91242,x91241))+~P106(f857(f137(x91241),f732(x91242,x91241)))+~P106(f857(f137(f920(x91241)),x91242))+P106(f857(f137(x91241),f857(f142(f920(x91241),f920(x91241),f134(x91241),f113(x91241)),x91242)))
% 15.02/14.80 [9210]~P42(x92102)+~P42(x92101)+~P106(f857(f857(f234(f927(a919,a915)),f857(f309(a1,a919,a104),x92101)),f857(f309(a1,a919,a104),x92102)))+P106(f857(f857(f234(f927(a1,a915)),x92101),x92102))
% 15.02/14.80 [9211]~P42(x92112)+~P42(x92111)+~P106(f857(f857(f235(f927(a919,a915)),f857(f309(a1,a919,a104),x92111)),f857(f309(a1,a919,a104),x92112)))+P106(f857(f857(f235(f927(a1,a915)),x92111),x92112))
% 15.02/14.80 [9217]~E(f733(x92172,x92171),f731(x92172,x92171))+~P106(f857(f137(f920(x92171)),x92172))+P106(f857(f137(x92171),f857(f142(f920(x92171),f920(x92171),f134(x92171),f113(x92171)),x92172)))+P106(f857(f857(f328(f920(x92171)),f732(x92172,x92171)),f857(f172(f920(x92171)),x92172)))
% 15.02/14.80 [9258]~P106(f857(f137(x92581),f732(x92582,x92581)))+~P106(f857(f137(f920(x92581)),x92582))+P106(f857(f137(x92581),f857(f142(f920(x92581),f920(x92581),f134(x92581),f113(x92581)),x92582)))+P106(f857(f857(f328(f920(x92581)),f731(x92582,x92581)),f857(f172(f920(x92581)),x92582)))
% 15.02/14.80 [9259]~P106(f857(f137(x92591),f732(x92592,x92591)))+~P106(f857(f137(f920(x92591)),x92592))+P106(f857(f137(x92591),f857(f142(f920(x92591),f920(x92591),f134(x92591),f113(x92591)),x92592)))+P106(f857(f857(f328(f920(x92591)),f733(x92592,x92591)),f857(f172(f920(x92591)),x92592)))
% 15.02/14.80 [9336]~P106(f857(f137(f920(x93361)),x93362))+P106(f857(f137(x93361),f857(f142(f920(x93361),f920(x93361),f134(x93361),f113(x93361)),x93362)))+P106(f857(f857(f328(f920(x93361)),f731(x93362,x93361)),f857(f172(f920(x93361)),x93362)))+P106(f857(f857(f328(f920(x93361)),f732(x93362,x93361)),f857(f172(f920(x93361)),x93362)))
% 15.02/14.80 [9337]~P106(f857(f137(f920(x93371)),x93372))+P106(f857(f137(x93371),f857(f142(f920(x93371),f920(x93371),f134(x93371),f113(x93371)),x93372)))+P106(f857(f857(f328(f920(x93371)),f733(x93372,x93371)),f857(f172(f920(x93371)),x93372)))+P106(f857(f857(f328(f920(x93371)),f732(x93372,x93371)),f857(f172(f920(x93371)),x93372)))
% 15.02/14.80 [9351]~E(f857(f857(f101(f927(x93511,a915)),f857(f172(x93511),f731(x93512,x93511))),f857(f172(x93511),f733(x93512,x93511))),f189(f927(x93511,a915)))+~P106(f857(f137(x93511),f732(x93512,x93511)))+~P106(f857(f137(f920(x93511)),x93512))+P106(f857(f137(x93511),f857(f142(f920(x93511),f920(x93511),f134(x93511),f113(x93511)),x93512)))
% 15.02/14.80 [9413]~E(f857(f857(f101(f927(x94131,a915)),f857(f172(x94131),f731(x94132,x94131))),f857(f172(x94131),f733(x94132,x94131))),f189(f927(x94131,a915)))+~P106(f857(f137(f920(x94131)),x94132))+P106(f857(f137(x94131),f857(f142(f920(x94131),f920(x94131),f134(x94131),f113(x94131)),x94132)))+P106(f857(f857(f328(f920(x94131)),f732(x94132,x94131)),f857(f172(f920(x94131)),x94132)))
% 15.02/14.80 [9697]E(x96971,f2(a1))+E(x96972,f2(a1))+E(f857(f857(f85(a1,f926(a1,a1)),f857(f857(a218,x96972),x96971)),f857(f857(f20(a1,a1,f926(a1,a1)),f857(f857(f10(a1,f927(a1,f926(a1,a1)),a1),f251(a1,a1)),f857(f35(a1),x96972))),f857(f35(a1),x96971))),f216(x96972,x96971))+P106(f857(f857(f235(a1),x96971),f2(a1)))
% 15.02/14.80 [8440]~P94(x84402)+~P120(x84402)+~P106(f857(f857(f234(x84402),f857(f103(x84402),x84401)),f77(x84402)))+P106(f857(f857(f234(a1),x84401),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))
% 15.02/14.80 [8441]~P94(x84412)+~P120(x84412)+~P106(f857(f857(f235(x84412),f857(f103(x84412),x84411)),f77(x84412)))+P106(f857(f857(f235(a1),x84411),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))
% 15.02/14.80 [8709]~P120(x87091)+~P94(x87091)+P106(f857(f857(f234(x87091),f857(f103(x87091),x87092)),f77(x87091)))+~P106(f857(f857(f234(a1),x87092),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))
% 15.02/14.80 [8710]~P120(x87101)+~P94(x87101)+P106(f857(f857(f235(x87101),f857(f103(x87101),x87102)),f77(x87101)))+~P106(f857(f857(f235(a1),x87102),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))
% 15.02/14.80 [8921]~P94(x89212)+~P120(x89212)+~P106(f857(f857(f234(x89212),f77(x89212)),f857(f103(x89212),x89211)))+P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),x89211))
% 15.02/14.80 [8922]~P94(x89222)+~P120(x89222)+~P106(f857(f857(f235(x89222),f77(x89222)),f857(f103(x89222),x89221)))+P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),x89221))
% 15.02/14.80 [9296]~P120(x92961)+~P94(x92961)+P106(f857(f857(f234(x92961),f77(x92961)),f857(f103(x92961),x92962)))+~P106(f857(f857(f234(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),x92962))
% 15.02/14.80 [9297]~P120(x92971)+~P94(x92971)+P106(f857(f857(f235(x92971),f77(x92971)),f857(f103(x92971),x92972)))+~P106(f857(f857(f235(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),x92972))
% 15.02/14.80 [9827]~P144(x98272)+E(x98271,f77(x98272))+E(x98271,f857(f78(x98272),f77(x98272)))+~E(f857(f857(f243(x98272),x98271),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f77(x98272))
% 15.02/14.80 [10095]~P67(x100951)+~P94(x100951)+~P106(f857(f857(f235(x100951),f2(x100951)),x100952))+P106(f857(f857(f235(x100951),f2(x100951)),f857(f857(f290(x100951),x100952),f857(f103(x100951),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.80 [10149]~P67(x101491)+~P94(x101491)+P106(f857(f857(f235(x101491),f2(x101491)),x101492))+~P106(f857(f857(f235(x101491),f2(x101491)),f857(f857(f290(x101491),x101492),f857(f103(x101491),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.80 [10445]~P143(x104452)+E(x104451,f2(a1))+P106(f857(f857(f235(a1),x104451),f2(a1)))+E(f857(f857(f256(a1,a1,x104452),f857(f857(f9(a1,f927(a1,f927(x104452,x104452)),f927(a1,x104452)),f857(f857(f10(f927(f927(x104452,x104452),x104452),f927(f927(a1,f927(x104452,x104452)),f927(a1,x104452)),a1),f10(f927(x104452,x104452),x104452,a1)),f857(f857(f10(x104452,f927(f927(x104452,x104452),x104452),a1),f85(x104452,x104452)),f102(x104452)))),f857(f857(f9(a1,f927(x104452,x104452),f927(x104452,x104452)),f857(f857(f10(f927(x104452,f927(x104452,x104452)),f927(f927(x104452,x104452),f927(x104452,x104452)),a1),f20(x104452,x104452,x104452)),f857(f857(f9(a1,f927(x104452,x104452),f927(x104452,f927(x104452,x104452))),f857(f857(f10(f927(x104452,f927(x104452,x104452)),f927(f927(x104452,x104452),f927(x104452,f927(x104452,x104452))),a1),f10(x104452,f927(x104452,x104452),x104452)),f857(f857(f10(a915,f927(x104452,f927(x104452,x104452)),a1),f96(x104452)),f857(f857(f9(a1,a1,a915),a324),f2(a1))))),f857(f857(f20(x104452,x104452,x104452),f79(x104452)),f7(x104452))))),f857(f857(f9(x104452,x104452,x104452),f857(f857(f10(x104452,f927(x104452,x104452),x104452),f79(x104452)),f857(f857(f20(x104452,x104452,x104452),f79(x104452)),f7(x104452)))),f77(x104452))))),f45(x104451,f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f102(x104452),x104451))
% 15.02/14.80 [5519]~P40(x55191,x55193)+~P53(x55191,x55193)+~P54(x55191,x55192,x55193)+P9(x55191,x55192,x55193)
% 15.02/14.80 [5056]~P93(x50563)+~P94(x50563)+E(x50561,x50562)+~E(f857(f103(x50563),x50561),f857(f103(x50563),x50562))
% 15.02/14.80 [5529]~P51(x55291,x55292)+~P52(x55291,x55292)+P16(x55291,x55292)+~P106(f857(f857(x55292,x55293),x55293))
% 15.02/14.80 [6027]P16(x60272,x60271)+E(f857(x60271,f806(x60271)),f857(x60271,f807(x60271)))+P106(f857(f857(x60271,f806(x60271)),f807(x60271)))+~P106(f857(f857(x60271,x60273),x60273))
% 15.02/14.80 [6233]~P106(f857(x62331,x62332))+~P106(f857(x62331,x62333))+~P106(f857(f857(f234(a919),x62333),f905(x62332,x62331)))+P106(f857(x62331,f2(a919)))
% 15.02/14.80 [6304]P16(x63041,x63042)+P106(f857(f857(x63042,f806(x63042)),f806(x63042)))+P106(f857(f857(x63042,f806(x63042)),f807(x63042)))+~P106(f857(f857(x63042,x63043),x63043))
% 15.02/14.80 [6305]P16(x63051,x63052)+P106(f857(f857(x63052,f806(x63052)),f807(x63052)))+P106(f857(f857(x63052,f807(x63052)),f807(x63052)))+~P106(f857(f857(x63052,x63053),x63053))
% 15.02/14.80 [6661]P148(x66612,x66611,x66613)+E(x66611,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f863(x66613,x66611,x66612)))+P106(f857(f857(f235(a1),x66611),f2(a1)))
% 15.02/14.80 [6662]P149(x66622,x66621,x66623)+E(x66621,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f868(x66623,x66621,x66622)))+P106(f857(f857(f235(a1),x66621),f2(a1)))
% 15.02/14.80 [6788]P148(x67881,x67882,x67883)+~P106(f857(x67881,x67883))+P106(f857(f857(f234(a1),f2(a1)),f863(x67883,x67882,x67881)))+P106(f857(f857(f235(a1),x67882),f2(a1)))
% 15.02/14.80 [6813]P149(x68131,x68132,x68133)+P106(f857(f857(f234(a1),f2(a1)),f868(x68133,x68132,x68131)))+~P106(f857(x68131,f2(a1)))+P106(f857(f857(f235(a1),x68132),f2(a1)))
% 15.02/14.80 [6843]P148(x68432,x68431,x68433)+E(x68431,f2(a1))+~P106(f857(x68432,f863(x68433,x68431,x68432)))+P106(f857(f857(f235(a1),x68431),f2(a1)))
% 15.02/14.80 [6844]P149(x68442,x68441,x68443)+E(x68441,f2(a1))+~P106(f857(x68442,f869(x68443,x68441,x68442)))+P106(f857(f857(f235(a1),x68441),f2(a1)))
% 15.02/14.80 [6945]~P109(x69451)+~P6(x69451)+~P106(f857(f857(f235(x69451),x69452),f36(x69451,x69453)))+P106(f857(f857(f235(x69451),x69452),f876(x69453,x69452,x69451)))
% 15.02/14.80 [6955]P148(x69551,x69552,x69553)+~P106(f857(x69551,x69553))+~P106(f857(x69551,f863(x69553,x69552,x69551)))+P106(f857(f857(f235(a1),x69552),f2(a1)))
% 15.02/14.80 [6985]P149(x69851,x69852,x69853)+~P106(f857(x69851,f869(x69853,x69852,x69851)))+~P106(f857(x69851,f2(a1)))+P106(f857(f857(f235(a1),x69852),f2(a1)))
% 15.02/14.80 [7235]P148(x72352,x72351,x72353)+E(x72351,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f863(x72353,x72351,x72352)))+P106(f857(f857(f235(a1),x72351),f862(x72353,x72351,x72352)))
% 15.02/14.80 [7236]P149(x72362,x72361,x72363)+E(x72361,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f868(x72363,x72361,x72362)))+P106(f857(f857(f235(a1),x72361),f867(x72363,x72361,x72362)))
% 15.02/14.80 [7356]P148(x73561,x73562,x73563)+~P106(f857(x73561,x73563))+P106(f857(f857(f234(a1),f2(a1)),f863(x73563,x73562,x73561)))+P106(f857(f857(f235(a1),x73562),f862(x73563,x73562,x73561)))
% 15.02/14.80 [7377]P149(x73771,x73772,x73773)+P106(f857(f857(f234(a1),f2(a1)),f868(x73773,x73772,x73771)))+P106(f857(f857(f235(a1),x73772),f867(x73773,x73772,x73771)))+~P106(f857(x73771,f2(a1)))
% 15.02/14.80 [7410]P148(x74102,x74101,x74103)+E(x74101,f2(a1))+~P106(f857(x74102,f863(x74103,x74101,x74102)))+P106(f857(f857(f235(a1),x74101),f862(x74103,x74101,x74102)))
% 15.02/14.80 [7411]P149(x74112,x74111,x74113)+E(x74111,f2(a1))+~P106(f857(x74112,f869(x74113,x74111,x74112)))+P106(f857(f857(f235(a1),x74111),f867(x74113,x74111,x74112)))
% 15.02/14.80 [7455]P148(x74552,x74551,x74553)+E(x74551,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f863(x74553,x74551,x74552)))+~P106(f857(x74552,f862(x74553,x74551,x74552)))
% 15.02/14.80 [7456]P149(x74562,x74561,x74563)+E(x74561,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f868(x74563,x74561,x74562)))+~P106(f857(x74562,f870(x74563,x74561,x74562)))
% 15.02/14.80 [7550]P148(x75501,x75502,x75503)+~P106(f857(x75501,x75503))+~P106(f857(x75501,f863(x75503,x75502,x75501)))+P106(f857(f857(f235(a1),x75502),f862(x75503,x75502,x75501)))
% 15.02/14.80 [7565]P149(x75651,x75652,x75653)+~P106(f857(x75651,f869(x75653,x75652,x75651)))+P106(f857(f857(f235(a1),x75652),f867(x75653,x75652,x75651)))+~P106(f857(x75651,f2(a1)))
% 15.02/14.80 [7568]P148(x75681,x75682,x75683)+~P106(f857(x75681,x75683))+P106(f857(f857(f234(a1),f2(a1)),f863(x75683,x75682,x75681)))+~P106(f857(x75681,f862(x75683,x75682,x75681)))
% 15.02/14.80 [7585]P149(x75851,x75852,x75853)+P106(f857(f857(f234(a1),f2(a1)),f868(x75853,x75852,x75851)))+~P106(f857(x75851,f870(x75853,x75852,x75851)))+~P106(f857(x75851,f2(a1)))
% 15.02/14.80 [7607]P148(x76072,x76071,x76073)+E(x76071,f2(a1))+~P106(f857(x76072,f863(x76073,x76071,x76072)))+~P106(f857(x76072,f862(x76073,x76071,x76072)))
% 15.02/14.80 [7608]P149(x76082,x76081,x76083)+E(x76081,f2(a1))+~P106(f857(x76082,f869(x76083,x76081,x76082)))+~P106(f857(x76082,f870(x76083,x76081,x76082)))
% 15.02/14.80 [7694]P148(x76941,x76942,x76943)+~P106(f857(x76941,x76943))+~P106(f857(x76941,f863(x76943,x76942,x76941)))+~P106(f857(x76941,f862(x76943,x76942,x76941)))
% 15.02/14.80 [7711]P149(x77111,x77112,x77113)+~P106(f857(x77111,f869(x77113,x77112,x77111)))+~P106(f857(x77111,f870(x77113,x77112,x77111)))+~P106(f857(x77111,f2(a1)))
% 15.02/14.80 [7756]P148(x77562,x77561,x77563)+E(x77561,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f863(x77563,x77561,x77562)))+P106(f857(f857(f234(a1),f862(x77563,x77561,x77562)),f2(a1)))
% 15.02/14.80 [7757]P149(x77572,x77571,x77573)+E(x77571,f2(a1))+P106(f857(f857(f234(a1),f2(a1)),f868(x77573,x77571,x77572)))+P106(f857(f857(f234(a1),f867(x77573,x77571,x77572)),f2(a1)))
% 15.02/14.80 [7758]~P89(x77581)+~P106(f857(f857(f234(x77581),x77583),f2(x77581)))+~P106(f857(f857(f234(x77581),x77582),f2(x77581)))+P106(f857(f857(f234(x77581),f857(f857(f79(x77581),x77582),x77583)),f2(x77581)))
% 15.02/14.80 [7759]~P143(x77591)+~P106(f857(f857(f328(x77591),x77593),f109(x77591)))+~P106(f857(f857(f328(x77591),x77592),f109(x77591)))+P106(f857(f857(f328(x77591),f857(f857(f3(x77591),x77592),x77593)),f109(x77591)))
% 15.02/14.80 [7760]~P143(x77601)+~P106(f857(f857(f328(x77601),x77603),f109(x77601)))+~P106(f857(f857(f328(x77601),x77602),f109(x77601)))+P106(f857(f857(f328(x77601),f857(f857(f80(x77601),x77602),x77603)),f109(x77601)))
% 15.02/14.80 [7761]~P146(x77611)+~P106(f857(f857(f328(x77611),x77613),f186(x77611)))+~P106(f857(f857(f328(x77611),x77612),f186(x77611)))+P106(f857(f857(f328(x77611),f857(f857(f80(x77611),x77612),x77613)),f186(x77611)))
% 15.02/14.80 [7762]~P143(x77621)+~P106(f857(f857(f328(x77621),x77623),f109(x77621)))+~P106(f857(f857(f328(x77621),x77622),f109(x77621)))+P106(f857(f857(f328(x77621),f857(f857(f79(x77621),x77622),x77623)),f109(x77621)))
% 15.02/14.80 [7763]~P146(x77631)+~P106(f857(f857(f328(x77631),x77633),f186(x77631)))+~P106(f857(f857(f328(x77631),x77632),f186(x77631)))+P106(f857(f857(f328(x77631),f857(f857(f79(x77631),x77632),x77633)),f186(x77631)))
% 15.02/14.80 [7764]~P89(x77641)+~P106(f857(f857(f234(x77641),x77643),f2(x77641)))+~P106(f857(f857(f235(x77641),x77642),f2(x77641)))+P106(f857(f857(f235(x77641),f857(f857(f79(x77641),x77642),x77643)),f2(x77641)))
% 15.02/14.80 [7765]~P89(x77651)+~P106(f857(f857(f234(x77651),x77652),f2(x77651)))+~P106(f857(f857(f235(x77651),x77653),f2(x77651)))+P106(f857(f857(f235(x77651),f857(f857(f79(x77651),x77652),x77653)),f2(x77651)))
% 15.02/14.80 [7766]~P89(x77661)+~P106(f857(f857(f235(x77661),x77663),f2(x77661)))+~P106(f857(f857(f235(x77661),x77662),f2(x77661)))+P106(f857(f857(f235(x77661),f857(f857(f79(x77661),x77662),x77663)),f2(x77661)))
% 15.02/14.80 [7793]P148(x77933,x77931,x77932)+E(x77931,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x77931),f864(x77932,x77931,x77933))),f863(x77932,x77931,x77933)),x77932)+P106(f857(f857(f235(a1),x77931),f2(a1)))
% 15.02/14.80 [7794]P149(x77943,x77941,x77942)+E(x77941,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x77941),f869(x77942,x77941,x77943))),f868(x77942,x77941,x77943)),x77942)+P106(f857(f857(f235(a1),x77941),f2(a1)))
% 15.02/14.80 [7877]P148(x78771,x78772,x78773)+~P106(f857(x78771,x78773))+P106(f857(f857(f234(a1),f2(a1)),f863(x78773,x78772,x78771)))+P106(f857(f857(f234(a1),f862(x78773,x78772,x78771)),f2(a1)))
% 15.02/14.80 [7907]P149(x79071,x79072,x79073)+P106(f857(f857(f234(a1),f2(a1)),f868(x79073,x79072,x79071)))+~P106(f857(x79071,f2(a1)))+P106(f857(f857(f234(a1),f867(x79073,x79072,x79071)),f2(a1)))
% 15.02/14.80 [7916]P148(x79163,x79161,x79162)+~P106(f857(x79163,x79162))+E(f857(f857(f79(a1),f857(f857(f80(a1),x79161),f864(x79162,x79161,x79163))),f863(x79162,x79161,x79163)),x79162)+P106(f857(f857(f235(a1),x79161),f2(a1)))
% 15.02/14.80 [7922]P148(x79222,x79221,x79223)+E(x79221,f2(a1))+~P106(f857(x79222,f863(x79223,x79221,x79222)))+P106(f857(f857(f234(a1),f862(x79223,x79221,x79222)),f2(a1)))
% 15.02/14.80 [7923]P149(x79232,x79231,x79233)+E(x79231,f2(a1))+~P106(f857(x79232,f869(x79233,x79231,x79232)))+P106(f857(f857(f234(a1),f867(x79233,x79231,x79232)),f2(a1)))
% 15.02/14.80 [7928]P149(x79283,x79281,x79282)+E(f857(f857(f79(a1),f857(f857(f80(a1),x79281),f869(x79282,x79281,x79283))),f868(x79282,x79281,x79283)),x79282)+~P106(f857(x79283,f2(a1)))+P106(f857(f857(f235(a1),x79281),f2(a1)))
% 15.02/14.80 [7984]P148(x79841,x79842,x79843)+~P106(f857(x79841,x79843))+~P106(f857(x79841,f863(x79843,x79842,x79841)))+P106(f857(f857(f234(a1),f862(x79843,x79842,x79841)),f2(a1)))
% 15.02/14.80 [7988]P149(x79881,x79882,x79883)+~P106(f857(x79881,f869(x79883,x79882,x79881)))+~P106(f857(x79881,f2(a1)))+P106(f857(f857(f234(a1),f867(x79883,x79882,x79881)),f2(a1)))
% 15.02/14.80 [8055]~P129(x80551)+~P106(f857(f857(f234(x80551),f857(f857(f80(x80551),x80553),x80552)),f2(x80551)))+P106(f857(f857(f234(x80551),x80552),f2(x80551)))+P106(f857(f857(f234(x80551),x80553),f2(x80551)))
% 15.02/14.80 [8056]~P67(x80561)+~P106(f857(f857(f234(x80561),f857(f857(f290(x80561),x80563),x80562)),f2(x80561)))+P106(f857(f857(f234(x80561),x80562),f2(x80561)))+P106(f857(f857(f234(x80561),x80563),f2(x80561)))
% 15.02/14.80 [8057]~P67(x80571)+~P106(f857(f857(f235(x80571),f857(f857(f290(x80571),x80573),x80572)),f2(x80571)))+P106(f857(f857(f235(x80571),x80572),f2(x80571)))+P106(f857(f857(f235(x80571),x80573),f2(x80571)))
% 15.02/14.80 [8170]P148(x81703,x81701,x81702)+E(x81701,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x81701),f864(x81702,x81701,x81703))),f863(x81702,x81701,x81703)),x81702)+P106(f857(f857(f235(a1),x81701),f862(x81702,x81701,x81703)))
% 15.02/14.80 [8171]P149(x81713,x81711,x81712)+E(x81711,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x81711),f869(x81712,x81711,x81713))),f868(x81712,x81711,x81713)),x81712)+P106(f857(f857(f235(a1),x81711),f867(x81712,x81711,x81713)))
% 15.02/14.80 [8184]P148(x81843,x81841,x81842)+E(x81841,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x81841),f865(x81842,x81841,x81843))),f862(x81842,x81841,x81843)),x81842)+P106(f857(f857(f234(a1),f2(a1)),f863(x81842,x81841,x81843)))
% 15.02/14.80 [8185]P149(x81853,x81851,x81852)+E(x81851,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x81851),f870(x81852,x81851,x81853))),f867(x81852,x81851,x81853)),x81852)+P106(f857(f857(f234(a1),f2(a1)),f868(x81852,x81851,x81853)))
% 15.02/14.80 [8227]P148(x82273,x82271,x82272)+~P106(f857(x82273,x82272))+E(f857(f857(f79(a1),f857(f857(f80(a1),x82271),f864(x82272,x82271,x82273))),f863(x82272,x82271,x82273)),x82272)+P106(f857(f857(f235(a1),x82271),f862(x82272,x82271,x82273)))
% 15.02/14.80 [8236]P149(x82363,x82361,x82362)+E(f857(f857(f79(a1),f857(f857(f80(a1),x82361),f869(x82362,x82361,x82363))),f868(x82362,x82361,x82363)),x82362)+P106(f857(f857(f235(a1),x82361),f867(x82362,x82361,x82363)))+~P106(f857(x82363,f2(a1)))
% 15.02/14.80 [8242]P148(x82423,x82421,x82422)+~P106(f857(x82423,x82422))+E(f857(f857(f79(a1),f857(f857(f80(a1),x82421),f865(x82422,x82421,x82423))),f862(x82422,x82421,x82423)),x82422)+P106(f857(f857(f234(a1),f2(a1)),f863(x82422,x82421,x82423)))
% 15.02/14.80 [8248]P149(x82483,x82481,x82482)+E(f857(f857(f79(a1),f857(f857(f80(a1),x82481),f870(x82482,x82481,x82483))),f867(x82482,x82481,x82483)),x82482)+P106(f857(f857(f234(a1),f2(a1)),f868(x82482,x82481,x82483)))+~P106(f857(x82483,f2(a1)))
% 15.02/14.80 [8259]P148(x82593,x82591,x82592)+E(x82591,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x82591),f864(x82592,x82591,x82593))),f863(x82592,x82591,x82593)),x82592)+~P106(f857(x82593,f862(x82592,x82591,x82593)))
% 15.02/14.80 [8260]P149(x82603,x82601,x82602)+E(x82601,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x82601),f869(x82602,x82601,x82603))),f868(x82602,x82601,x82603)),x82602)+~P106(f857(x82603,f870(x82602,x82601,x82603)))
% 15.02/14.80 [8261]P148(x82613,x82611,x82612)+E(x82611,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x82611),f865(x82612,x82611,x82613))),f862(x82612,x82611,x82613)),x82612)+~P106(f857(x82613,f863(x82612,x82611,x82613)))
% 15.02/14.80 [8262]P149(x82623,x82621,x82622)+E(x82621,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x82621),f870(x82622,x82621,x82623))),f867(x82622,x82621,x82623)),x82622)+~P106(f857(x82623,f869(x82622,x82621,x82623)))
% 15.02/14.80 [8320]P148(x83203,x83201,x83202)+~P106(f857(x83203,x83202))+E(f857(f857(f79(a1),f857(f857(f80(a1),x83201),f864(x83202,x83201,x83203))),f863(x83202,x83201,x83203)),x83202)+~P106(f857(x83203,f862(x83202,x83201,x83203)))
% 15.02/14.80 [8321]P148(x83213,x83211,x83212)+~P106(f857(x83213,x83212))+E(f857(f857(f79(a1),f857(f857(f80(a1),x83211),f865(x83212,x83211,x83213))),f862(x83212,x83211,x83213)),x83212)+~P106(f857(x83213,f863(x83212,x83211,x83213)))
% 15.02/14.80 [8334]P149(x83343,x83341,x83342)+E(f857(f857(f79(a1),f857(f857(f80(a1),x83341),f869(x83342,x83341,x83343))),f868(x83342,x83341,x83343)),x83342)+~P106(f857(x83343,f870(x83342,x83341,x83343)))+~P106(f857(x83343,f2(a1)))
% 15.02/14.80 [8335]P149(x83353,x83351,x83352)+E(f857(f857(f79(a1),f857(f857(f80(a1),x83351),f870(x83352,x83351,x83353))),f867(x83352,x83351,x83353)),x83352)+~P106(f857(x83353,f869(x83352,x83351,x83353)))+~P106(f857(x83353,f2(a1)))
% 15.02/14.80 [8433]P148(x84333,x84331,x84332)+E(x84331,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x84331),f864(x84332,x84331,x84333))),f863(x84332,x84331,x84333)),x84332)+P106(f857(f857(f234(a1),f862(x84332,x84331,x84333)),f2(a1)))
% 15.02/14.80 [8434]P149(x84343,x84341,x84342)+E(x84341,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x84341),f869(x84342,x84341,x84343))),f868(x84342,x84341,x84343)),x84342)+P106(f857(f857(f234(a1),f867(x84342,x84341,x84343)),f2(a1)))
% 15.02/14.80 [8473]P148(x84733,x84731,x84732)+~P106(f857(x84733,x84732))+E(f857(f857(f79(a1),f857(f857(f80(a1),x84731),f864(x84732,x84731,x84733))),f863(x84732,x84731,x84733)),x84732)+P106(f857(f857(f234(a1),f862(x84732,x84731,x84733)),f2(a1)))
% 15.02/14.80 [8478]P149(x84783,x84781,x84782)+E(f857(f857(f79(a1),f857(f857(f80(a1),x84781),f869(x84782,x84781,x84783))),f868(x84782,x84781,x84783)),x84782)+~P106(f857(x84783,f2(a1)))+P106(f857(f857(f234(a1),f867(x84782,x84781,x84783)),f2(a1)))
% 15.02/14.80 [8611]P148(x86113,x86111,x86112)+E(x86111,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x86111),f865(x86112,x86111,x86113))),f862(x86112,x86111,x86113)),x86112)+E(f857(f857(f79(a1),f857(f857(f80(a1),x86111),f864(x86112,x86111,x86113))),f863(x86112,x86111,x86113)),x86112)
% 15.02/14.80 [8612]P149(x86123,x86121,x86122)+E(x86121,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x86121),f870(x86122,x86121,x86123))),f867(x86122,x86121,x86123)),x86122)+E(f857(f857(f79(a1),f857(f857(f80(a1),x86121),f869(x86122,x86121,x86123))),f868(x86122,x86121,x86123)),x86122)
% 15.02/14.80 [8632]P148(x86323,x86321,x86322)+~P106(f857(x86323,x86322))+E(f857(f857(f79(a1),f857(f857(f80(a1),x86321),f865(x86322,x86321,x86323))),f862(x86322,x86321,x86323)),x86322)+E(f857(f857(f79(a1),f857(f857(f80(a1),x86321),f864(x86322,x86321,x86323))),f863(x86322,x86321,x86323)),x86322)
% 15.02/14.80 [8643]P149(x86433,x86431,x86432)+E(f857(f857(f79(a1),f857(f857(f80(a1),x86431),f870(x86432,x86431,x86433))),f867(x86432,x86431,x86433)),x86432)+E(f857(f857(f79(a1),f857(f857(f80(a1),x86431),f869(x86432,x86431,x86433))),f868(x86432,x86431,x86433)),x86432)+~P106(f857(x86433,f2(a1)))
% 15.02/14.80 [9304]~P129(x93041)+~E(x93043,f2(x93041))+~E(x93042,f2(x93041))+P106(f857(f857(f234(x93041),f857(f857(f79(x93041),f857(f857(f80(x93041),x93042),x93042)),f857(f857(f80(x93041),x93043),x93043))),f2(x93041)))
% 15.02/14.80 [10382]~P120(x103821)+~E(x103823,f2(x103821))+~E(x103822,f2(x103821))+P106(f857(f857(f234(x103821),f857(f857(f79(x103821),f857(f857(f243(x103821),x103822),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103821),x103823),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))),f2(x103821)))
% 15.02/14.80 [5004]~E(x50043,x50041)+~P124(x50042)+E(x50041,f2(x50042))+E(f857(f857(f290(x50042),x50043),x50041),f77(x50042))
% 15.02/14.80 [5057]~P3(x50571)+~E(x50573,f189(x50571))+~E(x50572,f189(x50571))+E(f857(f857(f110(x50571),x50572),x50573),f189(x50571))
% 15.02/14.80 [5058]~P100(x50581)+~E(x50583,f241(x50581))+~E(x50582,f241(x50581))+E(f857(f857(f101(x50581),x50582),x50583),f241(x50581))
% 15.02/14.80 [5151]~P124(x51513)+E(x51511,x51512)+E(x51512,f2(x51513))+~E(f857(f857(f290(x51513),x51511),x51512),f77(x51513))
% 15.02/14.80 [5169]~P133(x51692)+E(x51691,f2(x51692))+E(x51693,f2(x51692))+~E(f857(f857(f80(x51692),x51693),x51691),f2(x51692))
% 15.02/14.80 [5170]~P142(x51702)+E(x51701,f2(x51702))+E(x51703,f2(x51702))+~E(f857(f857(f80(x51702),x51703),x51701),f2(x51702))
% 15.02/14.80 [5548]~P122(x55483)+E(x55481,x55482)+E(x55481,f857(f78(x55483),x55482))+~E(f857(f857(f80(x55483),x55481),x55481),f857(f857(f80(x55483),x55482),x55482))
% 15.02/14.80 [5587]~P96(x55871)+E(f857(f78(x55871),x55872),x55873)+~E(f857(f857(f110(x55871),x55872),x55873),f241(x55871))+~E(f857(f857(f101(x55871),x55872),x55873),f189(x55871))
% 15.02/14.80 [5667]~P120(x56673)+E(x56671,x56672)+P106(f857(f857(f235(x56673),x56672),x56671))+P106(f857(f857(f235(x56673),x56671),x56672))
% 15.02/14.80 [5668]~P109(x56683)+E(x56681,x56682)+P106(f857(f857(f235(x56683),x56682),x56681))+P106(f857(f857(f235(x56683),x56681),x56682))
% 15.02/14.80 [5669]~E(x56692,x56693)+~P109(x56691)+P106(f857(f857(f235(x56691),x56692),x56693))+P106(f857(f857(f234(x56691),x56692),x56693))
% 15.02/14.80 [5931]~P110(x59313)+E(x59311,x59312)+~P106(f857(f857(f234(x59313),x59312),x59311))+P106(f857(f857(f235(x59313),x59312),x59311))
% 15.02/14.80 [5933]~P109(x59333)+E(x59331,x59332)+~P106(f857(f857(f234(x59333),x59331),x59332))+P106(f857(f857(f235(x59333),x59331),x59332))
% 15.02/14.80 [5939]~P110(x59393)+E(x59391,x59392)+~P106(f857(f857(f234(x59393),x59391),x59392))+P106(f857(f857(f235(x59393),x59391),x59392))
% 15.02/14.80 [6044]P148(x60441,x60442,x60443)+~P106(f857(x60441,x60443))+P106(f857(f857(f235(a1),x60442),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x60442))
% 15.02/14.80 [6098]P149(x60981,x60982,x60983)+~P106(f857(x60981,f2(a1)))+P106(f857(f857(f235(a1),x60982),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x60982))
% 15.02/14.80 [6103]~P2(x61031)+E(f857(f857(f110(x61031),x61032),f13(x61031,x61033)),x61032)+~P106(f857(f60(x61031),x61033))+~P106(f857(f857(f328(x61031),x61032),x61033))
% 15.02/14.80 [6104]~P2(x61041)+E(f857(f857(f101(x61041),x61042),f12(x61041,x61043)),x61042)+~P106(f857(f60(x61041),x61043))+~P106(f857(f857(f328(x61041),x61042),x61043))
% 15.02/14.80 [6142]~P2(x61421)+E(f857(f857(f110(x61421),x61422),f12(x61421,x61423)),f12(x61421,x61423))+~P106(f857(f60(x61421),x61423))+~P106(f857(f857(f328(x61421),x61422),x61423))
% 15.02/14.80 [6143]~P2(x61431)+E(f857(f857(f101(x61431),x61432),f13(x61431,x61433)),f13(x61431,x61433))+~P106(f857(f60(x61431),x61433))+~P106(f857(f857(f328(x61431),x61432),x61433))
% 15.02/14.80 [6144]~P109(x61441)+E(f857(f857(f188(x61441),x61442),f16(x61441,x61443)),f16(x61441,x61443))+~P106(f857(f60(x61441),x61443))+~P106(f857(f857(f328(x61441),x61442),x61443))
% 15.02/14.80 [6145]~P109(x61451)+E(f857(f857(f233(x61451),x61452),f17(x61451,x61453)),f17(x61451,x61453))+~P106(f857(f60(x61451),x61453))+~P106(f857(f857(f328(x61451),x61452),x61453))
% 15.02/14.80 [6184]E(x61841,x61842)+~P110(x61843)+~P106(f857(f857(f234(x61843),x61842),x61841))+~P106(f857(f857(f234(x61843),x61841),x61842))
% 15.02/14.80 [6333]~P107(x63331)+P106(f857(f857(f235(x63331),x63333),x63332))+~P106(f857(f857(f234(x63331),x63333),x63332))+P106(f857(f857(f234(x63331),x63332),x63333))
% 15.02/14.80 [6359]~P109(x63591)+~P106(f857(f60(x63591),x63593))+P106(f857(f857(f234(x63591),x63592),f17(x63591,x63593)))+~P106(f857(f857(f328(x63591),x63592),x63593))
% 15.02/14.80 [6406]~P109(x64061)+E(f857(f857(f188(x64061),x64062),f15(x64061,f233(x64061),x64063)),x64062)+~P106(f857(f60(x64061),x64063))+~P106(f857(f857(f328(x64061),x64062),x64063))
% 15.02/14.80 [6407]~P109(x64071)+E(f857(f857(f233(x64071),x64072),f14(x64071,f188(x64071),x64073)),x64072)+~P106(f857(f60(x64071),x64073))+~P106(f857(f857(f328(x64071),x64072),x64073))
% 15.02/14.80 [6551]E(x65511,x65512)+~E(f857(f857(f3(a919),x65511),x65513),f857(f857(f3(a919),x65512),x65513))+~P106(f857(f857(f234(a919),x65513),x65511))+~P106(f857(f857(f234(a919),x65513),x65512))
% 15.02/14.80 [6578]~P109(x65781)+~P106(f857(f60(x65781),x65782))+~P106(f857(f857(f328(x65781),x65783),x65782))+P106(f857(f857(f234(x65781),f16(x65781,x65782)),x65783))
% 15.02/14.80 [6640]P148(x66402,x66401,x66403)+E(x66401,f2(a1))+P106(f857(f857(f235(a1),x66401),f862(x66403,x66401,x66402)))+P106(f857(f857(f235(a1),f2(a1)),x66401))
% 15.02/14.80 [6641]P149(x66412,x66411,x66413)+E(x66411,f2(a1))+P106(f857(f857(f235(a1),x66411),f867(x66413,x66411,x66412)))+P106(f857(f857(f235(a1),f2(a1)),x66411))
% 15.02/14.80 [6642]~P109(x66421)+E(f857(f857(f188(x66421),x66422),f14(x66421,f188(x66421),x66423)),f14(x66421,f188(x66421),x66423))+~P106(f857(f60(x66421),x66423))+~P106(f857(f857(f328(x66421),x66422),x66423))
% 15.02/14.80 [6643]~P109(x66431)+E(f857(f857(f233(x66431),x66432),f15(x66431,f233(x66431),x66433)),f15(x66431,f233(x66431),x66433))+~P106(f857(f60(x66431),x66433))+~P106(f857(f857(f328(x66431),x66432),x66433))
% 15.02/14.80 [6648]~P106(f857(x66481,x66482))+P106(f857(x66481,f378(x66482,x66481,x66483)))+P106(f857(x66481,f2(a919)))+~P106(f857(f857(f235(a919),x66482),x66483))
% 15.02/14.80 [6706]~P106(f857(x67061,x67062))+~P106(f857(f60(x67063),x67062))+P106(f857(x67061,f493(x67061,x67062,x67063)))+P106(f857(x67061,f189(f927(x67063,a915))))
% 15.02/14.80 [6719]~P120(x67191)+~P94(x67191)+P106(f857(f857(f234(x67191),f857(f103(x67191),x67192)),f857(f103(x67191),x67193)))+~P106(f857(f857(f234(a1),x67192),x67193))
% 15.02/14.80 [6720]~P120(x67201)+~P94(x67201)+P106(f857(f857(f235(x67201),f857(f103(x67201),x67202)),f857(f103(x67201),x67203)))+~P106(f857(f857(f235(a1),x67202),x67203))
% 15.02/14.80 [6723]~P106(f857(x67231,x67233))+~P106(f857(f60(x67232),x67233))+P106(f857(f60(x67232),f493(x67231,x67233,x67232)))+P106(f857(x67231,f189(f927(x67232,a915))))
% 15.02/14.80 [6757]P148(x67571,x67572,x67573)+~P106(f857(x67571,x67573))+P106(f857(f857(f235(a1),x67572),f862(x67573,x67572,x67571)))+P106(f857(f857(f235(a1),f2(a1)),x67572))
% 15.02/14.80 [6794]P149(x67941,x67942,x67943)+P106(f857(f857(f235(a1),x67942),f867(x67943,x67942,x67941)))+~P106(f857(x67941,f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x67942))
% 15.02/14.80 [6824]~P108(x68241)+~P95(x68241)+E(f857(f857(f188(x68241),f857(f103(x68241),x68242)),f857(f103(x68241),x68243)),f857(f103(x68241),x68243))+P106(f857(f857(f234(x68241),f857(f103(x68241),x68242)),f857(f103(x68241),x68243)))
% 15.02/14.80 [6825]~P108(x68251)+~P95(x68251)+E(f857(f857(f233(x68251),f857(f103(x68251),x68252)),f857(f103(x68251),x68253)),f857(f103(x68251),x68252))+P106(f857(f857(f234(x68251),f857(f103(x68251),x68252)),f857(f103(x68251),x68253)))
% 15.02/14.80 [6883]P148(x68832,x68831,x68833)+E(x68831,f2(a1))+~P106(f857(x68832,f862(x68833,x68831,x68832)))+P106(f857(f857(f235(a1),f2(a1)),x68831))
% 15.02/14.80 [6884]P149(x68842,x68841,x68843)+E(x68841,f2(a1))+~P106(f857(x68842,f870(x68843,x68841,x68842)))+P106(f857(f857(f235(a1),f2(a1)),x68841))
% 15.02/14.80 [6888]P106(f857(x68881,x68882))+~P106(f857(f60(x68883),x68882))+P106(f857(x68881,f719(x68881,x68882,x68883)))+~P106(f857(x68881,f189(f927(x68883,a915))))
% 15.02/14.80 [6908]P106(f857(x69081,x69082))+P106(f857(f60(x69083),f719(x69081,x69082,x69083)))+~P106(f857(f60(x69083),x69082))+~P106(f857(x69081,f189(f927(x69083,a915))))
% 15.02/14.80 [6974]P148(x69741,x69742,x69743)+~P106(f857(x69741,x69743))+~P106(f857(x69741,f862(x69743,x69742,x69741)))+P106(f857(f857(f235(a1),f2(a1)),x69742))
% 15.02/14.80 [7004]P149(x70041,x70042,x70043)+~P106(f857(x70041,f870(x70043,x70042,x70041)))+~P106(f857(x70041,f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x70042))
% 15.02/14.80 [7112]~P94(x71123)+~P120(x71123)+~P106(f857(f857(f234(x71123),f857(f103(x71123),x71121)),f857(f103(x71123),x71122)))+P106(f857(f857(f234(a1),x71121),x71122))
% 15.02/14.80 [7113]~P94(x71133)+~P120(x71133)+~P106(f857(f857(f235(x71133),f857(f103(x71133),x71131)),f857(f103(x71133),x71132)))+P106(f857(f857(f235(a1),x71131),x71132))
% 15.02/14.80 [7141]~P109(x71411)+~P14(x71411,x71413)+P14(x71411,f857(f857(f151(x71411),x71412),x71413))+~P106(f857(f857(f234(x71411),x71412),f711(x71413,x71412,x71411)))
% 15.02/14.80 [7142]~P109(x71421)+~P14(x71421,x71423)+P14(x71421,f857(f857(f151(x71421),x71422),x71423))+~P106(f857(f857(f234(x71421),x71422),f714(x71423,x71422,x71421)))
% 15.02/14.80 [7143]~P109(x71431)+~P14(x71431,x71433)+P14(x71431,f857(f857(f151(x71431),x71432),x71433))+~P106(f857(f857(f234(x71431),x71432),f752(x71432,x71433,x71431)))
% 15.02/14.80 [7227]P148(x72272,x72271,x72273)+E(x72271,f2(a1))+P106(f857(f857(f235(a1),x72271),f2(a1)))+P106(f857(f857(f235(a1),f863(x72273,x72271,x72272)),x72271))
% 15.02/14.80 [7228]P149(x72282,x72281,x72283)+E(x72281,f2(a1))+P106(f857(f857(f235(a1),x72281),f2(a1)))+P106(f857(f857(f235(a1),f868(x72283,x72281,x72282)),x72281))
% 15.02/14.80 [7266]P148(x72662,x72661,x72663)+E(x72661,f2(a1))+P106(f857(f857(f234(a1),f862(x72663,x72661,x72662)),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x72661))
% 15.02/14.80 [7267]P149(x72672,x72671,x72673)+E(x72671,f2(a1))+P106(f857(f857(f234(a1),f867(x72673,x72671,x72672)),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x72671))
% 15.02/14.80 [7292]~P109(x72921)+~P14(x72921,x72923)+E(f857(f857(f148(x72921,x72921,f7(x72921)),x72922),f170(x72921,x72922,x72923)),x72923)+~P106(f857(f857(f328(x72921),x72922),f857(f172(x72921),x72923)))
% 15.02/14.80 [7339]P148(x73391,x73392,x73393)+~P106(f857(x73391,x73393))+P106(f857(f857(f235(a1),x73392),f2(a1)))+P106(f857(f857(f235(a1),f863(x73393,x73392,x73391)),x73392))
% 15.02/14.80 [7345]~P108(x73451)+~P95(x73451)+E(f857(f857(f188(x73451),f857(f103(x73451),x73452)),f857(f103(x73451),x73453)),f857(f103(x73451),x73452))+~P106(f857(f857(f234(x73451),f857(f103(x73451),x73452)),f857(f103(x73451),x73453)))
% 15.02/14.80 [7346]~P108(x73461)+~P95(x73461)+E(f857(f857(f233(x73461),f857(f103(x73461),x73462)),f857(f103(x73461),x73463)),f857(f103(x73461),x73463))+~P106(f857(f857(f234(x73461),f857(f103(x73461),x73462)),f857(f103(x73461),x73463)))
% 15.02/14.80 [7360]P149(x73601,x73602,x73603)+~P106(f857(x73601,f2(a1)))+P106(f857(f857(f235(a1),x73602),f2(a1)))+P106(f857(f857(f235(a1),f868(x73603,x73602,x73601)),x73602))
% 15.02/14.80 [7370]P148(x73701,x73702,x73703)+~P106(f857(x73701,x73703))+P106(f857(f857(f234(a1),f862(x73703,x73702,x73701)),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x73702))
% 15.02/14.80 [7394]P149(x73941,x73942,x73943)+~P106(f857(x73941,f2(a1)))+P106(f857(f857(f234(a1),f867(x73943,x73942,x73941)),f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x73942))
% 15.02/14.80 [7422]~P106(f857(x74221,x74222))+P106(f857(x74221,f2(a919)))+~P106(f857(f857(f235(a919),x74222),x74223))+P106(f857(f857(f235(a919),f378(x74222,x74221,x74223)),x74223))
% 15.02/14.80 [7439]~P109(x74391)+~P14(x74391,x74393)+P14(x74391,f857(f857(f151(x74391),x74392),x74393))+P106(f857(f857(f328(x74391),f711(x74393,x74392,x74391)),f857(f172(x74391),x74393)))
% 15.02/14.80 [7440]~P109(x74401)+~P14(x74401,x74403)+P14(x74401,f857(f857(f151(x74401),x74402),x74403))+P106(f857(f857(f328(x74401),f714(x74403,x74402,x74401)),f857(f172(x74401),x74403)))
% 15.02/14.80 [7441]~P109(x74411)+~P14(x74411,x74413)+P14(x74411,f857(f857(f151(x74411),x74412),x74413))+P106(f857(f857(f328(x74411),f752(x74412,x74413,x74411)),f857(f172(x74411),x74413)))
% 15.02/14.80 [7554]~P109(x75541)+~P6(x75541)+~P106(f857(f857(f235(x75541),x75543),f36(x75541,x75542)))+P106(f857(f857(f328(x75541),f876(x75542,x75543,x75541)),x75542))
% 15.02/14.80 [7709]~P109(x77091)+~P6(x77091)+~P106(f857(f857(f235(x77091),f37(x77091,x77093)),x77092))+P106(f857(f857(f328(x77091),f383(x77092,x77093,x77091)),x77093))
% 15.02/14.80 [7710]~P109(x77101)+~P6(x77101)+~P106(f857(f857(f235(x77101),f37(x77101,x77103)),x77102))+P106(f857(f857(f235(x77101),f383(x77102,x77103,x77101)),x77102))
% 15.02/14.80 [7722]P148(x77222,x77221,x77223)+E(x77221,f2(a1))+P106(f857(f857(f235(a1),x77221),f862(x77223,x77221,x77222)))+P106(f857(f857(f235(a1),f863(x77223,x77221,x77222)),x77221))
% 15.02/14.80 [7723]P149(x77232,x77231,x77233)+E(x77231,f2(a1))+P106(f857(f857(f235(a1),x77231),f867(x77233,x77231,x77232)))+P106(f857(f857(f235(a1),f868(x77233,x77231,x77232)),x77231))
% 15.02/14.80 [7816]P148(x78163,x78161,x78162)+E(x78161,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x78161),f865(x78162,x78161,x78163))),f862(x78162,x78161,x78163)),x78162)+P106(f857(f857(f235(a1),f2(a1)),x78161))
% 15.02/14.80 [7817]P149(x78173,x78171,x78172)+E(x78171,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x78171),f870(x78172,x78171,x78173))),f867(x78172,x78171,x78173)),x78172)+P106(f857(f857(f235(a1),f2(a1)),x78171))
% 15.02/14.80 [7819]~P129(x78191)+~P106(f857(f857(f234(x78191),x78193),f2(x78191)))+P106(f857(f857(f234(x78191),f857(f857(f80(x78191),x78192),x78193)),f2(x78191)))+~P106(f857(f857(f234(x78191),f2(x78191)),x78192))
% 15.02/14.80 [7820]~P129(x78201)+~P106(f857(f857(f234(x78201),x78202),f2(x78201)))+P106(f857(f857(f234(x78201),f857(f857(f80(x78201),x78202),x78203)),f2(x78201)))+~P106(f857(f857(f234(x78201),f2(x78201)),x78203))
% 15.02/14.80 [7822]~P136(x78221)+~P106(f857(f857(f234(x78221),x78223),f2(x78221)))+P106(f857(f857(f234(x78221),f857(f857(f80(x78221),x78222),x78223)),f2(x78221)))+~P106(f857(f857(f234(x78221),f2(x78221)),x78222))
% 15.02/14.80 [7824]~P136(x78241)+~P106(f857(f857(f234(x78241),x78242),f2(x78241)))+P106(f857(f857(f234(x78241),f857(f857(f80(x78241),x78242),x78243)),f2(x78241)))+~P106(f857(f857(f234(x78241),f2(x78241)),x78243))
% 15.02/14.80 [7825]~P67(x78251)+~P106(f857(f857(f234(x78251),x78253),f2(x78251)))+P106(f857(f857(f234(x78251),f857(f857(f290(x78251),x78252),x78253)),f2(x78251)))+~P106(f857(f857(f234(x78251),f2(x78251)),x78252))
% 15.02/14.80 [7826]~P67(x78261)+~P106(f857(f857(f234(x78261),x78262),f2(x78261)))+P106(f857(f857(f234(x78261),f857(f857(f290(x78261),x78262),x78263)),f2(x78261)))+~P106(f857(f857(f234(x78261),f2(x78261)),x78263))
% 15.02/14.80 [7827]~P68(x78271)+~P106(f857(f857(f234(x78271),x78272),f2(x78271)))+P106(f857(f857(f234(x78271),f857(f857(f290(x78271),x78272),x78273)),f2(x78271)))+~P106(f857(f857(f235(x78271),f2(x78271)),x78273))
% 15.02/14.80 [7828]~P68(x78281)+~P106(f857(f857(f235(x78281),x78283),f2(x78281)))+P106(f857(f857(f234(x78281),f857(f857(f290(x78281),x78282),x78283)),f2(x78281)))+~P106(f857(f857(f234(x78281),f2(x78281)),x78282))
% 15.02/14.80 [7830]~P135(x78301)+~P106(f857(f857(f235(x78301),x78303),f2(x78301)))+P106(f857(f857(f235(x78301),f857(f857(f80(x78301),x78302),x78303)),f2(x78301)))+~P106(f857(f857(f235(x78301),f2(x78301)),x78302))
% 15.02/14.80 [7831]~P135(x78311)+~P106(f857(f857(f235(x78311),x78312),f2(x78311)))+P106(f857(f857(f235(x78311),f857(f857(f80(x78311),x78312),x78313)),f2(x78311)))+~P106(f857(f857(f235(x78311),f2(x78311)),x78313))
% 15.02/14.80 [7832]~P67(x78321)+~P106(f857(f857(f235(x78321),x78323),f2(x78321)))+P106(f857(f857(f235(x78321),f857(f857(f290(x78321),x78322),x78323)),f2(x78321)))+~P106(f857(f857(f235(x78321),f2(x78321)),x78322))
% 15.02/14.80 [7833]~P67(x78331)+~P106(f857(f857(f235(x78331),x78332),f2(x78331)))+P106(f857(f857(f235(x78331),f857(f857(f290(x78331),x78332),x78333)),f2(x78331)))+~P106(f857(f857(f235(x78331),f2(x78331)),x78333))
% 15.02/14.80 [7834]~P68(x78341)+~P106(f857(f857(f235(x78341),x78343),f2(x78341)))+P106(f857(f857(f235(x78341),f857(f857(f290(x78341),x78342),x78343)),f2(x78341)))+~P106(f857(f857(f235(x78341),f2(x78341)),x78342))
% 15.02/14.80 [7835]~P68(x78351)+~P106(f857(f857(f235(x78351),x78352),f2(x78351)))+P106(f857(f857(f235(x78351),f857(f857(f290(x78351),x78352),x78353)),f2(x78351)))+~P106(f857(f857(f235(x78351),f2(x78351)),x78353))
% 15.02/14.80 [7850]P148(x78501,x78502,x78503)+~P106(f857(x78501,x78503))+P106(f857(f857(f235(a1),x78502),f862(x78503,x78502,x78501)))+P106(f857(f857(f235(a1),f863(x78503,x78502,x78501)),x78502))
% 15.02/14.80 [7863]P149(x78631,x78632,x78633)+P106(f857(f857(f235(a1),x78632),f867(x78633,x78632,x78631)))+~P106(f857(x78631,f2(a1)))+P106(f857(f857(f235(a1),f868(x78633,x78632,x78631)),x78632))
% 15.02/14.80 [7914]P148(x79142,x79141,x79143)+E(x79141,f2(a1))+~P106(f857(x79142,f862(x79143,x79141,x79142)))+P106(f857(f857(f235(a1),f863(x79143,x79141,x79142)),x79141))
% 15.02/14.80 [7915]P149(x79152,x79151,x79153)+E(x79151,f2(a1))+~P106(f857(x79152,f870(x79153,x79151,x79152)))+P106(f857(f857(f235(a1),f868(x79153,x79151,x79152)),x79151))
% 15.02/14.80 [7925]P148(x79253,x79251,x79252)+~P106(f857(x79253,x79252))+E(f857(f857(f79(a1),f857(f857(f80(a1),x79251),f865(x79252,x79251,x79253))),f862(x79252,x79251,x79253)),x79252)+P106(f857(f857(f235(a1),f2(a1)),x79251))
% 15.02/14.80 [7940]P149(x79403,x79401,x79402)+E(f857(f857(f79(a1),f857(f857(f80(a1),x79401),f870(x79402,x79401,x79403))),f867(x79402,x79401,x79403)),x79402)+~P106(f857(x79403,f2(a1)))+P106(f857(f857(f235(a1),f2(a1)),x79401))
% 15.02/14.80 [7968]~P106(f857(x79681,x79683))+~P106(f857(f60(x79682),x79683))+P106(f857(f857(f328(x79682),f484(x79681,x79683,x79682)),f493(x79681,x79683,x79682)))+P106(f857(x79681,f189(f927(x79682,a915))))
% 15.02/14.80 [7979]P148(x79791,x79792,x79793)+~P106(f857(x79791,x79793))+~P106(f857(x79791,f862(x79793,x79792,x79791)))+P106(f857(f857(f235(a1),f863(x79793,x79792,x79791)),x79792))
% 15.02/14.80 [7985]P149(x79851,x79852,x79853)+~P106(f857(x79851,f870(x79853,x79852,x79851)))+~P106(f857(x79851,f2(a1)))+P106(f857(f857(f235(a1),f868(x79853,x79852,x79851)),x79852))
% 15.02/14.80 [8086]~P129(x80861)+~P106(f857(f857(f234(x80861),f857(f857(f80(x80861),x80863),x80862)),f2(x80861)))+P106(f857(f857(f234(x80861),x80862),f2(x80861)))+P106(f857(f857(f234(x80861),f2(x80861)),x80862))
% 15.02/14.80 [8087]~P129(x80871)+~P106(f857(f857(f234(x80871),f857(f857(f80(x80871),x80872),x80873)),f2(x80871)))+P106(f857(f857(f234(x80871),x80872),f2(x80871)))+P106(f857(f857(f234(x80871),f2(x80871)),x80872))
% 15.02/14.80 [8088]~P67(x80881)+~P106(f857(f857(f234(x80881),f857(f857(f290(x80881),x80883),x80882)),f2(x80881)))+P106(f857(f857(f234(x80881),x80882),f2(x80881)))+P106(f857(f857(f234(x80881),f2(x80881)),x80882))
% 15.02/14.80 [8089]~P67(x80891)+~P106(f857(f857(f234(x80891),f857(f857(f290(x80891),x80892),x80893)),f2(x80891)))+P106(f857(f857(f234(x80891),x80892),f2(x80891)))+P106(f857(f857(f234(x80891),f2(x80891)),x80892))
% 15.02/14.80 [8090]~P67(x80901)+~P106(f857(f857(f235(x80901),f857(f857(f290(x80901),x80903),x80902)),f2(x80901)))+P106(f857(f857(f235(x80901),x80902),f2(x80901)))+P106(f857(f857(f235(x80901),f2(x80901)),x80902))
% 15.02/14.80 [8091]~P67(x80911)+~P106(f857(f857(f235(x80911),f857(f857(f290(x80911),x80912),x80913)),f2(x80911)))+P106(f857(f857(f235(x80911),x80912),f2(x80911)))+P106(f857(f857(f235(x80911),f2(x80911)),x80912))
% 15.02/14.80 [8115]~P129(x81151)+~P106(f857(f857(f234(x81151),f857(f857(f80(x81151),x81152),x81153)),f2(x81151)))+P106(f857(f857(f234(x81151),f2(x81151)),x81152))+P106(f857(f857(f234(x81151),f2(x81151)),x81153))
% 15.02/14.80 [8116]~P67(x81161)+~P106(f857(f857(f234(x81161),f857(f857(f290(x81161),x81162),x81163)),f2(x81161)))+P106(f857(f857(f234(x81161),f2(x81161)),x81162))+P106(f857(f857(f234(x81161),f2(x81161)),x81163))
% 15.02/14.80 [8117]~P67(x81171)+~P106(f857(f857(f235(x81171),f857(f857(f290(x81171),x81172),x81173)),f2(x81171)))+P106(f857(f857(f235(x81171),f2(x81171)),x81172))+P106(f857(f857(f235(x81171),f2(x81171)),x81173))
% 15.02/14.80 [8139]P148(x81392,x81391,x81393)+E(x81391,f2(a1))+P106(f857(f857(f234(a1),f862(x81393,x81391,x81392)),f2(a1)))+P106(f857(f857(f235(a1),f863(x81393,x81391,x81392)),x81391))
% 15.02/14.80 [8140]P149(x81402,x81401,x81403)+E(x81401,f2(a1))+P106(f857(f857(f234(a1),f867(x81403,x81401,x81402)),f2(a1)))+P106(f857(f857(f235(a1),f868(x81403,x81401,x81402)),x81401))
% 15.02/14.80 [8147]~P127(x81471)+~P106(f857(f857(f235(x81471),x81472),f77(x81471)))+P106(f857(f857(f235(x81471),f857(f857(f243(x81471),x81472),f857(a112,x81473))),f77(x81471)))+~P106(f857(f857(f235(x81471),f2(x81471)),x81472))
% 15.02/14.80 [8201]~P109(x82011)+~E(x82013,f113(x82011))+~P14(x82011,f857(f168(x82011),x82013))+E(f857(f142(x82011,x82011,f857(f9(x82011,x82011,x82011),f233(x82011)),x82012),f857(f168(x82011),x82013)),x82012)
% 15.02/14.80 [8204]P148(x82041,x82042,x82043)+~P106(f857(x82041,x82043))+P106(f857(f857(f234(a1),f862(x82043,x82042,x82041)),f2(a1)))+P106(f857(f857(f235(a1),f863(x82043,x82042,x82041)),x82042))
% 15.02/14.80 [8211]P149(x82111,x82112,x82113)+~P106(f857(x82111,f2(a1)))+P106(f857(f857(f234(a1),f867(x82113,x82112,x82111)),f2(a1)))+P106(f857(f857(f235(a1),f868(x82113,x82112,x82111)),x82112))
% 15.02/14.80 [8428]P148(x84283,x84281,x84282)+E(x84281,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x84281),f865(x84282,x84281,x84283))),f862(x84282,x84281,x84283)),x84282)+P106(f857(f857(f235(a1),f863(x84282,x84281,x84283)),x84281))
% 15.02/14.80 [8429]P149(x84293,x84291,x84292)+E(x84291,f2(a1))+E(f857(f857(f79(a1),f857(f857(f80(a1),x84291),f870(x84292,x84291,x84293))),f867(x84292,x84291,x84293)),x84292)+P106(f857(f857(f235(a1),f868(x84292,x84291,x84293)),x84291))
% 15.02/14.80 [8464]P148(x84643,x84641,x84642)+~P106(f857(x84643,x84642))+E(f857(f857(f79(a1),f857(f857(f80(a1),x84641),f865(x84642,x84641,x84643))),f862(x84642,x84641,x84643)),x84642)+P106(f857(f857(f235(a1),f863(x84642,x84641,x84643)),x84641))
% 15.02/14.80 [8465]~P72(x84651)+~P77(x84651)+~P42(x84653)+E(f857(f857(f8(a919,x84651),f857(f857(f10(a1,x84651,a919),x84652),f100(a1))),f857(f309(a1,a919,a104),x84653)),f857(f857(f8(a1,x84651),x84652),x84653))
% 15.02/14.80 [8466]~P72(x84661)+~P77(x84661)+~P42(x84663)+E(f857(f857(f11(a919,x84661),f857(f857(f10(a1,x84661,a919),x84662),f100(a1))),f857(f309(a1,a919,a104),x84663)),f857(f857(f11(a1,x84661),x84662),x84663))
% 15.02/14.80 [8475]P149(x84753,x84751,x84752)+E(f857(f857(f79(a1),f857(f857(f80(a1),x84751),f870(x84752,x84751,x84753))),f867(x84752,x84751,x84753)),x84752)+~P106(f857(x84753,f2(a1)))+P106(f857(f857(f235(a1),f868(x84752,x84751,x84753)),x84751))
% 15.02/14.80 [8497]~E(x84972,f2(a919))+~E(f857(f250(a919,a919),x84973),f2(a919))+~E(x84971,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x84973)),x84972)),f857(f255(a919,a919),x84973)))+P106(f857(f47(x84971,x84972),x84973))
% 15.02/14.80 [8553]P106(f857(x85531,x85532))+~P106(f857(f857(f328(x85533),f712(x85531,x85532,x85533)),f719(x85531,x85532,x85533)))+~P106(f857(f60(x85533),x85532))+~P106(f857(x85531,f189(f927(x85533,a915))))
% 15.02/14.80 [9176]P106(f857(x91761,x91762))+~P106(f857(f60(x91763),x91762))+~P106(f857(x91761,f857(f857(f308(x91763),f712(x91761,x91762,x91763)),f719(x91761,x91762,x91763))))+~P106(f857(x91761,f189(f927(x91763,a915))))
% 15.02/14.80 [9406]P106(f857(f857(f234(a1),x94061),f2(a1)))+~P106(f857(f857(f235(a1),f857(f857(f79(a1),f857(f857(f80(a1),x94063),x94061)),x94062)),f2(a1)))+~P106(f857(f857(f234(a1),f2(a1)),x94062))+~P106(f857(f857(f235(a1),f2(a1)),x94063))
% 15.02/14.80 [6001]~P2(x60012)+E(x60011,f189(f927(x60012,a915)))+~P106(f857(f60(x60012),x60011))+E(f12(x60012,f857(f857(f308(x60012),x60013),x60011)),f857(f857(f110(x60012),x60013),f12(x60012,x60011)))
% 15.02/14.80 [6002]~P2(x60022)+E(x60021,f189(f927(x60022,a915)))+~P106(f857(f60(x60022),x60021))+E(f13(x60022,f857(f857(f308(x60022),x60023),x60021)),f857(f857(f101(x60022),x60023),f13(x60022,x60021)))
% 15.02/14.80 [6003]~P109(x60032)+E(x60031,f189(f927(x60032,a915)))+~P106(f857(f60(x60032),x60031))+E(f16(x60032,f857(f857(f308(x60032),x60033),x60031)),f857(f857(f188(x60032),x60033),f16(x60032,x60031)))
% 15.02/14.80 [6004]~P109(x60042)+E(x60041,f189(f927(x60042,a915)))+~P106(f857(f60(x60042),x60041))+E(f17(x60042,f857(f857(f308(x60042),x60043),x60041)),f857(f857(f233(x60042),x60043),f17(x60042,x60041)))
% 15.02/14.80 [6329]~P129(x63291)+~E(x63293,f2(x63291))+~E(x63292,f2(x63291))+E(f857(f857(f79(x63291),f857(f857(f80(x63291),x63292),x63292)),f857(f857(f80(x63291),x63293),x63293)),f2(x63291))
% 15.02/14.80 [6399]~P97(x63992)+E(x63991,f189(f927(x63992,a915)))+~P106(f857(f60(x63992),x63991))+E(f857(f62(x63992,f80(x63992)),f857(f857(f308(x63992),x63993),x63991)),f857(f857(f80(x63992),x63993),f857(f62(x63992,f80(x63992)),x63991)))
% 15.02/14.80 [6527]~P109(x65272)+E(x65271,f189(f927(x65272,a915)))+~P106(f857(f60(x65272),x65271))+E(f14(x65272,f188(x65272),f857(f857(f308(x65272),x65273),x65271)),f857(f857(f188(x65272),x65273),f14(x65272,f188(x65272),x65271)))
% 15.02/14.80 [6528]~P109(x65282)+E(x65281,f189(f927(x65282,a915)))+~P106(f857(f60(x65282),x65281))+E(f15(x65282,f233(x65282),f857(f857(f308(x65282),x65283),x65281)),f857(f857(f233(x65282),x65283),f15(x65282,f233(x65282),x65281)))
% 15.02/14.80 [7038]~P70(x70381)+~P106(f857(f60(x70381),x70383))+E(f857(f62(x70381,f80(x70381)),f857(f857(f308(x70381),x70382),x70383)),f857(f857(f63(x70381,x70381,f80(x70381)),x70382),x70383))+P106(f857(f857(f328(x70381),x70382),x70383))
% 15.02/14.80 [7119]~E(f857(f857(f79(a1),x71192),f857(f857(f80(a1),x71193),x71191)),x71193)+~P106(f857(f857(f235(a1),f2(a1)),x71193))+P106(f857(f857(f234(a1),f77(a1)),x71191))+~P106(f857(f857(f235(a1),x71192),x71193))
% 15.02/14.80 [7148]~E(f857(f857(f79(a1),x71482),f857(f857(f80(a1),x71483),x71481)),x71483)+P106(f857(f857(f234(a1),x71481),f77(a1)))+~P106(f857(f857(f234(a1),f2(a1)),x71482))+~P106(f857(f857(f235(a1),f2(a1)),x71483))
% 15.02/14.80 [7165]E(x71651,f2(a919))+~P106(f857(f47(x71653,x71651),x71652))+~P106(f857(f857(f235(a919),f2(a919)),x71651))+P106(f857(f857(f235(a919),f857(f255(a919,a919),x71652)),x71651))
% 15.02/14.80 [7195]~P139(x71951)+~P106(f857(f857(f234(x71951),x71952),f2(x71951)))+~P106(f857(f857(f234(x71951),x71953),f2(x71951)))+E(f857(f857(f80(x71951),f857(f75(x71951),x71952)),f857(f75(x71951),x71953)),f857(f75(x71951),f857(f857(f80(x71951),x71952),x71953)))
% 15.02/14.80 [7243]~P139(x72431)+~P106(f857(f857(f234(x72431),x72432),f2(x72431)))+E(f857(f857(f80(x72431),f857(f75(x72431),x72432)),f857(f75(x72431),x72433)),f857(f75(x72431),f857(f857(f80(x72431),x72432),x72433)))+~P106(f857(f857(f234(x72431),f2(x72431)),x72433))
% 15.02/14.80 [7244]~P139(x72441)+~P106(f857(f857(f234(x72441),x72443),f2(x72441)))+E(f857(f857(f80(x72441),f857(f75(x72441),x72442)),f857(f75(x72441),x72443)),f857(f75(x72441),f857(f857(f80(x72441),x72442),x72443)))+~P106(f857(f857(f234(x72441),f2(x72441)),x72442))
% 15.02/14.80 [7300]~P139(x73001)+E(f857(f857(f80(x73001),f857(f75(x73001),x73002)),f857(f75(x73001),x73003)),f857(f75(x73001),f857(f857(f80(x73001),x73002),x73003)))+~P106(f857(f857(f234(x73001),f2(x73001)),x73002))+~P106(f857(f857(f234(x73001),f2(x73001)),x73003))
% 15.02/14.80 [7317]~P112(x73171)+~P106(f857(f857(f234(x73171),x73173),f2(x73171)))+~P106(f857(f857(f234(x73171),x73172),f2(x73171)))+P106(f857(f857(f234(x73171),f2(x73171)),f857(f857(f80(x73171),x73172),x73173)))
% 15.02/14.80 [7318]~P129(x73181)+~P106(f857(f857(f234(x73181),x73183),f2(x73181)))+~P106(f857(f857(f234(x73181),x73182),f2(x73181)))+P106(f857(f857(f234(x73181),f2(x73181)),f857(f857(f80(x73181),x73182),x73183)))
% 15.02/14.80 [7319]~P67(x73191)+~P106(f857(f857(f234(x73191),x73193),f2(x73191)))+~P106(f857(f857(f234(x73191),x73192),f2(x73191)))+P106(f857(f857(f234(x73191),f2(x73191)),f857(f857(f290(x73191),x73192),x73193)))
% 15.02/14.80 [7320]~P68(x73201)+~P106(f857(f857(f235(x73201),x73203),f2(x73201)))+~P106(f857(f857(f234(x73201),x73202),f2(x73201)))+P106(f857(f857(f234(x73201),f2(x73201)),f857(f857(f290(x73201),x73202),x73203)))
% 15.02/14.80 [7321]~P129(x73211)+~P106(f857(f857(f235(x73211),x73213),f2(x73211)))+~P106(f857(f857(f235(x73211),x73212),f2(x73211)))+P106(f857(f857(f235(x73211),f2(x73211)),f857(f857(f80(x73211),x73212),x73213)))
% 15.02/14.80 [7322]~P67(x73221)+~P106(f857(f857(f235(x73221),x73223),f2(x73221)))+~P106(f857(f857(f235(x73221),x73222),f2(x73221)))+P106(f857(f857(f235(x73221),f2(x73221)),f857(f857(f290(x73221),x73222),x73223)))
% 15.02/14.80 [7323]~P68(x73231)+~P106(f857(f857(f235(x73231),x73233),f2(x73231)))+~P106(f857(f857(f235(x73231),x73232),f2(x73231)))+P106(f857(f857(f235(x73231),f2(x73231)),f857(f857(f290(x73231),x73232),x73233)))
% 15.02/14.80 [7324]~P127(x73241)+~P106(f857(f857(f235(a919),f2(a919)),x73243))+~P106(f857(f857(f235(x73241),f77(x73241)),x73242))+P106(f857(f857(f235(x73241),f77(x73241)),f857(f857(f243(x73241),x73242),x73243)))
% 15.02/14.80 [7423]~P112(x74231)+~P106(f857(f857(f234(x74231),f2(x74231)),x74233))+~P106(f857(f857(f234(x74231),f2(x74231)),x74232))+P106(f857(f857(f234(x74231),f2(x74231)),f857(f857(f80(x74231),x74232),x74233)))
% 15.02/14.80 [7424]~P129(x74241)+~P106(f857(f857(f234(x74241),f2(x74241)),x74243))+~P106(f857(f857(f234(x74241),f2(x74241)),x74242))+P106(f857(f857(f234(x74241),f2(x74241)),f857(f857(f80(x74241),x74242),x74243)))
% 15.02/14.80 [7425]~P136(x74251)+~P106(f857(f857(f234(x74251),f2(x74251)),x74253))+~P106(f857(f857(f234(x74251),f2(x74251)),x74252))+P106(f857(f857(f234(x74251),f2(x74251)),f857(f857(f80(x74251),x74252),x74253)))
% 15.02/14.80 [7427]~P67(x74271)+~P106(f857(f857(f234(x74271),f2(x74271)),x74273))+~P106(f857(f857(f234(x74271),f2(x74271)),x74272))+P106(f857(f857(f234(x74271),f2(x74271)),f857(f857(f290(x74271),x74272),x74273)))
% 15.02/14.80 [7428]~P68(x74281)+~P106(f857(f857(f235(x74281),f2(x74281)),x74283))+~P106(f857(f857(f234(x74281),f2(x74281)),x74282))+P106(f857(f857(f234(x74281),f2(x74281)),f857(f857(f290(x74281),x74282),x74283)))
% 15.02/14.80 [7429]~P127(x74291)+~P106(f857(f857(f235(x74291),f77(x74291)),x74293))+~P106(f857(f857(f235(x74291),f77(x74291)),x74292))+P106(f857(f857(f235(x74291),f77(x74291)),f857(f857(f80(x74291),x74292),x74293)))
% 15.02/14.80 [7430]~P135(x74301)+~P106(f857(f857(f235(x74301),f2(x74301)),x74303))+~P106(f857(f857(f235(x74301),f2(x74301)),x74302))+P106(f857(f857(f235(x74301),f2(x74301)),f857(f857(f80(x74301),x74302),x74303)))
% 15.02/14.80 [7433]~P89(x74331)+~P106(f857(f857(f235(x74331),f2(x74331)),x74333))+~P106(f857(f857(f235(x74331),f2(x74331)),x74332))+P106(f857(f857(f235(x74331),f2(x74331)),f857(f857(f79(x74331),x74332),x74333)))
% 15.02/14.80 [7434]~P67(x74341)+~P106(f857(f857(f235(x74341),f2(x74341)),x74343))+~P106(f857(f857(f235(x74341),f2(x74341)),x74342))+P106(f857(f857(f235(x74341),f2(x74341)),f857(f857(f290(x74341),x74342),x74343)))
% 15.02/14.80 [7435]~P68(x74351)+~P106(f857(f857(f235(x74351),f2(x74351)),x74353))+~P106(f857(f857(f235(x74351),f2(x74351)),x74352))+P106(f857(f857(f235(x74351),f2(x74351)),f857(f857(f290(x74351),x74352),x74353)))
% 15.02/14.80 [7514]~P2(x75141)+~P106(f857(f60(x75141),x75143))+E(f12(x75141,f857(f857(f308(x75141),x75142),x75143)),x75142)+~E(f857(f857(f3(f927(x75141,a915)),x75143),f857(f857(f308(x75141),x75142),f189(f927(x75141,a915)))),f189(f927(x75141,a915)))
% 15.02/14.80 [7515]~P2(x75151)+~P106(f857(f60(x75151),x75153))+E(f13(x75151,f857(f857(f308(x75151),x75152),x75153)),x75152)+~E(f857(f857(f3(f927(x75151,a915)),x75153),f857(f857(f308(x75151),x75152),f189(f927(x75151,a915)))),f189(f927(x75151,a915)))
% 15.02/14.80 [7516]~P109(x75161)+~P106(f857(f60(x75161),x75163))+E(f16(x75161,f857(f857(f308(x75161),x75162),x75163)),x75162)+~E(f857(f857(f3(f927(x75161,a915)),x75163),f857(f857(f308(x75161),x75162),f189(f927(x75161,a915)))),f189(f927(x75161,a915)))
% 15.02/14.80 [7517]~P109(x75171)+~P106(f857(f60(x75171),x75173))+E(f17(x75171,f857(f857(f308(x75171),x75172),x75173)),x75172)+~E(f857(f857(f3(f927(x75171,a915)),x75173),f857(f857(f308(x75171),x75172),f189(f927(x75171,a915)))),f189(f927(x75171,a915)))
% 15.02/14.80 [7519]~P129(x75191)+P106(f857(f857(f234(x75191),x75192),f2(x75191)))+P106(f857(f857(f234(x75191),f2(x75191)),x75193))+~P106(f857(f857(f234(x75191),f2(x75191)),f857(f857(f80(x75191),x75193),x75192)))
% 15.02/14.80 [7520]~P129(x75201)+P106(f857(f857(f234(x75201),x75202),f2(x75201)))+P106(f857(f857(f234(x75201),f2(x75201)),x75203))+~P106(f857(f857(f234(x75201),f2(x75201)),f857(f857(f80(x75201),x75202),x75203)))
% 15.02/14.80 [7521]~P67(x75211)+P106(f857(f857(f234(x75211),x75212),f2(x75211)))+P106(f857(f857(f234(x75211),f2(x75211)),x75213))+~P106(f857(f857(f234(x75211),f2(x75211)),f857(f857(f290(x75211),x75213),x75212)))
% 15.02/14.80 [7522]~P67(x75221)+P106(f857(f857(f234(x75221),x75222),f2(x75221)))+P106(f857(f857(f234(x75221),f2(x75221)),x75223))+~P106(f857(f857(f234(x75221),f2(x75221)),f857(f857(f290(x75221),x75222),x75223)))
% 15.02/14.80 [7523]~P129(x75231)+P106(f857(f857(f234(x75231),x75232),f2(x75231)))+P106(f857(f857(f234(x75231),f2(x75231)),x75232))+~P106(f857(f857(f234(x75231),f2(x75231)),f857(f857(f80(x75231),x75233),x75232)))
% 15.02/14.80 [7524]~P129(x75241)+P106(f857(f857(f234(x75241),x75242),f2(x75241)))+P106(f857(f857(f234(x75241),f2(x75241)),x75242))+~P106(f857(f857(f234(x75241),f2(x75241)),f857(f857(f80(x75241),x75242),x75243)))
% 15.02/14.80 [7525]~P67(x75251)+P106(f857(f857(f234(x75251),x75252),f2(x75251)))+P106(f857(f857(f234(x75251),f2(x75251)),x75252))+~P106(f857(f857(f234(x75251),f2(x75251)),f857(f857(f290(x75251),x75253),x75252)))
% 15.02/14.80 [7526]~P67(x75261)+P106(f857(f857(f234(x75261),x75262),f2(x75261)))+P106(f857(f857(f234(x75261),f2(x75261)),x75262))+~P106(f857(f857(f234(x75261),f2(x75261)),f857(f857(f290(x75261),x75262),x75263)))
% 15.02/14.80 [7527]~P67(x75271)+P106(f857(f857(f235(x75271),x75272),f2(x75271)))+P106(f857(f857(f235(x75271),f2(x75271)),x75273))+~P106(f857(f857(f235(x75271),f2(x75271)),f857(f857(f290(x75271),x75273),x75272)))
% 15.02/14.80 [7528]~P67(x75281)+P106(f857(f857(f235(x75281),x75282),f2(x75281)))+P106(f857(f857(f235(x75281),f2(x75281)),x75283))+~P106(f857(f857(f235(x75281),f2(x75281)),f857(f857(f290(x75281),x75282),x75283)))
% 15.02/14.80 [7529]~P67(x75291)+P106(f857(f857(f235(x75291),x75292),f2(x75291)))+P106(f857(f857(f235(x75291),f2(x75291)),x75292))+~P106(f857(f857(f235(x75291),f2(x75291)),f857(f857(f290(x75291),x75293),x75292)))
% 15.02/14.80 [7530]~P67(x75301)+P106(f857(f857(f235(x75301),x75302),f2(x75301)))+P106(f857(f857(f235(x75301),f2(x75301)),x75302))+~P106(f857(f857(f235(x75301),f2(x75301)),f857(f857(f290(x75301),x75302),x75303)))
% 15.02/14.80 [7615]~E(f857(f857(f101(f927(x76151,a915)),f857(f172(x76151),x76152)),f857(f172(x76151),x76153)),f189(f927(x76151,a915)))+~P106(f857(f137(x76151),x76153))+~P106(f857(f137(x76151),x76152))+P106(f857(f137(x76151),f857(f857(f134(x76151),x76152),x76153)))
% 15.02/14.80 [7616]~P109(x76161)+~P106(f857(f60(x76161),x76163))+E(f14(x76161,f188(x76161),f857(f857(f308(x76161),x76162),x76163)),x76162)+~E(f857(f857(f3(f927(x76161,a915)),x76163),f857(f857(f308(x76161),x76162),f189(f927(x76161,a915)))),f189(f927(x76161,a915)))
% 15.02/14.80 [7617]~P109(x76171)+~P106(f857(f60(x76171),x76173))+E(f15(x76171,f233(x76171),f857(f857(f308(x76171),x76172),x76173)),x76172)+~E(f857(f857(f3(f927(x76171,a915)),x76173),f857(f857(f308(x76171),x76172),f189(f927(x76171,a915)))),f189(f927(x76171,a915)))
% 15.02/14.80 [7631]~P87(x76311)+~P106(f857(f857(f234(x76311),x76312),x76313))+~P106(f857(f857(f234(x76311),f857(f78(x76311),x76312)),x76313))+P106(f857(f857(f234(x76311),f857(f75(x76311),x76312)),x76313))
% 15.02/14.80 [7632]~P120(x76321)+~P106(f857(f857(f235(x76321),x76322),x76323))+~P106(f857(f857(f235(x76321),f857(f78(x76321),x76322)),x76323))+P106(f857(f857(f235(x76321),f857(f75(x76321),x76322)),x76323))
% 15.02/14.80 [7699]~P135(x76991)+P106(f857(f857(f235(x76991),f2(x76991)),x76992))+~P106(f857(f857(f235(x76991),f2(x76991)),x76993))+~P106(f857(f857(f235(x76991),f2(x76991)),f857(f857(f80(x76991),x76993),x76992)))
% 15.02/14.80 [7700]~P135(x77001)+P106(f857(f857(f235(x77001),f2(x77001)),x77002))+~P106(f857(f857(f235(x77001),f2(x77001)),x77003))+~P106(f857(f857(f235(x77001),f2(x77001)),f857(f857(f80(x77001),x77002),x77003)))
% 15.02/14.80 [7999]E(x79991,x79992)+~P106(f857(f60(x79993),x79991))+~P106(f857(f857(f234(a919),f857(f34(x79993),x79991)),f857(f34(x79993),x79992)))+~P106(f857(f857(f234(f927(x79993,a915)),x79992),x79991))
% 15.02/14.80 [8144]~P106(f857(f857(f235(a1),x81441),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x81442))+~P106(f857(f857(f234(a1),x81442),x81443))+P106(f857(f857(f234(a1),f857(f857(f35(a1),x81441),x81442)),f857(f857(f35(a1),x81441),x81443)))
% 15.02/14.80 [8154]~P106(f857(f857(f234(a1),f2(a1)),x81541))+~P106(f857(f857(f235(a1),f2(a1)),x81543))+~P106(f857(f857(f234(a1),x81543),x81542))+P106(f857(f857(f234(a1),f857(f857(f35(a1),x81541),x81542)),f857(f857(f35(a1),x81541),x81543)))
% 15.02/14.80 [8289]E(f857(x82891,f356(x82892,x82891,x82893)),x82892)+~P106(f857(f857(f234(a1),x82892),f857(x82891,x82893)))+P106(f857(f857(f235(a919),f357(x82892,x82891,x82893)),x82893))+~P106(f857(f857(f234(a1),f857(x82891,f2(a919))),x82892))
% 15.02/14.80 [8290]E(f857(x82901,f359(x82902,x82901,x82903)),x82902)+~P106(f857(f857(f234(a1),x82902),f857(x82901,x82903)))+P106(f857(f857(f235(a919),f360(x82902,x82901,x82903)),x82903))+~P106(f857(f857(f234(a1),f857(x82901,f2(a919))),x82902))
% 15.02/14.80 [8391]~P106(f857(f60(x83911),x83913))+~P106(f857(f857(f235(a919),f857(f34(x83911),x83912)),f857(f34(x83911),x83913)))+~P106(f857(f857(f234(f927(x83911,a915)),x83912),x83913))+P106(f857(f857(f235(f927(x83911,a915)),x83912),x83913))
% 15.02/14.80 [8418]E(f857(f857(f79(a1),f456(x84183,x84181,x84182)),f457(x84183,x84181,x84182)),x84181)+E(f857(f857(f3(a1),x84181),x84182),x84181)+~P106(f857(f857(f235(a1),f2(a1)),x84182))+~P106(f857(f857(f328(a1),f857(f857(f3(a1),x84181),f77(a1))),x84183))
% 15.02/14.80 [8419]E(f857(f857(f3(a1),f464(x84193,x84191,x84192)),f465(x84193,x84191,x84192)),x84191)+E(f857(f857(f79(a1),x84191),x84192),x84191)+~P106(f857(f857(f235(a1),f2(a1)),x84192))+~P106(f857(f857(f328(a1),f857(f857(f79(a1),x84191),f77(a1))),x84193))
% 15.02/14.80 [8470]~P106(f857(f857(f234(a919),x84703),x84701))+P106(f857(f857(f234(a919),x84701),x84702))+~P106(f857(f857(f234(a919),x84703),x84702))+~P106(f857(f857(f234(a919),f857(f857(f3(a919),x84701),x84703)),f857(f857(f3(a919),x84702),x84703)))
% 15.02/14.80 [8471]~P106(f857(f857(f234(a919),x84713),x84711))+P106(f857(f857(f235(a919),x84711),x84712))+~P106(f857(f857(f234(a919),x84713),x84712))+~P106(f857(f857(f235(a919),f857(f857(f3(a919),x84711),x84713)),f857(f857(f3(a919),x84712),x84713)))
% 15.02/14.80 [8490]~P109(x84902)+E(x84901,f113(x84902))+~P14(x84902,f857(f168(x84902),x84901))+E(f857(f142(x84902,x84902,f857(f9(x84902,x84902,x84902),f233(x84902)),x84903),f857(f168(x84902),x84901)),f857(f857(f233(x84902),f857(f857(f164(x84902),x84901),f2(a919))),x84903))
% 15.02/14.80 [8558]E(f857(f857(f3(a1),x85581),x85582),x85581)+~P106(f857(f857(f235(a1),f2(a1)),x85582))+P106(f857(f857(f328(a1),f456(x85583,x85581,x85582)),x85583))+~P106(f857(f857(f328(a1),f857(f857(f3(a1),x85581),f77(a1))),x85583))
% 15.02/14.80 [8559]E(f857(f857(f79(a1),x85591),x85592),x85591)+~P106(f857(f857(f235(a1),f2(a1)),x85592))+P106(f857(f857(f328(a1),f464(x85593,x85591,x85592)),x85593))+~P106(f857(f857(f328(a1),f857(f857(f79(a1),x85591),f77(a1))),x85593))
% 15.02/14.80 [8630]~P106(f857(f857(f234(a1),x86301),f857(x86302,x86303)))+P106(f857(f857(f235(a919),f357(x86301,x86302,x86303)),x86303))+P106(f857(f857(f234(a919),f356(x86301,x86302,x86303)),x86303))+~P106(f857(f857(f234(a1),f857(x86302,f2(a919))),x86301))
% 15.02/14.80 [8631]~P106(f857(f857(f234(a1),x86311),f857(x86312,x86313)))+P106(f857(f857(f235(a919),f360(x86311,x86312,x86313)),x86313))+P106(f857(f857(f234(a919),f359(x86311,x86312,x86313)),x86313))+~P106(f857(f857(f234(a1),f857(x86312,f2(a919))),x86311))
% 15.02/14.80 [8703]E(f857(f857(f3(a1),x87031),x87032),x87031)+~P106(f857(f857(f235(a1),f2(a1)),x87032))+P106(f857(f857(f328(a1),f457(x87033,x87031,x87032)),f302(a1,f77(a1),x87032)))+~P106(f857(f857(f328(a1),f857(f857(f3(a1),x87031),f77(a1))),x87033))
% 15.02/14.80 [8704]E(f857(f857(f79(a1),x87041),x87042),x87041)+~P106(f857(f857(f235(a1),f2(a1)),x87042))+P106(f857(f857(f328(a1),f465(x87043,x87041,x87042)),f302(a1,f77(a1),x87042)))+~P106(f857(f857(f328(a1),f857(f857(f79(a1),x87041),f77(a1))),x87043))
% 15.02/14.80 [8837]~P127(x88371)+~P106(f857(f857(f235(x88371),x88372),f77(x88371)))+~P106(f857(f857(f235(x88371),f2(x88371)),x88372))+P106(f857(f857(f235(x88371),f857(f857(f80(x88371),x88372),f857(f857(f243(x88371),x88372),x88373))),f857(f857(f243(x88371),x88372),x88373)))
% 15.02/14.80 [8930]~P106(f857(x89301,x89302))+P106(f857(x89301,f2(a919)))+~P106(f857(f857(f235(a919),x89302),x89303))+~P106(f857(x89301,f44(a919,f857(a112,f378(x89302,x89301,x89303)),x89303)))
% 15.02/14.80 [9082]E(f394(x90821,x90822,x90823),f2(a919))+P106(f857(f857(x90821,x90823),x90822))+P106(f857(f857(x90821,f394(x90821,x90822,x90823)),f44(a919,f393(x90821,x90822,x90823),f394(x90821,x90822,x90823))))+~P106(f857(f314(f926(a919,a919),a220),f857(f857(f251(a919,a919),x90823),x90822)))
% 15.02/14.80 [9118]~P26(x91181,x91181,x91182,x91183)+E(f857(f309(x91181,x91181,x91182),x91183),x91183)+~P106(f857(f60(x91181),x91183))+~P106(f857(f857(f234(f927(x91181,a915)),f857(f309(x91181,x91181,x91182),x91183)),x91183))
% 15.02/14.80 [9333]P106(f857(f857(x93331,x93332),x93333))+P106(f857(f857(f235(a1),f772(x93331,x93333,x93332)),f773(x93331,x93333,x93332)))+P106(f857(f857(x93331,f772(x93331,x93333,x93332)),f857(f857(f79(a1),f773(x93331,x93333,x93332)),f77(a1))))+~P106(f857(f314(f926(a1,a1),a133),f857(f857(f251(a1,a1),x93332),x93333)))
% 15.02/14.80 [9350]P106(f857(f857(x93501,x93502),x93503))+~P106(f857(f857(f235(a1),f404(x93501,x93503,x93502)),f2(a1)))+P106(f857(f857(x93501,f857(f78(a1),f402(x93501,x93503,x93502))),f857(f78(a1),f404(x93501,x93503,x93502))))+~P106(f857(f314(f926(a1,a1),a222),f857(f857(f251(a1,a1),x93502),x93503)))
% 15.02/14.80 [9539]P106(f857(f857(x95391,x95392),x95393))+P106(f857(f857(x95391,f857(f857(f79(a1),f676(x95391,x95393,x95392)),f77(a1))),f679(x95391,x95393,x95392)))+~P106(f857(f857(f234(a1),f676(x95391,x95393,x95392)),f679(x95391,x95393,x95392)))+~P106(f857(f314(f926(a1,a1),a182),f857(f857(f251(a1,a1),x95392),x95393)))
% 15.02/14.80 [9980]~P64(x99802)+~P64(x99801)+~P106(f857(f55(f926(x99801,x99802)),x99803))+P106(f857(f55(x99801),f857(f857(f10(f927(x99802,a915),a915,x99801),f55(x99802)),f857(f857(f10(f927(x99802,f926(x99801,x99802)),f927(x99802,a915),x99801),f857(f10(f926(x99801,x99802),a915,x99802),x99803)),f251(x99801,x99802)))))
% 15.02/14.80 [9981]~P64(x99812)+~P64(x99811)+~P106(f857(f56(f926(x99811,x99812)),x99813))+P106(f857(f56(x99811),f857(f857(f10(f927(x99812,a915),a915,x99811),f56(x99812)),f857(f857(f10(f927(x99812,f926(x99811,x99812)),f927(x99812,a915),x99811),f857(f10(f926(x99811,x99812),a915,x99812),x99813)),f251(x99811,x99812)))))
% 15.02/14.80 [10076]~P64(x100762)+~P64(x100761)+P106(f857(f55(f926(x100761,x100762)),x100763))+~P106(f857(f55(x100761),f857(f857(f10(f927(x100762,a915),a915,x100761),f55(x100762)),f857(f857(f10(f927(x100762,f926(x100761,x100762)),f927(x100762,a915),x100761),f857(f10(f926(x100761,x100762),a915,x100762),x100763)),f251(x100761,x100762)))))
% 15.02/14.80 [10077]~P64(x100772)+~P64(x100771)+P106(f857(f56(f926(x100771,x100772)),x100773))+~P106(f857(f56(x100771),f857(f857(f10(f927(x100772,a915),a915,x100771),f56(x100772)),f857(f857(f10(f927(x100772,f926(x100771,x100772)),f927(x100772,a915),x100771),f857(f10(f926(x100771,x100772),a915,x100772),x100773)),f251(x100771,x100772)))))
% 15.02/14.80 [10251]E(f857(x102511,f356(x102512,x102511,x102513)),x102512)+~P106(f857(f857(f234(a1),x102512),f857(x102511,x102513)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x102511,f857(f857(f79(a919),f357(x102512,x102511,x102513)),f77(a919)))),f857(x102511,f357(x102512,x102511,x102513))))),f77(a1)))+~P106(f857(f857(f234(a1),f857(x102511,f2(a919))),x102512))
% 15.02/14.80 [10252]E(f857(x102521,f359(x102522,x102521,x102523)),x102522)+~P106(f857(f857(f234(a1),x102522),f857(x102521,x102523)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x102521,f857(f857(f79(a919),f360(x102522,x102521,x102523)),f77(a919)))),f857(x102521,f360(x102522,x102521,x102523))))),f77(a1)))+~P106(f857(f857(f234(a1),f857(x102521,f2(a919))),x102522))
% 15.02/14.80 [10255]~P106(f857(f857(f234(a1),x102551),f857(x102552,x102553)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x102552,f857(f857(f79(a919),f357(x102551,x102552,x102553)),f77(a919)))),f857(x102552,f357(x102551,x102552,x102553))))),f77(a1)))+P106(f857(f857(f234(a919),f356(x102551,x102552,x102553)),x102553))+~P106(f857(f857(f234(a1),f857(x102552,f2(a919))),x102551))
% 15.02/14.80 [10256]~P106(f857(f857(f234(a1),x102561),f857(x102562,x102563)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x102562,f857(f857(f79(a919),f360(x102561,x102562,x102563)),f77(a919)))),f857(x102562,f360(x102561,x102562,x102563))))),f77(a1)))+P106(f857(f857(f234(a919),f359(x102561,x102562,x102563)),x102563))+~P106(f857(f857(f234(a1),f857(x102562,f2(a919))),x102561))
% 15.02/14.80 [10315]E(x103151,x103152)+~E(f857(f142(f920(x103153),f920(x103153),f134(x103153),f113(x103153)),x103151),f857(f142(f920(x103153),f920(x103153),f134(x103153),f113(x103153)),x103152))+~E(f857(f190(f920(f920(x103153))),x103151),f857(f190(f920(f920(x103153))),x103152))+~P106(f857(f857(f256(f920(x103153),f920(x103153),a915),f857(f857(f9(f920(x103153),f927(f920(x103153),a919),f927(f920(x103153),a915)),f857(f857(f10(f927(a919,a915),f927(f927(f920(x103153),a919),f927(f920(x103153),a915)),f920(x103153)),f10(a919,a915,f920(x103153))),f857(f857(f10(a919,f927(a919,a915),f920(x103153)),a324),f190(f920(x103153))))),f190(f920(x103153)))),f704(x103152,x103151,x103153)))
% 15.02/14.80 [10316]E(x103161,x103162)+~E(f857(f142(f920(x103163),f920(x103163),f134(x103163),f113(x103163)),x103161),f857(f142(f920(x103163),f920(x103163),f134(x103163),f113(x103163)),x103162))+~E(f857(f190(f920(f920(x103163))),x103161),f857(f190(f920(f920(x103163))),x103162))+~P106(f857(f857(f256(f920(x103163),f920(x103163),a915),f857(f857(f9(f920(x103163),f927(f920(x103163),a919),f927(f920(x103163),a915)),f857(f857(f10(f927(a919,a915),f927(f927(f920(x103163),a919),f927(f920(x103163),a915)),f920(x103163)),f10(a919,a915,f920(x103163))),f857(f857(f10(a919,f927(a919,a915),f920(x103163)),a324),f190(f920(x103163))))),f190(f920(x103163)))),f705(x103161,x103162,x103163)))
% 15.02/14.80 [7026]~E(f77(a919),f2(a919))+~P106(f857(f60(x70261),x70263))+~P106(f857(f60(x70261),x70262))+E(f857(f857(f79(a919),f857(f34(x70261),x70262)),f857(f34(x70261),x70263)),f857(f34(x70261),f857(f857(f110(f927(x70261,a915)),x70262),x70263)))
% 15.02/14.80 [7442]~P102(x74421)+~P106(f857(f60(x74421),x74422))+~P106(f857(f857(f328(x74421),x74423),x74422))+P106(f857(f857(f234(x74421),f857(f62(x74421,f101(x74421)),x74422)),x74423))
% 15.02/14.80 [7443]~P109(x74431)+~P106(f857(f60(x74431),x74432))+~P106(f857(f857(f328(x74431),x74433),x74432))+P106(f857(f857(f234(x74431),f857(f62(x74431,f188(x74431)),x74432)),x74433))
% 15.02/14.80 [7693]~P106(f857(f60(x76931),x76933))+~P106(f857(f60(x76931),x76932))+~E(f857(f857(f101(f927(x76931,a915)),x76932),x76933),f189(f927(x76931,a915)))+E(f857(f857(f79(a919),f857(f34(x76931),x76932)),f857(f34(x76931),x76933)),f857(f34(x76931),f857(f857(f110(f927(x76931,a915)),x76932),x76933)))
% 15.02/14.80 [8476]~P39(x84761,x84763)+~P39(x84761,x84762)+~E(f857(f857(f101(f927(x84761,a915)),f857(f263(x84761,x84761),x84762)),f857(f283(x84761,x84761),x84763)),f189(f927(x84761,a915)))+P39(x84761,f857(f857(f110(f927(f926(x84761,x84761),a915)),x84762),x84763))
% 15.02/14.80 [8570]E(x85701,f857(f857(f35(a919),x85702),x85703))+~P106(f857(f857(f235(a919),f2(a919)),x85703))+~P106(f857(f857(f235(a919),x85702),f857(f857(f80(a919),x85703),f857(a112,x85701))))+~P106(f857(f857(f234(a919),f857(f857(f80(a919),x85703),x85701)),x85702))
% 15.02/14.80 [8701]~P106(f857(f60(x87011),x87012))+~P106(f857(f60(x87011),x87013))+E(f857(f857(f79(a919),f857(f34(x87011),x87012)),f857(f34(x87011),x87013)),f857(f34(x87011),f857(f857(f110(f927(x87011,a915)),x87012),x87013)))+P106(f857(f857(f328(x87011),f899(x87013,x87012,x87011)),f857(f857(f101(f927(x87011,a915)),x87012),x87013)))
% 15.02/14.80 [9094]~P129(x90942)+~E(x90941,f2(x90942))+~E(x90943,f2(x90942))+~P106(f857(f857(f235(x90942),f2(x90942)),f857(f857(f79(x90942),f857(f857(f80(x90942),x90943),x90943)),f857(f857(f80(x90942),x90941),x90941))))
% 15.02/14.80 [9620]~P39(x96201,x96203)+~P39(x96201,x96202)+P39(x96201,f857(f857(f110(f927(f926(x96201,x96201),a915)),x96202),x96203))+~P106(f857(f857(f234(f927(f926(x96201,x96201),a915)),f857(f857(f288(x96201,x96201,x96201),x96202),x96203)),x96202))
% 15.02/14.80 [9756]~P106(f857(x97561,x97563))+~P106(f857(f60(x97562),x97563))+P106(f857(x97561,f189(f927(x97562,a915))))+~P106(f857(x97561,f857(f857(f3(f927(x97562,a915)),f493(x97561,x97563,x97562)),f857(f857(f308(x97562),f484(x97561,x97563,x97562)),f189(f927(x97562,a915))))))
% 15.02/14.80 [8877]~P106(f857(f857(f235(a1),f2(a1)),x88773))+P106(f857(f857(f234(a1),f2(a1)),x88771))+~P106(f857(f857(f235(a1),x88772),x88773))+~P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),f857(f857(f80(a1),x88773),x88771)),x88772)))
% 15.02/14.80 [8901]~P2(x89011)+~P106(f857(f60(x89011),x89012))+E(f857(f857(f3(f927(x89011,a915)),x89012),f857(f857(f308(x89011),x89013),f189(f927(x89011,a915)))),f189(f927(x89011,a915)))+E(f857(f857(f110(x89011),x89013),f12(x89011,f857(f857(f3(f927(x89011,a915)),x89012),f857(f857(f308(x89011),x89013),f189(f927(x89011,a915)))))),f12(x89011,f857(f857(f308(x89011),x89013),x89012)))
% 15.02/14.80 [8902]~P2(x89021)+~P106(f857(f60(x89021),x89022))+E(f857(f857(f3(f927(x89021,a915)),x89022),f857(f857(f308(x89021),x89023),f189(f927(x89021,a915)))),f189(f927(x89021,a915)))+E(f857(f857(f101(x89021),x89023),f13(x89021,f857(f857(f3(f927(x89021,a915)),x89022),f857(f857(f308(x89021),x89023),f189(f927(x89021,a915)))))),f13(x89021,f857(f857(f308(x89021),x89023),x89022)))
% 15.02/14.80 [8903]~P109(x89031)+~P106(f857(f60(x89031),x89032))+E(f857(f857(f3(f927(x89031,a915)),x89032),f857(f857(f308(x89031),x89033),f189(f927(x89031,a915)))),f189(f927(x89031,a915)))+E(f857(f857(f188(x89031),x89033),f16(x89031,f857(f857(f3(f927(x89031,a915)),x89032),f857(f857(f308(x89031),x89033),f189(f927(x89031,a915)))))),f16(x89031,f857(f857(f308(x89031),x89033),x89032)))
% 15.02/14.80 [8904]~P109(x89041)+~P106(f857(f60(x89041),x89042))+E(f857(f857(f3(f927(x89041,a915)),x89042),f857(f857(f308(x89041),x89043),f189(f927(x89041,a915)))),f189(f927(x89041,a915)))+E(f857(f857(f233(x89041),x89043),f17(x89041,f857(f857(f3(f927(x89041,a915)),x89042),f857(f857(f308(x89041),x89043),f189(f927(x89041,a915)))))),f17(x89041,f857(f857(f308(x89041),x89043),x89042)))
% 15.02/14.80 [8976]~P109(x89761)+~P106(f857(f60(x89761),x89762))+E(f857(f857(f3(f927(x89761,a915)),x89762),f857(f857(f308(x89761),x89763),f189(f927(x89761,a915)))),f189(f927(x89761,a915)))+E(f857(f857(f188(x89761),x89763),f14(x89761,f188(x89761),f857(f857(f3(f927(x89761,a915)),x89762),f857(f857(f308(x89761),x89763),f189(f927(x89761,a915)))))),f14(x89761,f188(x89761),f857(f857(f308(x89761),x89763),x89762)))
% 15.02/14.80 [8977]~P109(x89771)+~P106(f857(f60(x89771),x89772))+E(f857(f857(f3(f927(x89771,a915)),x89772),f857(f857(f308(x89771),x89773),f189(f927(x89771,a915)))),f189(f927(x89771,a915)))+E(f857(f857(f233(x89771),x89773),f15(x89771,f233(x89771),f857(f857(f3(f927(x89771,a915)),x89772),f857(f857(f308(x89771),x89773),f189(f927(x89771,a915)))))),f15(x89771,f233(x89771),f857(f857(f308(x89771),x89773),x89772)))
% 15.02/14.80 [9558]E(x95581,x95582)+~E(f857(f142(f920(x95583),f920(x95583),f134(x95583),f113(x95583)),x95581),f857(f142(f920(x95583),f920(x95583),f134(x95583),f113(x95583)),x95582))+~E(f857(f190(f920(f920(x95583))),x95581),f857(f190(f920(f920(x95583))),x95582))+P106(f857(f857(f328(f926(f920(x95583),f920(x95583))),f704(x95582,x95581,x95583)),f857(f172(f926(f920(x95583),f920(x95583))),f857(f857(f181(f920(x95583),f920(x95583)),x95581),x95582))))
% 15.02/14.80 [9559]E(x95591,x95592)+~E(f857(f142(f920(x95593),f920(x95593),f134(x95593),f113(x95593)),x95591),f857(f142(f920(x95593),f920(x95593),f134(x95593),f113(x95593)),x95592))+~E(f857(f190(f920(f920(x95593))),x95591),f857(f190(f920(f920(x95593))),x95592))+P106(f857(f857(f328(f926(f920(x95593),f920(x95593))),f705(x95591,x95592,x95593)),f857(f172(f926(f920(x95593),f920(x95593))),f857(f857(f181(f920(x95593),f920(x95593)),x95592),x95591))))
% 15.02/14.80 [10425]~P99(x104252)+E(x104251,f189(f927(x104252,a915)))+~P106(f857(f60(x104252),x104251))+E(f13(x104252,f857(f261(x104252),f857(f857(f10(f927(x104252,a915),a915,x104252),f86(x104252)),f857(f857(f9(x104252,f927(x104252,a915),f927(x104252,a915)),f857(f857(f10(f927(x104252,f927(a915,a915)),f927(f927(x104252,a915),f927(x104252,a915)),x104252),f20(x104252,a915,a915)),f857(f857(f10(f927(x104252,a915),f927(x104252,f927(a915,a915)),x104252),f857(f10(a915,f927(a915,a915),x104252),a325)),f857(f857(f9(x104252,f927(x104252,x104252),f927(x104252,a915)),f857(f857(f10(f927(x104252,a915),f927(f927(x104252,x104252),f927(x104252,a915)),x104252),f10(x104252,a915,x104252)),a324)),f857(f110(x104252),x104253))))),f857(f857(f9(x104252,f927(x104252,a915),a915),f328(x104252)),x104251))))),f857(f857(f110(x104252),x104253),f13(x104252,x104251)))
% 15.02/14.80 [10426]~P99(x104262)+E(x104261,f189(f927(x104262,a915)))+~P106(f857(f60(x104262),x104261))+E(f12(x104262,f857(f261(x104262),f857(f857(f10(f927(x104262,a915),a915,x104262),f86(x104262)),f857(f857(f9(x104262,f927(x104262,a915),f927(x104262,a915)),f857(f857(f10(f927(x104262,f927(a915,a915)),f927(f927(x104262,a915),f927(x104262,a915)),x104262),f20(x104262,a915,a915)),f857(f857(f10(f927(x104262,a915),f927(x104262,f927(a915,a915)),x104262),f857(f10(a915,f927(a915,a915),x104262),a325)),f857(f857(f9(x104262,f927(x104262,x104262),f927(x104262,a915)),f857(f857(f10(f927(x104262,a915),f927(f927(x104262,x104262),f927(x104262,a915)),x104262),f10(x104262,a915,x104262)),a324)),f857(f101(x104262),x104263))))),f857(f857(f9(x104262,f927(x104262,a915),a915),f328(x104262)),x104261))))),f857(f857(f101(x104262),x104263),f12(x104262,x104261)))
% 15.02/14.80 [10427]~P79(x104272)+E(x104271,f189(f927(x104272,a915)))+~P106(f857(f60(x104272),x104271))+E(f16(x104272,f857(f261(x104272),f857(f857(f10(f927(x104272,a915),a915,x104272),f86(x104272)),f857(f857(f9(x104272,f927(x104272,a915),f927(x104272,a915)),f857(f857(f10(f927(x104272,f927(a915,a915)),f927(f927(x104272,a915),f927(x104272,a915)),x104272),f20(x104272,a915,a915)),f857(f857(f10(f927(x104272,a915),f927(x104272,f927(a915,a915)),x104272),f857(f10(a915,f927(a915,a915),x104272),a325)),f857(f857(f9(x104272,f927(x104272,x104272),f927(x104272,a915)),f857(f857(f10(f927(x104272,a915),f927(f927(x104272,x104272),f927(x104272,a915)),x104272),f10(x104272,a915,x104272)),a324)),f857(f79(x104272),x104273))))),f857(f857(f9(x104272,f927(x104272,a915),a915),f328(x104272)),x104271))))),f857(f857(f79(x104272),x104273),f16(x104272,x104271)))
% 15.02/14.80 [10428]~P79(x104282)+E(x104281,f189(f927(x104282,a915)))+~P106(f857(f60(x104282),x104281))+E(f17(x104282,f857(f261(x104282),f857(f857(f10(f927(x104282,a915),a915,x104282),f86(x104282)),f857(f857(f9(x104282,f927(x104282,a915),f927(x104282,a915)),f857(f857(f10(f927(x104282,f927(a915,a915)),f927(f927(x104282,a915),f927(x104282,a915)),x104282),f20(x104282,a915,a915)),f857(f857(f10(f927(x104282,a915),f927(x104282,f927(a915,a915)),x104282),f857(f10(a915,f927(a915,a915),x104282),a325)),f857(f857(f9(x104282,f927(x104282,x104282),f927(x104282,a915)),f857(f857(f10(f927(x104282,a915),f927(f927(x104282,x104282),f927(x104282,a915)),x104282),f10(x104282,a915,x104282)),a324)),f857(f79(x104282),x104283))))),f857(f857(f9(x104282,f927(x104282,a915),a915),f328(x104282)),x104281))))),f857(f857(f79(x104282),x104283),f17(x104282,x104281)))
% 15.02/14.80 [10429]~P109(x104292)+E(x104291,f189(f927(x104292,a915)))+~P106(f857(f60(x104292),x104291))+E(f15(x104292,f233(x104292),f857(f261(x104292),f857(f857(f10(f927(x104292,a915),a915,x104292),f86(x104292)),f857(f857(f9(x104292,f927(x104292,a915),f927(x104292,a915)),f857(f857(f10(f927(x104292,f927(a915,a915)),f927(f927(x104292,a915),f927(x104292,a915)),x104292),f20(x104292,a915,a915)),f857(f857(f10(f927(x104292,a915),f927(x104292,f927(a915,a915)),x104292),f857(f10(a915,f927(a915,a915),x104292),a325)),f857(f857(f9(x104292,f927(x104292,x104292),f927(x104292,a915)),f857(f857(f10(f927(x104292,a915),f927(f927(x104292,x104292),f927(x104292,a915)),x104292),f10(x104292,a915,x104292)),a324)),f857(f188(x104292),x104293))))),f857(f857(f9(x104292,f927(x104292,a915),a915),f328(x104292)),x104291))))),f857(f857(f188(x104292),x104293),f15(x104292,f233(x104292),x104291)))
% 15.02/14.80 [10430]~P109(x104302)+E(x104301,f189(f927(x104302,a915)))+~P106(f857(f60(x104302),x104301))+E(f14(x104302,f188(x104302),f857(f261(x104302),f857(f857(f10(f927(x104302,a915),a915,x104302),f86(x104302)),f857(f857(f9(x104302,f927(x104302,a915),f927(x104302,a915)),f857(f857(f10(f927(x104302,f927(a915,a915)),f927(f927(x104302,a915),f927(x104302,a915)),x104302),f20(x104302,a915,a915)),f857(f857(f10(f927(x104302,a915),f927(x104302,f927(a915,a915)),x104302),f857(f10(a915,f927(a915,a915),x104302),a325)),f857(f857(f9(x104302,f927(x104302,x104302),f927(x104302,a915)),f857(f857(f10(f927(x104302,a915),f927(f927(x104302,x104302),f927(x104302,a915)),x104302),f10(x104302,a915,x104302)),a324)),f857(f233(x104302),x104303))))),f857(f857(f9(x104302,f927(x104302,a915),a915),f328(x104302)),x104301))))),f857(f857(f233(x104302),x104303),f14(x104302,f188(x104302),x104301)))
% 15.02/14.80 [10142]~P120(x101421)+~E(x101423,f2(x101421))+~E(x101422,f2(x101421))+E(f857(f857(f79(x101421),f857(f857(f243(x101421),x101422),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x101421),x101423),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f2(x101421))
% 15.02/14.80 [10296]~P127(x102961)+~P106(f857(f857(f234(x102961),f2(x102961)),x102963))+P106(f857(f857(f234(x102961),x102962),x102963))+~P106(f857(f857(f234(x102961),f857(f857(f243(x102961),x102962),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x102961),x102963),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))))
% 15.02/14.80 [10354]~P120(x103542)+~E(x103541,f2(x103542))+~E(x103543,f2(x103542))+~P106(f857(f857(f235(x103542),f2(x103542)),f857(f857(f79(x103542),f857(f857(f243(x103542),x103543),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97))))),f857(f857(f243(x103542),x103541),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))))
% 15.02/14.80 [6906]~P8(x69063,x69062)+~P106(f857(x69061,x69064))+~P106(f857(f857(f328(x69063),x69064),f269(x69063,x69062)))+P106(f857(x69061,f820(x69061,x69062,x69063)))
% 15.02/14.80 [8812]P27(x88121,x88122,f824(x88123,x88122,x88124,x88121),x88124,x88123)+~E(f857(f34(x88121),x88124),f857(f34(x88122),x88123))+~P106(f857(f60(x88122),x88123))+~P106(f857(f60(x88121),x88124))
% 15.02/14.80 [9521]E(x95211,x95212)+~E(f657(x95211,x95212,x95214,x95213),f658(x95211,x95212,x95214,x95213))+P106(f857(f857(f328(f926(f920(x95213),f920(x95213))),f857(f857(f251(f920(x95213),f920(x95213)),x95212),x95211)),f147(x95213,x95214)))+P106(f857(f857(f328(f926(f920(x95213),f920(x95213))),f857(f857(f251(f920(x95213),f920(x95213)),x95211),x95212)),f147(x95213,x95214)))
% 15.02/14.80 [5042]~P65(x50422)+~E(x50424,f2(x50422))+~E(x50421,f2(x50422))+E(x50421,f857(f857(f290(x50422),x50423),x50424))
% 15.02/14.80 [5043]~P65(x50431)+~E(x50433,f2(x50431))+~E(x50434,f2(x50431))+E(f857(f857(f290(x50431),x50432),x50433),x50434)
% 15.02/14.80 [5159]~P65(x51592)+E(x51591,f2(x51592))+~E(x51593,f2(x51592))+~E(x51591,f857(f857(f290(x51592),x51594),x51593))
% 15.02/14.80 [5160]~P65(x51602)+E(x51601,f2(x51602))+~E(x51603,f2(x51602))+~E(f857(f857(f290(x51602),x51604),x51603),x51601)
% 15.02/14.80 [5342]~P124(x53422)+E(x53421,f2(x53422))+~E(f857(f857(f290(x53422),x53423),x53421),x53424)+E(x53423,f857(f857(f80(x53422),x53424),x53421))
% 15.02/14.80 [5344]~P124(x53442)+E(x53441,f2(x53442))+~E(f857(f857(f80(x53442),x53443),x53441),x53444)+E(x53443,f857(f857(f290(x53442),x53444),x53441))
% 15.02/14.80 [5345]~P65(x53452)+E(x53451,f2(x53452))+~E(f857(f857(f290(x53452),x53453),x53451),x53454)+E(x53453,f857(f857(f80(x53452),x53454),x53451))
% 15.02/14.80 [5346]~P65(x53462)+E(x53461,f2(x53462))+~E(f857(f857(f80(x53462),x53463),x53461),x53464)+E(x53463,f857(f857(f290(x53462),x53464),x53461))
% 15.02/14.80 [5347]~P124(x53472)+E(x53471,f2(x53472))+~E(x53473,f857(f857(f290(x53472),x53474),x53471))+E(f857(f857(f80(x53472),x53473),x53471),x53474)
% 15.02/14.80 [5349]~P124(x53492)+E(x53491,f2(x53492))+~E(x53493,f857(f857(f80(x53492),x53494),x53491))+E(f857(f857(f290(x53492),x53493),x53491),x53494)
% 15.02/14.80 [5350]~P65(x53502)+E(x53501,f2(x53502))+~E(x53503,f857(f857(f290(x53502),x53504),x53501))+E(f857(f857(f80(x53502),x53503),x53501),x53504)
% 15.02/14.80 [5351]~P65(x53512)+E(x53511,f2(x53512))+~E(x53513,f857(f857(f80(x53512),x53514),x53511))+E(f857(f857(f290(x53512),x53513),x53511),x53514)
% 15.02/14.80 [5375]~P65(x53752)+~E(x53751,f2(x53752))+~E(f857(f857(f80(x53752),x53751),x53754),x53753)+E(x53751,f857(f857(f290(x53752),x53753),x53754))
% 15.02/14.80 [5376]~P65(x53761)+~E(x53764,f2(x53761))+~E(x53762,f857(f857(f80(x53761),x53764),x53763))+E(f857(f857(f290(x53761),x53762),x53763),x53764)
% 15.02/14.80 [5450]~E(x54503,x54504)+~E(x54502,x54503)+~P110(x54501)+E(f302(x54501,x54502,x54503),f857(f857(f308(x54501),x54504),f189(f927(x54501,a915))))
% 15.02/14.80 [5657]~E(f114(x56572,x56571),x56573)+~E(f144(x56572,x56571),x56574)+E(x56571,f113(x56572))+E(f857(f857(f134(x56572),x56573),f857(f857(f151(x56572),x56574),f113(x56572))),x56571)
% 15.02/14.80 [6295]~P127(x62953)+E(x62951,x62952)+~E(f857(f857(f243(x62953),x62954),x62951),f857(f857(f243(x62953),x62954),x62952))+~P106(f857(f857(f235(x62953),f77(x62953)),x62954))
% 15.02/14.80 [6296]E(x62961,x62962)+~E(f857(f857(f308(x62963),x62964),x62961),f857(f857(f308(x62963),x62964),x62962))+P106(f857(f857(f328(x62963),x62964),x62962))+P106(f857(f857(f328(x62963),x62964),x62961))
% 15.02/14.80 [6339]E(f857(x63391,x63392),f77(a919))+~E(f857(f857(f11(x63393,a919),x63391),x63394),f77(a919))+~P106(f857(f60(x63393),x63394))+~P106(f857(f857(f328(x63393),x63392),x63394))
% 15.02/14.80 [6340]E(f857(x63401,x63402),f2(a919))+~E(f857(f857(f8(x63403,a919),x63401),x63404),f2(a919))+~P106(f857(f60(x63403),x63404))+~P106(f857(f857(f328(x63403),x63402),x63404))
% 15.02/14.80 [6562]~P110(x65621)+~P106(f857(f857(f234(x65621),x65624),x65623))+P106(f857(f857(f234(x65621),x65622),x65623))+~P106(f857(f857(f234(x65621),x65622),x65624))
% 15.02/14.80 [6563]~P107(x65631)+~P106(f857(f857(f234(x65631),x65632),x65634))+P106(f857(f857(f234(x65631),x65632),x65633))+~P106(f857(f857(f234(x65631),x65634),x65633))
% 15.02/14.80 [6564]~P110(x65641)+~P106(f857(f857(f235(x65641),x65644),x65643))+P106(f857(f857(f235(x65641),x65642),x65643))+~P106(f857(f857(f234(x65641),x65642),x65644))
% 15.02/14.80 [6565]~P110(x65651)+~P106(f857(f857(f235(x65651),x65652),x65654))+P106(f857(f857(f235(x65651),x65652),x65653))+~P106(f857(f857(f234(x65651),x65654),x65653))
% 15.02/14.80 [6566]~P110(x65661)+~P106(f857(f857(f235(x65661),x65664),x65663))+P106(f857(f857(f235(x65661),x65662),x65663))+~P106(f857(f857(f235(x65661),x65662),x65664))
% 15.02/14.80 [6567]~P107(x65671)+~P106(f857(f857(f235(x65671),x65672),x65674))+P106(f857(f857(f235(x65671),x65672),x65673))+~P106(f857(f857(f234(x65671),x65674),x65673))
% 15.02/14.80 [6568]~P107(x65681)+~P106(f857(f857(f235(x65681),x65684),x65683))+P106(f857(f857(f235(x65681),x65682),x65683))+~P106(f857(f857(f234(x65681),x65682),x65684))
% 15.02/14.80 [6569]~P107(x65691)+~P106(f857(f857(f235(x65691),x65692),x65694))+P106(f857(f857(f235(x65691),x65692),x65693))+~P106(f857(f857(f235(x65691),x65694),x65693))
% 15.02/14.80 [6570]~P113(x65701)+~P106(f857(f857(f286(x65701),x65702),x65704))+P106(f857(f857(f286(x65701),x65702),x65703))+~P106(f857(f857(f286(x65701),x65704),x65703))
% 15.02/14.80 [6649]~P37(x66494,x66493,x66492)+E(x66491,f758(x66492,x66493,x66494))+~P106(f857(x66493,x66491))+~P106(f857(f857(f328(x66494),x66491),f857(f172(x66494),x66492)))
% 15.02/14.80 [6650]~P37(x66504,x66503,x66502)+E(x66501,f768(x66502,x66503,x66504))+~P106(f857(x66503,x66501))+~P106(f857(f857(f328(x66504),x66501),f857(f172(x66504),x66502)))
% 15.02/14.80 [6800]~P6(x68001)+~P106(f857(f857(f234(x68001),x68002),f37(x68001,x68004)))+P106(f857(f857(f234(x68001),x68002),x68003))+~P106(f857(f857(f328(x68001),x68003),x68004))
% 15.02/14.80 [6948]~P109(x69481)+~P14(x69481,f857(f857(f151(x69481),x69482),x69484))+~P106(f857(f857(f328(x69481),x69483),f857(f172(x69481),x69484)))+P106(f857(f857(f234(x69481),x69482),x69483))
% 15.02/14.80 [7036]~P6(x70361)+~P106(f857(f857(f234(x70361),f36(x70361,x70364)),x70363))+P106(f857(f857(f234(x70361),x70362),x70363))+~P106(f857(f857(f328(x70361),x70362),x70364))
% 15.02/14.80 [7445]~P109(x74451)+E(f857(f857(f110(f927(x74451,a915)),f857(f301(x74451,x74452),x74453)),f857(f301(x74451,x74453),x74454)),f857(f301(x74451,x74452),x74454))+~P106(f857(f857(f234(x74451),x74453),x74454))+~P106(f857(f857(f234(x74451),x74452),x74453))
% 15.02/14.80 [7489]P37(x74891,x74892,x74893)+~E(f769(x74893,x74892,x74891,x74894),x74894)+~P106(f857(x74892,x74894))+~P106(f857(f857(f328(x74891),x74894),f857(f172(x74891),x74893)))
% 15.02/14.80 [7490]P37(x74901,x74902,x74903)+~E(f776(x74903,x74902,x74901,x74904),x74904)+~P106(f857(x74902,x74904))+~P106(f857(f857(f328(x74901),x74904),f857(f172(x74901),x74903)))
% 15.02/14.80 [7564]~P109(x75641)+E(f857(f857(f110(f927(x75641,a915)),f857(f301(x75641,x75642),x75643)),f302(x75641,x75643,x75644)),f302(x75641,x75642,x75644))+~P106(f857(f857(f234(x75641),x75643),x75644))+~P106(f857(f857(f234(x75641),x75642),x75643))
% 15.02/14.80 [7626]~P109(x76261)+E(f857(f857(f110(f927(x76261,a915)),f305(x76261,x76262,x76263)),f857(f301(x76261,x76263),x76264)),f305(x76261,x76262,x76264))+~P106(f857(f857(f234(x76261),x76263),x76264))+~P106(f857(f857(f235(x76261),x76262),x76263))
% 15.02/14.80 [7643]~P109(x76431)+E(f857(f857(f110(f927(x76431,a915)),f302(x76431,x76432,x76433)),f305(x76431,x76433,x76434)),f857(f301(x76431,x76432),x76434))+~P106(f857(f857(f234(x76431),x76432),x76433))+~P106(f857(f857(f235(x76431),x76433),x76434))
% 15.02/14.80 [7674]~P109(x76741)+E(f857(f857(f110(f927(x76741,a915)),f302(x76741,x76742,x76743)),f304(x76741,x76743,x76744)),f302(x76741,x76742,x76744))+~P106(f857(f857(f234(x76741),x76743),x76744))+~P106(f857(f857(f234(x76741),x76742),x76743))
% 15.02/14.80 [7675]~P109(x76751)+E(f857(f857(f110(f927(x76751,a915)),f305(x76751,x76752,x76753)),f302(x76751,x76753,x76754)),f304(x76751,x76752,x76754))+~P106(f857(f857(f234(x76751),x76753),x76754))+~P106(f857(f857(f235(x76751),x76752),x76753))
% 15.02/14.80 [7676]~P109(x76761)+E(f857(f857(f110(f927(x76761,a915)),f304(x76761,x76762,x76763)),f305(x76761,x76763,x76764)),f305(x76761,x76762,x76764))+~P106(f857(f857(f234(x76761),x76762),x76763))+~P106(f857(f857(f235(x76761),x76763),x76764))
% 15.02/14.80 [7677]~P109(x76771)+E(f857(f857(f110(f927(x76771,a915)),f304(x76771,x76772,x76773)),f304(x76771,x76773,x76774)),f304(x76771,x76772,x76774))+~P106(f857(f857(f234(x76771),x76773),x76774))+~P106(f857(f857(f234(x76771),x76772),x76773))
% 15.02/14.80 [8460]P26(x84601,x84602,f505(x84603,x84602,x84604,x84601),x84604)+~P106(f857(f60(x84602),x84603))+~P106(f857(f60(x84601),x84604))+~P106(f857(f857(f234(a919),f857(f34(x84601),x84604)),f857(f34(x84602),x84603)))
% 15.02/14.80 [8481]P37(x84811,x84812,x84813)+~P106(f857(x84812,x84814))+P106(f857(x84812,f769(x84813,x84812,x84811,x84814)))+~P106(f857(f857(f328(x84811),x84814),f857(f172(x84811),x84813)))
% 15.02/14.80 [8482]P37(x84821,x84822,x84823)+~P106(f857(x84822,x84824))+P106(f857(x84822,f776(x84823,x84822,x84821,x84824)))+~P106(f857(f857(f328(x84821),x84824),f857(f172(x84821),x84823)))
% 15.02/14.80 [8536]~P77(x85361)+~E(f857(x85363,f888(x85363,x85364,x85362,x85361)),f77(x85361))+E(f857(f857(f857(f64(x85361,x85362,f80(x85361)),x85363),f77(x85361)),x85364),f77(x85361))+~P106(f857(f60(x85362),x85364))
% 15.02/14.80 [8801]~P127(x88011)+~P106(f857(f857(f234(x88011),f2(x88011)),x88013))+P106(f857(f857(f234(x88011),x88012),x88013))+~P106(f857(f857(f234(x88011),f857(f857(f243(x88011),x88012),f857(a112,x88014))),f857(f857(f243(x88011),x88013),f857(a112,x88014))))
% 15.02/14.80 [9119]P37(x91191,x91192,x91193)+~P106(f857(x91192,x91194))+~P106(f857(f857(f328(x91191),x91194),f857(f172(x91191),x91193)))+P106(f857(f857(f328(x91191),f769(x91193,x91192,x91191,x91194)),f857(f172(x91191),x91193)))
% 15.02/14.80 [9120]P37(x91201,x91202,x91203)+~P106(f857(x91202,x91204))+~P106(f857(f857(f328(x91201),x91204),f857(f172(x91201),x91203)))+P106(f857(f857(f328(x91201),f776(x91203,x91202,x91201,x91204)),f857(f172(x91201),x91203)))
% 15.02/14.80 [9196]~P77(x91961)+E(f857(f857(f857(f64(x91961,x91962,f80(x91961)),x91963),f77(x91961)),x91964),f77(x91961))+~P106(f857(f60(x91962),x91964))+P106(f857(f857(f328(x91962),f888(x91963,x91964,x91962,x91961)),x91964))
% 15.02/14.80 [9693]~P106(f857(f857(f286(a919),x96931),x96933))+~P106(f857(f857(f286(a919),x96931),x96932))+~P106(f857(f857(f286(a919),x96934),x96933))+~P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x96931,x96933)),f289(a919,f286(a919),x96932,x96934)))
% 15.02/14.80 [9698]~P106(f857(f857(f234(a1),x96984),f2(a1)))+P106(f857(f857(f234(a1),f857(f857(f79(a1),f857(f857(f80(a1),x96981),f44(a1,x96982,x96983))),x96984)),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x96983))+~P106(f857(f857(f235(a1),x96981),x96984))
% 15.02/14.80 [10135]~P106(f857(f60(x101351),x101352))+~P106(f857(f857(f328(x101351),x101354),x101352))+~P106(f857(f857(f328(x101351),x101353),x101352))+P106(f857(f857(f235(a919),f857(f34(x101351),f857(f857(f3(f927(x101351,a915)),f857(f857(f3(f927(x101351,a915)),x101352),f857(f857(f308(x101351),x101353),f189(f927(x101351,a915))))),f857(f857(f308(x101351),x101354),f189(f927(x101351,a915)))))),f857(f34(x101351),x101352)))
% 15.02/14.80 [7094]~P147(x70943)+~P123(x70943)+P106(f857(x70941,f853(x70942,x70941,x70943)))+~P106(f857(x70941,f857(f857(f80(x70943),x70942),x70944)))
% 15.02/14.80 [7152]~P102(x71521)+~P106(f857(f857(f234(x71521),x71522),x71524))+~P106(f857(f857(f234(x71521),x71522),x71523))+P106(f857(f857(f234(x71521),x71522),f857(f857(f101(x71521),x71523),x71524)))
% 15.02/14.80 [7155]~P109(x71551)+~P106(f857(f857(f234(x71551),x71552),x71554))+~P106(f857(f857(f234(x71551),x71552),x71553))+P106(f857(f857(f234(x71551),x71552),f857(f857(f188(x71551),x71553),x71554)))
% 15.02/14.80 [7156]~P109(x71561)+~P106(f857(f857(f235(x71561),x71562),x71564))+~P106(f857(f857(f235(x71561),x71562),x71563))+P106(f857(f857(f235(x71561),x71562),f857(f857(f188(x71561),x71563),x71564)))
% 15.02/14.80 [7157]~P115(x71571)+~P106(f857(f857(f286(x71571),x71572),x71574))+~P106(f857(f857(f286(x71571),x71572),x71573))+P106(f857(f857(f286(x71571),x71572),f857(f857(f3(x71571),x71573),x71574)))
% 15.02/14.80 [7177]~P66(x71772)+E(x71771,f2(x71772))+E(f857(f857(f290(x71772),f857(f857(f243(x71772),x71771),x71773)),f857(f857(f243(x71772),x71771),x71774)),f857(f857(f243(x71772),x71771),f857(f857(f3(a919),x71773),x71774)))+~P106(f857(f857(f234(a919),x71774),x71773))
% 15.02/14.80 [7221]~P109(x72211)+~P14(x72211,f857(f857(f151(x72211),x72213),x72214))+P14(x72211,f857(f857(f151(x72211),x72212),f857(f857(f151(x72211),x72213),x72214)))+~P106(f857(f857(f234(x72211),x72212),x72213))
% 15.02/14.80 [7259]~P89(x72591)+~P106(f857(f857(f234(x72591),f2(x72591)),x72594))+~P106(f857(f857(f234(x72591),x72592),x72593))+P106(f857(f857(f234(x72591),x72592),f857(f857(f79(x72591),x72593),x72594)))
% 15.02/14.80 [7260]~P89(x72601)+~P106(f857(f857(f234(x72601),f2(x72601)),x72603))+~P106(f857(f857(f234(x72601),x72602),x72604))+P106(f857(f857(f234(x72601),x72602),f857(f857(f79(x72601),x72603),x72604)))
% 15.02/14.80 [7261]~P127(x72611)+~P106(f857(f857(f235(x72611),f2(x72611)),x72613))+~P106(f857(f857(f235(x72611),x72612),x72614))+P106(f857(f857(f235(x72611),x72612),f857(f857(f79(x72611),x72613),x72614)))
% 15.02/14.80 [7262]~P89(x72621)+~P106(f857(f857(f234(x72621),x72622),x72624))+~P106(f857(f857(f235(x72621),f2(x72621)),x72623))+P106(f857(f857(f235(x72621),x72622),f857(f857(f79(x72621),x72623),x72624)))
% 15.02/14.80 [7263]~P89(x72631)+~P106(f857(f857(f234(x72631),f2(x72631)),x72633))+~P106(f857(f857(f235(x72631),x72632),x72634))+P106(f857(f857(f235(x72631),x72632),f857(f857(f79(x72631),x72633),x72634)))
% 15.02/14.80 [7304]~P109(x73041)+P106(f857(f857(f234(x73041),x73042),x73043))+P106(f857(f857(f234(x73041),x73042),x73044))+~P106(f857(f857(f234(x73041),x73042),f857(f857(f233(x73041),x73044),x73043)))
% 15.02/14.80 [7305]~P109(x73051)+P106(f857(f857(f235(x73051),x73052),x73053))+P106(f857(f857(f235(x73051),x73052),x73054))+~P106(f857(f857(f235(x73051),x73052),f857(f857(f233(x73051),x73054),x73053)))
% 15.02/14.80 [7598]~P110(x75982)+~P64(x75981)+~P106(f857(f857(f235(f927(x75981,x75982)),x75983),x75984))+P106(f857(f857(f234(f927(x75981,x75982)),x75983),x75984))
% 15.02/14.80 [7961]~P68(x79611)+~P106(f857(f857(f235(x79611),x79614),f2(x79611)))+~P106(f857(f857(f234(x79611),x79613),f857(f857(f290(x79611),x79612),x79614)))+P106(f857(f857(f234(x79611),x79612),f857(f857(f80(x79611),x79613),x79614)))
% 15.02/14.80 [7962]~P68(x79621)+~P106(f857(f857(f235(x79621),x79624),f2(x79621)))+~P106(f857(f857(f234(x79621),x79623),f857(f857(f80(x79621),x79622),x79624)))+P106(f857(f857(f234(x79621),x79622),f857(f857(f290(x79621),x79623),x79624)))
% 15.02/14.80 [7963]~P68(x79631)+~P106(f857(f857(f235(x79631),x79634),f2(x79631)))+~P106(f857(f857(f235(x79631),x79633),f857(f857(f290(x79631),x79632),x79634)))+P106(f857(f857(f235(x79631),x79632),f857(f857(f80(x79631),x79633),x79634)))
% 15.02/14.80 [7964]~P68(x79641)+~P106(f857(f857(f235(x79641),x79644),f2(x79641)))+~P106(f857(f857(f235(x79641),x79643),f857(f857(f80(x79641),x79642),x79644)))+P106(f857(f857(f235(x79641),x79642),f857(f857(f290(x79641),x79643),x79644)))
% 15.02/14.80 [8069]~P112(x80691)+~P106(f857(f857(f234(x80691),x80692),f2(x80691)))+~P106(f857(f857(f234(x80691),x80694),x80693))+P106(f857(f857(f234(x80691),f857(f857(f80(x80691),x80692),x80693)),f857(f857(f80(x80691),x80692),x80694)))
% 15.02/14.80 [8070]~P129(x80701)+~P106(f857(f857(f235(x80701),x80702),f2(x80701)))+~P106(f857(f857(f234(x80701),x80704),x80703))+P106(f857(f857(f234(x80701),f857(f857(f80(x80701),x80702),x80703)),f857(f857(f80(x80701),x80702),x80704)))
% 15.02/14.80 [8071]~P112(x80711)+~P106(f857(f857(f234(x80711),x80713),f2(x80711)))+~P106(f857(f857(f234(x80711),x80714),x80712))+P106(f857(f857(f234(x80711),f857(f857(f80(x80711),x80712),x80713)),f857(f857(f80(x80711),x80714),x80713)))
% 15.02/14.80 [8072]~P67(x80721)+~P106(f857(f857(f234(x80721),x80723),f2(x80721)))+~P106(f857(f857(f234(x80721),x80724),x80722))+P106(f857(f857(f234(x80721),f857(f857(f290(x80721),x80722),x80723)),f857(f857(f290(x80721),x80724),x80723)))
% 15.02/14.80 [8076]~P129(x80761)+~P106(f857(f857(f235(x80761),x80763),f2(x80761)))+~P106(f857(f857(f235(x80761),x80764),x80762))+P106(f857(f857(f235(x80761),f857(f857(f80(x80761),x80762),x80763)),f857(f857(f80(x80761),x80764),x80763)))
% 15.02/14.80 [8077]~P129(x80771)+~P106(f857(f857(f235(x80771),x80772),f2(x80771)))+~P106(f857(f857(f235(x80771),x80774),x80773))+P106(f857(f857(f235(x80771),f857(f857(f80(x80771),x80772),x80773)),f857(f857(f80(x80771),x80772),x80774)))
% 15.02/14.80 [8078]~P68(x80781)+~P106(f857(f857(f235(x80781),x80783),f2(x80781)))+~P106(f857(f857(f235(x80781),x80784),x80782))+P106(f857(f857(f235(x80781),f857(f857(f290(x80781),x80782),x80783)),f857(f857(f290(x80781),x80784),x80783)))
% 15.02/14.80 [8079]~P127(x80791)+~P106(f857(f857(f235(x80791),f77(x80791)),x80792))+~P106(f857(f857(f234(a919),x80793),x80794))+P106(f857(f857(f234(x80791),f857(f857(f243(x80791),x80792),x80793)),f857(f857(f243(x80791),x80792),x80794)))
% 15.02/14.80 [8080]~P127(x80801)+~P106(f857(f857(f234(x80801),f77(x80801)),x80802))+~P106(f857(f857(f234(a919),x80803),x80804))+P106(f857(f857(f234(x80801),f857(f857(f243(x80801),x80802),x80803)),f857(f857(f243(x80801),x80802),x80804)))
% 15.02/14.80 [8082]~P127(x80821)+~P106(f857(f857(f235(x80821),f77(x80821)),x80822))+~P106(f857(f857(f235(a919),x80823),x80824))+P106(f857(f857(f235(x80821),f857(f857(f243(x80821),x80822),x80823)),f857(f857(f243(x80821),x80822),x80824)))
% 15.02/14.80 [8109]P106(f857(f857(f235(a919),f2(a919)),f857(x81091,x81092)))+~P106(f857(f60(x81093),x81094))+~P106(f857(f857(f328(x81093),x81092),x81094))+~P106(f857(f857(f235(a919),f2(a919)),f857(f857(f11(x81093,a919),x81091),x81094)))
% 15.02/14.80 [8118]~P129(x81181)+~P106(f857(f857(f235(x81181),f2(x81181)),x81182))+~P106(f857(f857(f234(x81181),x81183),x81184))+P106(f857(f857(f234(x81181),f857(f857(f80(x81181),x81182),x81183)),f857(f857(f80(x81181),x81182),x81184)))
% 15.02/14.80 [8119]~P138(x81191)+~P106(f857(f857(f234(x81191),x81193),x81194))+~P106(f857(f857(f234(x81191),f2(x81191)),x81192))+P106(f857(f857(f234(x81191),f857(f857(f80(x81191),x81192),x81193)),f857(f857(f80(x81191),x81192),x81194)))
% 15.02/14.80 [8120]~P137(x81201)+~P106(f857(f857(f234(x81201),x81203),x81204))+~P106(f857(f857(f234(x81201),f2(x81201)),x81202))+P106(f857(f857(f234(x81201),f857(f857(f80(x81201),x81202),x81203)),f857(f857(f80(x81201),x81202),x81204)))
% 15.02/14.80 [8121]~P138(x81211)+~P106(f857(f857(f234(x81211),x81212),x81214))+~P106(f857(f857(f234(x81211),f2(x81211)),x81213))+P106(f857(f857(f234(x81211),f857(f857(f80(x81211),x81212),x81213)),f857(f857(f80(x81211),x81214),x81213)))
% 15.02/14.80 [8122]~P67(x81221)+~P106(f857(f857(f234(x81221),x81222),x81224))+~P106(f857(f857(f234(x81221),f2(x81221)),x81223))+P106(f857(f857(f234(x81221),f857(f857(f290(x81221),x81222),x81223)),f857(f857(f290(x81221),x81224),x81223)))
% 15.02/14.80 [8123]~P127(x81231)+~P106(f857(f857(f234(x81231),x81232),x81234))+~P106(f857(f857(f234(x81231),f2(x81231)),x81232))+P106(f857(f857(f234(x81231),f857(f857(f243(x81231),x81232),x81233)),f857(f857(f243(x81231),x81234),x81233)))
% 15.02/14.80 [8125]~P121(x81251)+~P106(f857(f857(f235(x81251),x81253),x81254))+~P106(f857(f857(f235(x81251),f2(x81251)),x81252))+P106(f857(f857(f235(x81251),f857(f857(f80(x81251),x81252),x81253)),f857(f857(f80(x81251),x81252),x81254)))
% 15.02/14.80 [8126]~P135(x81261)+~P106(f857(f857(f235(x81261),x81263),x81264))+~P106(f857(f857(f235(x81261),f2(x81261)),x81262))+P106(f857(f857(f235(x81261),f857(f857(f80(x81261),x81262),x81263)),f857(f857(f80(x81261),x81262),x81264)))
% 15.02/14.80 [8127]~P129(x81271)+~P106(f857(f857(f235(x81271),x81272),x81274))+~P106(f857(f857(f235(x81271),f2(x81271)),x81273))+P106(f857(f857(f235(x81271),f857(f857(f80(x81271),x81272),x81273)),f857(f857(f80(x81271),x81274),x81273)))
% 15.02/14.80 [8128]~P135(x81281)+~P106(f857(f857(f235(x81281),x81282),x81284))+~P106(f857(f857(f235(x81281),f2(x81281)),x81283))+P106(f857(f857(f235(x81281),f857(f857(f80(x81281),x81282),x81283)),f857(f857(f80(x81281),x81284),x81283)))
% 15.02/14.80 [8129]~P129(x81291)+~P106(f857(f857(f235(x81291),x81293),x81294))+~P106(f857(f857(f235(x81291),f2(x81291)),x81292))+P106(f857(f857(f235(x81291),f857(f857(f80(x81291),x81292),x81293)),f857(f857(f80(x81291),x81292),x81294)))
% 15.02/14.80 [8130]~P68(x81301)+~P106(f857(f857(f235(x81301),x81302),x81304))+~P106(f857(f857(f235(x81301),f2(x81301)),x81303))+P106(f857(f857(f235(x81301),f857(f857(f290(x81301),x81302),x81303)),f857(f857(f290(x81301),x81304),x81303)))
% 15.02/14.80 [8173]~P108(x81732)+P106(f857(f857(f235(f927(x81731,x81732)),x81734),x81733))+~P106(f857(f857(f234(f927(x81731,x81732)),x81734),x81733))+P106(f857(f857(f234(f927(x81731,x81732)),x81733),x81734))
% 15.02/14.80 [8213]P106(f857(f857(f328(x82131),x82132),x82133))+P106(f857(f857(f328(x82131),x82132),x82134))+~P106(f857(f857(f234(f927(x82131,a915)),x82134),x82133))+P106(f857(f857(f235(f927(x82131,a915)),x82134),f857(f857(f308(x82131),x82132),x82133)))
% 15.02/14.80 [8323]~P122(x83232)+E(x83231,f2(x83232))+P106(f857(f857(f286(x83232),x83233),x83234))+~P106(f857(f857(f286(x83232),f857(f857(f80(x83232),x83233),x83231)),f857(f857(f80(x83232),x83234),x83231)))
% 15.02/14.80 [8324]~P122(x83242)+E(x83241,f2(x83242))+P106(f857(f857(f286(x83242),x83243),x83244))+~P106(f857(f857(f286(x83242),f857(f857(f80(x83242),x83241),x83243)),f857(f857(f80(x83242),x83241),x83244)))
% 15.02/14.80 [8373]P106(f857(f857(f328(x83731),x83732),x83733))+P106(f857(f857(f328(x83731),x83732),x83734))+~P106(f857(f857(f235(f927(x83731,a915)),x83734),f857(f857(f308(x83731),x83732),x83733)))+P106(f857(f857(f234(f927(x83731,a915)),x83734),x83733))
% 15.02/14.80 [8438]~P129(x84381)+P106(f857(f857(f235(x84381),x84383),x84382))+P106(f857(f857(f235(x84381),x84382),x84383))+~P106(f857(f857(f235(x84381),f857(f857(f80(x84381),x84384),x84382)),f857(f857(f80(x84381),x84384),x84383)))
% 15.02/14.80 [8439]~P129(x84391)+P106(f857(f857(f235(x84391),x84393),x84392))+P106(f857(f857(f235(x84391),x84392),x84393))+~P106(f857(f857(f235(x84391),f857(f857(f80(x84391),x84392),x84394)),f857(f857(f80(x84391),x84393),x84394)))
% 15.02/14.80 [8450]~P129(x84501)+P106(f857(f857(f235(x84501),x84504),f2(x84501)))+P106(f857(f857(f235(x84501),x84502),x84503))+~P106(f857(f857(f235(x84501),f857(f857(f80(x84501),x84502),x84504)),f857(f857(f80(x84501),x84503),x84504)))
% 15.02/14.80 [8451]~P129(x84511)+P106(f857(f857(f235(x84511),x84514),f2(x84511)))+P106(f857(f857(f235(x84511),x84512),x84513))+~P106(f857(f857(f235(x84511),f857(f857(f80(x84511),x84514),x84512)),f857(f857(f80(x84511),x84514),x84513)))
% 15.02/14.80 [8454]~P129(x84541)+P106(f857(f857(f235(x84541),x84542),x84543))+P106(f857(f857(f235(x84541),f2(x84541)),x84544))+~P106(f857(f857(f235(x84541),f857(f857(f80(x84541),x84544),x84543)),f857(f857(f80(x84541),x84544),x84542)))
% 15.02/14.80 [8455]~P129(x84551)+P106(f857(f857(f235(x84551),x84552),x84553))+P106(f857(f857(f235(x84551),f2(x84551)),x84554))+~P106(f857(f857(f235(x84551),f857(f857(f80(x84551),x84553),x84554)),f857(f857(f80(x84551),x84552),x84554)))
% 15.02/14.80 [8468]~P129(x84681)+P106(f857(f857(f235(x84681),x84682),f2(x84681)))+P106(f857(f857(f235(x84681),f2(x84681)),x84682))+~P106(f857(f857(f235(x84681),f857(f857(f80(x84681),x84683),x84682)),f857(f857(f80(x84681),x84684),x84682)))
% 15.02/14.80 [8469]~P129(x84691)+P106(f857(f857(f235(x84691),x84692),f2(x84691)))+P106(f857(f857(f235(x84691),f2(x84691)),x84692))+~P106(f857(f857(f235(x84691),f857(f857(f80(x84691),x84692),x84693)),f857(f857(f80(x84691),x84692),x84694)))
% 15.02/14.80 [8498]~P129(x84981)+~P106(f857(f857(f235(x84981),x84984),f2(x84981)))+P106(f857(f857(f234(x84981),x84982),x84983))+~P106(f857(f857(f234(x84981),f857(f857(f80(x84981),x84984),x84983)),f857(f857(f80(x84981),x84984),x84982)))
% 15.02/14.80 [8499]~P129(x84991)+~P106(f857(f857(f235(x84991),x84994),f2(x84991)))+P106(f857(f857(f235(x84991),x84992),x84993))+~P106(f857(f857(f235(x84991),f857(f857(f80(x84991),x84994),x84993)),f857(f857(f80(x84991),x84994),x84992)))
% 15.02/14.80 [8510]~P127(x85103)+~P106(f857(f857(f235(x85103),f77(x85103)),x85104))+P106(f857(f857(f234(a919),x85101),x85102))+~P106(f857(f857(f234(x85103),f857(f857(f243(x85103),x85104),x85101)),f857(f857(f243(x85103),x85104),x85102)))
% 15.02/14.80 [8512]~P127(x85123)+~P106(f857(f857(f235(x85123),f77(x85123)),x85124))+P106(f857(f857(f235(a919),x85121),x85122))+~P106(f857(f857(f235(x85123),f857(f857(f243(x85123),x85124),x85121)),f857(f857(f243(x85123),x85124),x85122)))
% 15.02/14.80 [8522]~P129(x85221)+P106(f857(f857(f234(x85221),x85222),x85223))+~P106(f857(f857(f235(x85221),f2(x85221)),x85224))+~P106(f857(f857(f234(x85221),f857(f857(f80(x85221),x85224),x85222)),f857(f857(f80(x85221),x85224),x85223)))
% 15.02/14.80 [8523]~P135(x85231)+P106(f857(f857(f234(x85231),x85232),x85233))+~P106(f857(f857(f235(x85231),f2(x85231)),x85234))+~P106(f857(f857(f234(x85231),f857(f857(f80(x85231),x85234),x85232)),f857(f857(f80(x85231),x85234),x85233)))
% 15.02/14.80 [8524]~P135(x85241)+P106(f857(f857(f234(x85241),x85242),x85243))+~P106(f857(f857(f235(x85241),f2(x85241)),x85244))+~P106(f857(f857(f234(x85241),f857(f857(f80(x85241),x85242),x85244)),f857(f857(f80(x85241),x85243),x85244)))
% 15.02/14.80 [8525]~P129(x85251)+P106(f857(f857(f235(x85251),x85252),x85253))+~P106(f857(f857(f235(x85251),f2(x85251)),x85254))+~P106(f857(f857(f235(x85251),f857(f857(f80(x85251),x85254),x85252)),f857(f857(f80(x85251),x85254),x85253)))
% 15.02/14.80 [8526]~P135(x85261)+P106(f857(f857(f235(x85261),x85262),x85263))+~P106(f857(f857(f234(x85261),f2(x85261)),x85264))+~P106(f857(f857(f235(x85261),f857(f857(f80(x85261),x85264),x85262)),f857(f857(f80(x85261),x85264),x85263)))
% 15.02/14.80 [8527]~P131(x85271)+P106(f857(f857(f235(x85271),x85272),x85273))+~P106(f857(f857(f234(x85271),f2(x85271)),x85274))+~P106(f857(f857(f235(x85271),f857(f857(f80(x85271),x85274),x85272)),f857(f857(f80(x85271),x85274),x85273)))
% 15.02/14.80 [8528]~P127(x85281)+~P106(f857(f857(f234(x85281),f2(x85281)),x85283))+P106(f857(f857(f235(x85281),x85282),x85283))+~P106(f857(f857(f235(x85281),f857(f857(f243(x85281),x85282),x85284)),f857(f857(f243(x85281),x85283),x85284)))
% 15.02/14.80 [8529]~P135(x85291)+P106(f857(f857(f235(x85291),x85292),x85293))+~P106(f857(f857(f234(x85291),f2(x85291)),x85294))+~P106(f857(f857(f235(x85291),f857(f857(f80(x85291),x85292),x85294)),f857(f857(f80(x85291),x85293),x85294)))
% 15.02/14.80 [8530]~P131(x85301)+P106(f857(f857(f235(x85301),x85302),x85303))+~P106(f857(f857(f234(x85301),f2(x85301)),x85304))+~P106(f857(f857(f235(x85301),f857(f857(f80(x85301),x85302),x85304)),f857(f857(f80(x85301),x85303),x85304)))
% 15.02/14.80 [8573]P106(f857(f857(f328(x85731),x85732),x85733))+~P106(f857(f857(f234(f927(x85731,a915)),x85733),x85734))+~P106(f857(f857(f235(f927(x85731,a915)),x85733),x85734))+P106(f857(f857(f235(f927(x85731,a915)),x85733),f857(f857(f308(x85731),x85732),x85734)))
% 15.02/14.80 [8605]~P147(x86051)+~P123(x86051)+P106(f857(f857(f286(x86051),x86052),f857(f857(f79(x86051),f853(x86052,x86053,x86051)),f2(x86051))))+~P106(f857(x86053,f857(f857(f80(x86051),x86052),x86054)))
% 15.02/14.80 [8951]E(f857(f857(f3(a1),f445(x89511,x89512,x89513,x89514)),f446(x89511,x89512,x89513,x89514)),x89514)+~P106(f857(f857(f235(a1),f2(a1)),x89513))+~P106(f857(f857(f234(a1),x89511),x89514))+P106(f857(f857(f234(a1),x89511),f857(f857(f79(a1),x89514),x89513)))
% 15.02/14.80 [8952]E(f857(f857(f3(a1),f475(x89521,x89522,x89523,x89524)),f476(x89521,x89522,x89523,x89524)),x89524)+~P106(f857(f857(f235(a1),f2(a1)),x89523))+~P106(f857(f857(f235(a1),x89521),x89524))+P106(f857(f857(f235(a1),x89521),f857(f857(f79(a1),x89524),x89523)))
% 15.02/14.80 [9102]~E(f857(f857(f164(x91021),x91023),f677(x91024,x91023,x91021,x91022)),f857(f857(f164(x91021),x91024),f677(x91024,x91023,x91021,x91022)))+E(f857(f857(f175(x91021),x91022),x91023),f857(f857(f175(x91021),x91022),x91024))+~P106(f857(f857(f234(a919),x91022),f857(f190(f920(x91021)),x91023)))+~P106(f857(f857(f234(a919),x91022),f857(f190(f920(x91021)),x91024)))
% 15.02/14.80 [9164]~P106(f857(f857(f235(a1),f2(a1)),x91643))+~P106(f857(f857(f234(a1),x91641),x91644))+P106(f857(f857(f328(a1),f445(x91641,x91642,x91643,x91644)),x91642))+P106(f857(f857(f234(a1),x91641),f857(f857(f79(a1),x91644),x91643)))
% 15.02/14.80 [9165]~P106(f857(f857(f235(a1),f2(a1)),x91653))+~P106(f857(f857(f235(a1),x91651),x91654))+P106(f857(f857(f328(a1),f475(x91651,x91652,x91653,x91654)),x91652))+P106(f857(f857(f235(a1),x91651),f857(f857(f79(a1),x91654),x91653)))
% 15.02/14.80 [9205]~P102(x92051)+~P106(f857(f60(x92051),x92053))+~P106(f857(f857(f328(x92051),x92054),x92053))+P106(f857(f857(f234(x92051),f857(f857(f63(x92051,x92051,f101(x92051)),x92052),x92053)),f857(f857(f101(x92051),x92054),x92052)))
% 15.02/14.80 [9206]~P109(x92061)+~P106(f857(f60(x92061),x92063))+~P106(f857(f857(f328(x92061),x92064),x92063))+P106(f857(f857(f234(x92061),f857(f857(f63(x92061,x92061,f188(x92061)),x92062),x92063)),f857(f857(f188(x92061),x92064),x92062)))
% 15.02/14.80 [9250]E(f857(f857(f175(x92501),x92502),x92503),f857(f857(f175(x92501),x92502),x92504))+P106(f857(f857(f235(a919),f677(x92503,x92504,x92501,x92502)),x92502))+~P106(f857(f857(f234(a919),x92502),f857(f190(f920(x92501)),x92503)))+~P106(f857(f857(f234(a919),x92502),f857(f190(f920(x92501)),x92504)))
% 15.02/14.80 [9255]~P106(f857(f857(f235(a1),f2(a1)),x92553))+~P106(f857(f857(f234(a1),x92551),x92552))+P106(f857(f857(f328(a1),f446(x92551,x92554,x92553,x92552)),f302(a1,f77(a1),x92553)))+P106(f857(f857(f234(a1),x92551),f857(f857(f79(a1),x92552),x92553)))
% 15.02/14.80 [9256]~P106(f857(f857(f235(a1),f2(a1)),x92563))+~P106(f857(f857(f235(a1),x92561),x92562))+P106(f857(f857(f328(a1),f476(x92561,x92564,x92563,x92562)),f302(a1,f77(a1),x92563)))+P106(f857(f857(f235(a1),x92561),f857(f857(f79(a1),x92562),x92563)))
% 15.02/14.80 [9579]~P101(x95791)+~P106(f857(f60(x95791),x95794))+P106(f857(f857(f328(x95791),f345(x95792,x95793,x95794,x95791)),x95794))+P106(f857(f857(f234(x95791),f857(f857(f63(x95791,x95791,f110(x95791)),x95792),x95794)),f857(f857(f110(x95791),x95793),x95792)))
% 15.02/14.80 [9580]~P109(x95801)+~P106(f857(f60(x95801),x95804))+P106(f857(f857(f328(x95801),f605(x95802,x95803,x95804,x95801)),x95804))+P106(f857(f857(f234(x95801),f857(f857(f63(x95801,x95801,f233(x95801)),x95802),x95804)),f857(f857(f233(x95801),x95803),x95802)))
% 15.02/14.80 [9715]~P101(x97151)+~P106(f857(f60(x97151),x97153))+~P106(f857(f857(f234(x97151),f345(x97152,x97154,x97153,x97151)),x97154))+P106(f857(f857(f234(x97151),f857(f857(f63(x97151,x97151,f110(x97151)),x97152),x97153)),f857(f857(f110(x97151),x97154),x97152)))
% 15.02/14.80 [9716]~P109(x97161)+~P106(f857(f60(x97161),x97163))+~P106(f857(f857(f234(x97161),f605(x97162,x97164,x97163,x97161)),x97164))+P106(f857(f857(f234(x97161),f857(f857(f63(x97161,x97161,f233(x97161)),x97162),x97163)),f857(f857(f233(x97161),x97164),x97162)))
% 15.02/14.80 [9718]~P106(f857(f857(f234(a1),f2(a1)),x97184))+~P106(f857(f857(f235(a1),f2(a1)),x97183))+~P106(f857(f857(f235(a1),x97184),x97181))+P106(f857(f857(f235(a1),f857(f857(f79(a1),f857(f857(f80(a1),x97181),f44(a1,x97182,x97183))),x97184)),f857(f857(f80(a1),x97181),x97183)))
% 15.02/14.80 [10105]E(x101051,x101052)+P106(f857(f857(f328(f926(f920(x101053),f920(x101053))),f857(f857(f251(f920(x101053),f920(x101053)),x101052),x101051)),f147(x101053,x101054)))+P106(f857(f857(f328(f926(f920(x101053),f920(x101053))),f857(f857(f251(f920(x101053),f920(x101053)),x101051),x101052)),f147(x101053,x101054)))+~P106(f857(f857(f328(f926(x101053,x101053)),f857(f857(f251(x101053,x101053),f657(x101051,x101052,x101054,x101053)),f658(x101051,x101052,x101054,x101053))),x101054))
% 15.02/14.80 [10106]E(x101061,x101062)+P106(f857(f857(f328(f926(f920(x101063),f920(x101063))),f857(f857(f251(f920(x101063),f920(x101063)),x101062),x101061)),f147(x101063,x101064)))+P106(f857(f857(f328(f926(f920(x101063),f920(x101063))),f857(f857(f251(f920(x101063),f920(x101063)),x101061),x101062)),f147(x101063,x101064)))+~P106(f857(f857(f328(f926(x101063,x101063)),f857(f857(f251(x101063,x101063),f658(x101061,x101062,x101064,x101063)),f657(x101061,x101062,x101064,x101063))),x101064))
% 15.02/14.80 [7665]~P101(x76651)+~P106(f857(f857(f234(x76651),x76653),x76654))+~P106(f857(f857(f234(x76651),x76652),x76654))+P106(f857(f857(f234(x76651),f857(f857(f110(x76651),x76652),x76653)),x76654))
% 15.02/14.80 [7668]~P109(x76681)+~P106(f857(f857(f234(x76681),x76683),x76684))+~P106(f857(f857(f234(x76681),x76682),x76684))+P106(f857(f857(f234(x76681),f857(f857(f233(x76681),x76682),x76683)),x76684))
% 15.02/14.80 [7669]~P109(x76691)+~P106(f857(f857(f235(x76691),x76693),x76694))+~P106(f857(f857(f235(x76691),x76692),x76694))+P106(f857(f857(f235(x76691),f857(f857(f233(x76691),x76692),x76693)),x76694))
% 15.02/14.80 [7986]~E(x79861,x79863)+E(f139(a919,f857(f301(a919,x79861),x79862)),f857(f857(f151(a919),x79863),x79864))+~E(f139(a919,f857(f301(a919,f857(f857(f79(a919),x79861),f77(a919))),x79862)),x79864)+~P106(f857(f857(f235(a919),x79861),x79862))
% 15.02/14.80 [7994]~P109(x79941)+P106(f857(f857(f234(x79941),x79942),x79943))+P106(f857(f857(f234(x79941),x79944),x79943))+~P106(f857(f857(f234(x79941),f857(f857(f188(x79941),x79944),x79942)),x79943))
% 15.02/14.80 [7995]~P109(x79951)+P106(f857(f857(f235(x79951),x79952),x79953))+P106(f857(f857(f235(x79951),x79954),x79953))+~P106(f857(f857(f235(x79951),f857(f857(f188(x79951),x79954),x79952)),x79953))
% 15.02/14.80 [8271]~P67(x82711)+~P106(f857(f857(f235(x82711),f2(x82711)),x82713))+~P106(f857(f857(f234(x82711),x82712),f857(f857(f290(x82711),x82714),x82713)))+P106(f857(f857(f234(x82711),f857(f857(f80(x82711),x82712),x82713)),x82714))
% 15.02/14.80 [8272]~P68(x82721)+~P106(f857(f857(f235(x82721),f2(x82721)),x82723))+~P106(f857(f857(f234(x82721),x82722),f857(f857(f290(x82721),x82724),x82723)))+P106(f857(f857(f234(x82721),f857(f857(f80(x82721),x82722),x82723)),x82724))
% 15.02/14.80 [8273]~P67(x82731)+~P106(f857(f857(f235(x82731),f2(x82731)),x82733))+~P106(f857(f857(f234(x82731),x82732),f857(f857(f80(x82731),x82734),x82733)))+P106(f857(f857(f234(x82731),f857(f857(f290(x82731),x82732),x82733)),x82734))
% 15.02/14.80 [8275]~P68(x82751)+~P106(f857(f857(f235(x82751),f2(x82751)),x82753))+~P106(f857(f857(f234(x82751),x82752),f857(f857(f80(x82751),x82754),x82753)))+P106(f857(f857(f234(x82751),f857(f857(f290(x82751),x82752),x82753)),x82754))
% 15.02/14.80 [8276]~P67(x82761)+~P106(f857(f857(f235(x82761),f2(x82761)),x82763))+~P106(f857(f857(f235(x82761),x82762),f857(f857(f290(x82761),x82764),x82763)))+P106(f857(f857(f235(x82761),f857(f857(f80(x82761),x82762),x82763)),x82764))
% 15.02/14.80 [8277]~P68(x82771)+~P106(f857(f857(f235(x82771),f2(x82771)),x82773))+~P106(f857(f857(f235(x82771),x82772),f857(f857(f290(x82771),x82774),x82773)))+P106(f857(f857(f235(x82771),f857(f857(f80(x82771),x82772),x82773)),x82774))
% 15.02/14.80 [8278]~P67(x82781)+~P106(f857(f857(f235(x82781),f2(x82781)),x82783))+~P106(f857(f857(f235(x82781),x82782),f857(f857(f80(x82781),x82784),x82783)))+P106(f857(f857(f235(x82781),f857(f857(f290(x82781),x82782),x82783)),x82784))
% 15.02/14.80 [8280]~P68(x82801)+~P106(f857(f857(f235(x82801),f2(x82801)),x82803))+~P106(f857(f857(f235(x82801),x82802),f857(f857(f80(x82801),x82804),x82803)))+P106(f857(f857(f235(x82801),f857(f857(f290(x82801),x82802),x82803)),x82804))
% 15.02/14.80 [8408]~P67(x84081)+~P106(f857(f857(f235(x84081),f2(x84081)),x84084))+P106(f857(f857(f234(x84081),x84082),f857(f857(f80(x84081),x84083),x84084)))+~P106(f857(f857(f234(x84081),f857(f857(f290(x84081),x84082),x84084)),x84083))
% 15.02/14.80 [8409]~P67(x84091)+~P106(f857(f857(f235(x84091),f2(x84091)),x84094))+P106(f857(f857(f234(x84091),x84092),f857(f857(f290(x84091),x84093),x84094)))+~P106(f857(f857(f234(x84091),f857(f857(f80(x84091),x84092),x84094)),x84093))
% 15.02/14.80 [8411]~P68(x84111)+~P106(f857(f857(f235(x84111),f2(x84111)),x84114))+P106(f857(f857(f234(x84111),x84112),f857(f857(f80(x84111),x84113),x84114)))+~P106(f857(f857(f234(x84111),f857(f857(f290(x84111),x84112),x84114)),x84113))
% 15.02/14.80 [8412]~P68(x84121)+~P106(f857(f857(f235(x84121),f2(x84121)),x84124))+P106(f857(f857(f234(x84121),x84122),f857(f857(f290(x84121),x84123),x84124)))+~P106(f857(f857(f234(x84121),f857(f857(f80(x84121),x84122),x84124)),x84123))
% 15.02/14.80 [8413]~P67(x84131)+~P106(f857(f857(f235(x84131),f2(x84131)),x84134))+P106(f857(f857(f235(x84131),x84132),f857(f857(f80(x84131),x84133),x84134)))+~P106(f857(f857(f235(x84131),f857(f857(f290(x84131),x84132),x84134)),x84133))
% 15.02/14.80 [8414]~P67(x84141)+~P106(f857(f857(f235(x84141),f2(x84141)),x84144))+P106(f857(f857(f235(x84141),x84142),f857(f857(f290(x84141),x84143),x84144)))+~P106(f857(f857(f235(x84141),f857(f857(f80(x84141),x84142),x84144)),x84143))
% 15.02/14.80 [8416]~P68(x84161)+~P106(f857(f857(f235(x84161),f2(x84161)),x84164))+P106(f857(f857(f235(x84161),x84162),f857(f857(f80(x84161),x84163),x84164)))+~P106(f857(f857(f235(x84161),f857(f857(f290(x84161),x84162),x84164)),x84163))
% 15.02/14.80 [8417]~P68(x84171)+~P106(f857(f857(f235(x84171),f2(x84171)),x84174))+P106(f857(f857(f235(x84171),x84172),f857(f857(f290(x84171),x84173),x84174)))+~P106(f857(f857(f235(x84171),f857(f857(f80(x84171),x84172),x84174)),x84173))
% 15.02/14.80 [8576]~P68(x85761)+~P106(f857(f857(f235(x85761),x85763),f2(x85761)))+~P106(f857(f857(f234(x85761),f857(f857(f290(x85761),x85764),x85763)),x85762))+P106(f857(f857(f234(x85761),f857(f857(f80(x85761),x85762),x85763)),x85764))
% 15.02/14.80 [8577]~P68(x85771)+~P106(f857(f857(f235(x85771),x85773),f2(x85771)))+~P106(f857(f857(f234(x85771),f857(f857(f80(x85771),x85774),x85773)),x85772))+P106(f857(f857(f234(x85771),f857(f857(f290(x85771),x85772),x85773)),x85774))
% 15.02/14.80 [8578]~P68(x85781)+~P106(f857(f857(f235(x85781),x85783),f2(x85781)))+~P106(f857(f857(f235(x85781),f857(f857(f290(x85781),x85784),x85783)),x85782))+P106(f857(f857(f235(x85781),f857(f857(f80(x85781),x85782),x85783)),x85784))
% 15.02/14.80 [8579]~P68(x85791)+~P106(f857(f857(f235(x85791),x85793),f2(x85791)))+~P106(f857(f857(f235(x85791),f857(f857(f80(x85791),x85794),x85793)),x85792))+P106(f857(f857(f235(x85791),f857(f857(f290(x85791),x85792),x85793)),x85794))
% 15.02/14.80 [8591]~P106(f857(x85911,x85914))+~P106(f857(f857(f235(a919),x85912),f857(f857(f80(a919),x85913),f857(a112,x85914))))+P106(f857(x85911,f857(f857(f35(a919),x85912),x85913)))+~P106(f857(f857(f234(a919),f857(f857(f80(a919),x85913),x85914)),x85912))
% 15.02/14.80 [8799]~P101(x87991)+~P106(f857(f60(x87991),x87994))+~P106(f857(f857(f328(x87991),x87992),x87994))+P106(f857(f857(f234(x87991),f857(f857(f110(x87991),x87992),x87993)),f857(f857(f63(x87991,x87991,f110(x87991)),x87993),x87994)))
% 15.02/14.80 [8800]~P109(x88001)+~P106(f857(f60(x88001),x88004))+~P106(f857(f857(f328(x88001),x88002),x88004))+P106(f857(f857(f234(x88001),f857(f857(f233(x88001),x88002),x88003)),f857(f857(f63(x88001,x88001,f233(x88001)),x88003),x88004)))
% 15.02/14.80 [8953]~P106(f857(f60(x89531),x89532))+E(f857(f34(x89531),f857(f857(f3(f927(x89531,a915)),x89532),f857(f857(f308(x89531),x89533),x89534))),f857(f857(f3(a919),f857(f34(x89531),f857(f857(f3(f927(x89531,a915)),x89532),x89534))),f77(a919)))+P106(f857(f857(f328(x89531),x89533),x89534))+~P106(f857(f857(f328(x89531),x89533),x89532))
% 15.02/14.80 [9030]E(f857(f857(f79(a1),f467(x90301,x90302,x90303,x90304)),f468(x90301,x90302,x90303,x90304)),x90304)+~P106(f857(f857(f235(a1),f2(a1)),x90303))+~P106(f857(f857(f234(a1),x90304),x90301))+P106(f857(f857(f234(a1),f857(f857(f3(a1),x90304),x90303)),x90301))
% 15.02/14.80 [9031]E(f857(f857(f79(a1),f477(x90311,x90312,x90313,x90314)),f478(x90311,x90312,x90313,x90314)),x90314)+~P106(f857(f857(f235(a1),f2(a1)),x90313))+~P106(f857(f857(f235(a1),x90314),x90311))+P106(f857(f857(f235(a1),f857(f857(f3(a1),x90314),x90313)),x90311))
% 15.02/14.80 [9235]~P106(f857(f857(f235(a1),f2(a1)),x92353))+~P106(f857(f857(f234(a1),x92354),x92351))+P106(f857(f857(f328(a1),f467(x92351,x92352,x92353,x92354)),x92352))+P106(f857(f857(f234(a1),f857(f857(f3(a1),x92354),x92353)),x92351))
% 15.02/14.80 [9236]~P106(f857(f857(f235(a1),f2(a1)),x92363))+~P106(f857(f857(f235(a1),x92364),x92361))+P106(f857(f857(f328(a1),f477(x92361,x92362,x92363,x92364)),x92362))+P106(f857(f857(f235(a1),f857(f857(f3(a1),x92364),x92363)),x92361))
% 15.02/14.80 [9322]~P106(f857(f857(f235(a1),f2(a1)),x93222))+~P106(f857(f857(f234(a1),x93221),x93223))+P106(f857(f857(f328(a1),f468(x93223,x93224,x93222,x93221)),f302(a1,f77(a1),x93222)))+P106(f857(f857(f234(a1),f857(f857(f3(a1),x93221),x93222)),x93223))
% 15.02/14.80 [9323]~P106(f857(f857(f235(a1),f2(a1)),x93232))+~P106(f857(f857(f235(a1),x93231),x93233))+P106(f857(f857(f328(a1),f478(x93233,x93234,x93232,x93231)),f302(a1,f77(a1),x93232)))+P106(f857(f857(f235(a1),f857(f857(f3(a1),x93231),x93232)),x93233))
% 15.02/14.80 [9341]~P106(f857(f857(f234(a1),f2(a1)),x93414))+~P106(f857(f857(f235(a1),f2(a1)),x93413))+~P106(f857(f857(f235(a1),x93414),x93411))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),f857(f857(f80(a1),x93411),f44(a1,x93412,x93413))),x93414)))
% 15.02/14.80 [9370]E(x93701,x93702)+~P41(x93703,x93704)+~P106(f857(f857(f328(f926(x93703,x93703)),f857(f857(f251(x93703,x93703),x93702),x93701)),x93704))+~P106(f857(f857(f328(f926(x93703,x93703)),f857(f857(f251(x93703,x93703),x93701),x93702)),x93704))
% 15.02/14.80 [9402]~P102(x94021)+~P106(f857(f60(x94021),x94024))+~P106(f857(f857(f234(x94021),x94022),f344(x94023,x94022,x94024,x94021)))+P106(f857(f857(f234(x94021),f857(f857(f101(x94021),x94022),x94023)),f857(f857(f63(x94021,x94021,f101(x94021)),x94023),x94024)))
% 15.02/14.80 [9403]~P109(x94031)+~P106(f857(f60(x94031),x94034))+~P106(f857(f857(f234(x94031),x94032),f342(x94033,x94032,x94034,x94031)))+P106(f857(f857(f234(x94031),f857(f857(f188(x94031),x94032),x94033)),f857(f857(f63(x94031,x94031,f188(x94031)),x94033),x94034)))
% 15.02/14.80 [9420]~P106(f857(f857(f234(a1),x94204),f2(a1)))+~P106(f857(f857(f235(a1),f2(a1)),x94202))+~P106(f857(f857(f235(a1),x94201),x94204))+P106(f857(f857(f235(a1),f857(f857(f80(a1),x94201),x94202)),f857(f857(f79(a1),f857(f857(f80(a1),x94201),f44(a1,x94203,x94202))),x94204)))
% 15.02/14.80 [9445]P106(f857(f60(x94451),x94452))+~P106(f857(f60(x94451),x94453))+~P106(f857(f857(f328(f927(x94451,a915)),x94452),f857(f857(f59(x94451),x94453),x94454)))+~P106(f857(f857(f234(f927(f926(x94451,x94451),a915)),x94454),f857(f857(f253(x94451,x94451),x94453),f857(f18(f927(x94451,a915),x94451),x94453))))
% 15.02/14.80 [9469]~P109(x94691)+~P106(f857(f60(x94691),x94694))+P106(f857(f857(f328(x94691),f342(x94692,x94693,x94694,x94691)),x94694))+P106(f857(f857(f234(x94691),f857(f857(f188(x94691),x94693),x94692)),f857(f857(f63(x94691,x94691,f188(x94691)),x94692),x94694)))
% 15.02/14.80 [9470]~P102(x94701)+~P106(f857(f60(x94701),x94704))+P106(f857(f857(f328(x94701),f344(x94702,x94703,x94704,x94701)),x94704))+P106(f857(f857(f234(x94701),f857(f857(f101(x94701),x94703),x94702)),f857(f857(f63(x94701,x94701,f101(x94701)),x94702),x94704)))
% 15.02/14.80 [9882]~P106(f857(f60(x98822),x98824))+~P106(f857(f60(x98821),x98823))+~P106(f857(f857(f234(a919),f857(f34(x98822),x98824)),f857(f34(x98821),x98823)))+P106(f857(f857(f234(f927(x98821,a915)),f857(f309(x98822,x98821,f505(x98823,x98821,x98824,x98822)),x98824)),x98823))
% 15.02/14.80 [9520]~P106(f857(f857(f328(x95201),x95202),x95204))+P106(f857(f857(f328(x95201),x95202),x95203))+~P106(f857(f857(f235(f927(x95201,a915)),x95204),f857(f857(f308(x95201),x95202),x95203)))+P106(f857(f857(f235(f927(x95201,a915)),f857(f857(f3(f927(x95201,a915)),x95204),f857(f857(f308(x95201),x95202),f189(f927(x95201,a915))))),x95203))
% 15.02/14.80 [9695]~P106(f857(f857(f328(x96951),x96952),x96954))+P106(f857(f857(f328(x96951),x96952),x96953))+P106(f857(f857(f235(f927(x96951,a915)),x96954),f857(f857(f308(x96951),x96952),x96953)))+~P106(f857(f857(f235(f927(x96951,a915)),f857(f857(f3(f927(x96951,a915)),x96954),f857(f857(f308(x96951),x96952),f189(f927(x96951,a915))))),x96953))
% 15.02/14.80 [9721]P106(f857(f857(f328(x97211),x97212),x97213))+~P106(f857(f857(f234(f927(x97211,a915)),x97214),x97213))+P106(f857(f857(f235(f927(x97211,a915)),x97214),f857(f857(f308(x97211),x97212),x97213)))+~P106(f857(f857(f235(f927(x97211,a915)),f857(f857(f3(f927(x97211,a915)),x97214),f857(f857(f308(x97211),x97212),f189(f927(x97211,a915))))),x97213))
% 15.02/14.80 [9726]~P106(f857(f857(f328(x97261),x97263),x97262))+~P106(f857(f857(f235(f927(x97261,a915)),x97262),x97264))+P106(f857(f857(f235(f927(x97261,a915)),x97262),f857(f857(f308(x97261),x97263),x97264)))+~P106(f857(f857(f235(f927(x97261,a915)),f857(f857(f3(f927(x97261,a915)),x97262),f857(f857(f308(x97261),x97263),f189(f927(x97261,a915))))),x97264))
% 15.02/14.80 [9742]~P106(f857(f857(f234(f927(x97421,a915)),x97422),x97424))+~P106(f857(f857(f235(f927(x97421,a915)),x97422),x97424))+P106(f857(f857(f235(f927(x97421,a915)),x97422),f857(f857(f308(x97421),x97423),x97424)))+~P106(f857(f857(f235(f927(x97421,a915)),f857(f857(f3(f927(x97421,a915)),x97422),f857(f857(f308(x97421),x97423),f189(f927(x97421,a915))))),x97424))
% 15.02/14.80 [9787]~P110(x97872)+~P64(x97871)+~P106(f857(f857(f234(f927(x97871,x97872)),x97873),x97874))+P106(f857(f56(x97871),f857(f857(f20(x97871,x97872,a915),f857(f857(f10(x97872,f927(x97872,a915),x97871),f234(x97872)),x97873)),x97874)))
% 15.02/14.80 [9930]~P110(x99302)+~P64(x99301)+P106(f857(f857(f234(f927(x99301,x99302)),x99303),x99304))+~P106(f857(f56(x99301),f857(f857(f20(x99301,x99302,a915),f857(f857(f10(x99302,f927(x99302,a915),x99301),f234(x99302)),x99303)),x99304)))
% 15.02/14.80 [10096]E(f857(f857(f164(x100961),f857(f857(f164(f920(x100961)),f179(x100961,x100962)),x100963)),x100964),f857(f857(f164(x100961),f857(f857(f164(f920(x100961)),x100962),x100964)),x100963))+~P106(f857(f857(f235(a919),x100963),f857(f190(f920(f920(x100961))),f179(x100961,x100962))))+~P14(a919,f857(f168(a919),f857(f857(f154(f920(x100961),a919),f190(f920(x100961))),x100962)))+~P106(f857(f857(f235(a919),x100964),f857(f190(f920(f920(x100961))),f857(f136(f920(x100961),f857(f857(f10(a919,a915,f920(x100961)),f857(f235(a919),x100963)),f190(f920(x100961)))),x100962))))
% 15.02/14.80 [10117]~P106(f857(f857(f328(f926(a919,a919)),x101174),x101171))+~P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),x101174),x101172)),a32))+~P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x101171),x101173)),a68))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x101171),f857(f857(f308(f926(a919,a919)),x101172),x101173))),a68))
% 15.02/14.80 [10118]~P106(f857(f857(f328(f926(a919,a919)),x101184),x101181))+~P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),x101184),x101182)),a70))+~P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x101181),x101183)),a71))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x101181),f857(f857(f308(f926(a919,a919)),x101182),x101183))),a71))
% 15.02/14.80 [10007]~P110(x100072)+~P64(x100071)+~P106(f857(f857(f235(f927(x100071,x100072)),x100073),x100074))+P106(f857(f55(x100071),f857(f857(f10(a915,a915,x100071),a321),f857(f857(f20(x100071,x100072,a915),f857(f857(f10(x100072,f927(x100072,a915),x100071),a324),x100073)),x100074))))
% 15.02/14.80 [10131]~P106(f857(f857(f328(f926(a919,a919)),x101314),x101313))+~P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),x101311),x101314)),a32))+~P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x101312),x101313)),a33))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),f857(f857(f308(f926(a919,a919)),x101311),x101312)),x101313)),a33))
% 15.02/14.80 [10132]~P106(f857(f857(f328(f926(a919,a919)),x101324),x101323))+~P106(f857(f857(f328(f926(f926(a919,a919),f926(a919,a919))),f857(f857(f251(f926(a919,a919),f926(a919,a919)),x101321),x101324)),a70))+~P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),x101322),x101323)),a69))+P106(f857(f857(f328(f926(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915))),f857(f857(f251(f927(f926(a919,a919),a915),f927(f926(a919,a919),a915)),f857(f857(f308(f926(a919,a919)),x101321),x101322)),x101323)),a69))
% 15.02/14.80 [6242]~P8(x62424,x62421)+~P106(f857(f857(x62421,x62422),x62425))+P106(f857(f857(x62421,x62422),x62423))+~P106(f857(f857(x62421,x62425),x62423))
% 15.02/14.80 [6243]~P51(x62434,x62431)+~P106(f857(f857(x62431,x62432),x62435))+P106(f857(f857(x62431,x62432),x62433))+~P106(f857(f857(x62431,x62435),x62433))
% 15.02/14.80 [6244]~P16(x62444,x62441)+~P106(f857(f857(x62441,x62442),x62445))+P106(f857(f857(x62441,x62442),x62443))+~P106(f857(f857(x62441,x62445),x62443))
% 15.02/14.80 [8938]~P8(x89384,x89383)+~P106(f857(x89381,x89385))+P106(f857(x89382,f832(x89382,x89381,x89383,x89384)))+P106(f857(x89381,f830(x89382,x89381,x89383,x89384)))
% 15.02/14.80 [9172]~P8(x91724,x91723)+~P106(f857(x91722,x91725))+~P106(f857(x91721,f830(x91721,x91722,x91723,x91724)))+P106(f857(x91721,f832(x91721,x91722,x91723,x91724)))
% 15.02/14.80 [9354]~P8(x93544,x93543)+~P106(f857(x93541,x93545))+P106(f857(f857(f328(x93544),f832(x93542,x93541,x93543,x93544)),f269(x93544,x93543)))+P106(f857(x93541,f830(x93542,x93541,x93543,x93544)))
% 15.02/14.80 [9478]~P8(x94781,x94784)+~P106(f857(x94783,x94785))+~P106(f857(x94782,f830(x94782,x94783,x94784,x94781)))+P106(f857(f857(f328(x94781),f832(x94782,x94783,x94784,x94781)),f269(x94781,x94784)))
% 15.02/14.80 [9776]~P40(x97761,x97764)+P106(f857(f857(f328(f926(f920(x97761),f920(x97761))),f857(f857(f251(f920(x97761),f920(x97761)),x97762),x97763)),f147(x97761,x97764)))+~P106(f857(f857(f328(f926(f920(x97761),f920(x97761))),f857(f857(f251(f920(x97761),f920(x97761)),x97762),x97765)),f147(x97761,x97764)))+~P106(f857(f857(f328(f926(f920(x97761),f920(x97761))),f857(f857(f251(f920(x97761),f920(x97761)),x97765),x97763)),f147(x97761,x97764)))
% 15.02/14.80 [5479]~P69(x54795)+E(x54791,x54792)+~E(x54793,x54794)+~E(f857(f857(f3(x54795),x54793),x54794),f857(f857(f3(x54795),x54791),x54792))
% 15.02/14.80 [6360]~P18(x63605,x63601,x63603)+E(f857(f857(x63601,x63602),f857(x63603,x63604)),f857(x63603,x63604))+~P106(f857(f60(x63605),x63604))+~P106(f857(f857(f328(x63605),x63602),x63604))
% 15.02/14.80 [6553]~P80(x65531)+~E(f857(f857(f3(x65531),x65534),x65535),f857(f857(f3(x65531),x65532),x65533))+~P106(f857(f857(f234(x65531),x65534),x65535))+P106(f857(f857(f234(x65531),x65532),x65533))
% 15.02/14.80 [6555]~P80(x65551)+~E(f857(f857(f3(x65551),x65554),x65555),f857(f857(f3(x65551),x65552),x65553))+~P106(f857(f857(f235(x65551),x65554),x65555))+P106(f857(f857(f235(x65551),x65552),x65553))
% 15.02/14.80 [7532]~E(x75322,f857(f857(f151(x75321),x75324),x75325))+P106(f857(f857(f328(f920(x75321)),x75322),f161(x75321,x75323)))+~P106(f857(f857(f328(f920(x75321)),x75325),f161(x75321,x75323)))+~P106(f857(f857(f328(x75321),x75324),x75323))
% 15.02/14.80 [7935]~E(f857(f190(f920(x79351)),x79353),f857(f190(f920(x79352)),x79354))+~E(f857(f857(f154(f926(x79351,x79352),x79352),f255(x79351,x79352)),x79355),x79354)+~E(f857(f857(f154(f926(x79351,x79352),x79351),f250(x79351,x79352)),x79355),x79353)+E(f857(f857(f181(x79351,x79352),x79353),x79354),x79355)
% 15.02/14.80 [8267]~P110(x82671)+P106(f857(f857(f235(f927(x82671,a915)),f302(x82671,x82672,x82673)),f302(x82671,x82674,x82675)))+~P106(f857(f857(f234(x82671),x82674),x82675))+P106(f857(f857(f234(x82671),x82672),x82673))
% 15.02/14.80 [8366]~P110(x83661)+P106(f857(f857(f234(f927(x83661,a915)),f302(x83661,x83662,x83663)),f302(x83661,x83664,x83665)))+~P106(f857(f857(f234(x83661),x83663),x83665))+~P106(f857(f857(f234(x83661),x83664),x83662))
% 15.02/14.80 [8484]~P109(x84841)+P106(f857(f857(f234(x84841),x84842),x84843))+P106(f857(f857(f234(x84841),x84844),x84843))+~P106(f857(f857(f234(f927(x84841,a915)),f857(f301(x84841,x84843),x84842)),f857(f301(x84841,x84844),x84845)))
% 15.02/14.80 [8485]~P109(x84851)+P106(f857(f857(f234(x84851),x84852),x84853))+P106(f857(f857(f234(x84851),x84852),x84854))+~P106(f857(f857(f234(f927(x84851,a915)),f857(f301(x84851,x84853),x84852)),f857(f301(x84851,x84855),x84854)))
% 15.02/14.80 [8716]~P110(x87161)+~P106(f857(f857(f234(f927(x87161,a915)),f302(x87161,x87164,x87162)),f302(x87161,x87165,x87163)))+P106(f857(f857(f234(x87161),x87162),x87163))+~P106(f857(f857(f234(x87161),x87164),x87162))
% 15.02/14.80 [8717]~P110(x87171)+~P106(f857(f857(f235(f927(x87171,a915)),f302(x87171,x87174,x87172)),f302(x87171,x87175,x87173)))+P106(f857(f857(f234(x87171),x87172),x87173))+~P106(f857(f857(f234(x87171),x87174),x87172))
% 15.02/14.80 [8718]~P110(x87181)+~P106(f857(f857(f234(f927(x87181,a915)),f302(x87181,x87183,x87184)),f302(x87181,x87182,x87185)))+P106(f857(f857(f234(x87181),x87182),x87183))+~P106(f857(f857(f234(x87181),x87183),x87184))
% 15.02/14.80 [8719]~P110(x87191)+~P106(f857(f857(f235(f927(x87191,a915)),f302(x87191,x87193,x87194)),f302(x87191,x87192,x87195)))+P106(f857(f857(f234(x87191),x87192),x87193))+~P106(f857(f857(f234(x87191),x87193),x87194))
% 15.02/14.80 [6241]~P18(x62412,x62415,x62413)+E(x62411,f189(f927(x62412,a915)))+~P106(f857(f60(x62412),x62411))+E(f857(x62413,f857(f857(f308(x62412),x62414),x62411)),f857(f857(x62415,x62414),f857(x62413,x62411)))
% 15.02/14.80 [7024]~E(x70241,x70242)+~E(f857(f857(f101(f927(x70243,a915)),x70244),x70245),f189(f927(x70243,a915)))+~P106(f857(f857(f328(x70243),x70242),x70245))+~P106(f857(f857(f328(x70243),x70241),x70244))
% 15.02/14.80 [7105]~P19(x71052,x71055,x71051)+~P106(f857(f60(x71052),x71054))+E(f857(x71051,f857(f857(f308(x71052),x71053),x71054)),f857(f857(f63(x71052,x71052,x71055),x71053),x71054))+P106(f857(f857(f328(x71052),x71053),x71054))
% 15.02/14.80 [7173]~P72(x71732)+~P106(f857(f60(x71731),x71735))+E(f857(f857(f8(x71731,x71732),x71733),f857(f857(f308(x71731),x71734),x71735)),f857(f857(f79(x71732),f857(x71733,x71734)),f857(f857(f8(x71731,x71732),x71733),x71735)))+P106(f857(f857(f328(x71731),x71734),x71735))
% 15.02/14.80 [7175]~P77(x71752)+~P106(f857(f60(x71751),x71755))+E(f857(f857(f11(x71751,x71752),x71753),f857(f857(f308(x71751),x71754),x71755)),f857(f857(f80(x71752),f857(x71753,x71754)),f857(f857(f11(x71751,x71752),x71753),x71755)))+P106(f857(f857(f328(x71751),x71754),x71755))
% 15.02/14.80 [7578]~P113(x75781)+~P106(f857(f60(x75784),x75785))+~P106(f857(f857(f328(x75784),x75783),x75785))+P106(f857(f857(f286(x75781),f857(x75782,x75783)),f857(f857(f11(x75784,x75781),x75782),x75785)))
% 15.02/14.80 [7678]~P19(x76782,x76785,x76781)+~P106(f857(f60(x76782),x76784))+E(f857(x76781,f857(f857(f308(x76782),x76783),x76784)),x76783)+~E(f857(f857(f3(f927(x76782,a915)),x76784),f857(f857(f308(x76782),x76783),f189(f927(x76782,a915)))),f189(f927(x76782,a915)))
% 15.02/14.80 [8034]~P62(x80341)+E(f857(f857(f35(x80341),f857(f857(f80(x80341),x80342),x80343)),f857(f857(f80(x80341),x80344),x80345)),f857(f857(f80(x80341),f857(f857(f35(x80341),x80342),x80344)),f857(f857(f35(x80341),x80343),x80345)))+~P106(f857(f857(f286(x80341),x80345),x80343))+~P106(f857(f857(f286(x80341),x80344),x80342))
% 15.02/14.80 [8038]~P101(x80381)+~P106(f857(f857(f234(x80381),x80383),x80385))+~P106(f857(f857(f234(x80381),x80382),x80384))+P106(f857(f857(f234(x80381),f857(f857(f110(x80381),x80382),x80383)),f857(f857(f110(x80381),x80384),x80385)))
% 15.02/14.80 [8039]~P102(x80391)+~P106(f857(f857(f234(x80391),x80393),x80395))+~P106(f857(f857(f234(x80391),x80392),x80394))+P106(f857(f857(f234(x80391),f857(f857(f101(x80391),x80392),x80393)),f857(f857(f101(x80391),x80394),x80395)))
% 15.02/14.80 [8040]~P86(x80401)+~P106(f857(f857(f234(x80401),x80403),x80405))+~P106(f857(f857(f234(x80401),x80402),x80404))+P106(f857(f857(f234(x80401),f857(f857(f79(x80401),x80402),x80403)),f857(f857(f79(x80401),x80404),x80405)))
% 15.02/14.80 [8041]~P109(x80411)+~P106(f857(f857(f234(x80411),x80413),x80415))+~P106(f857(f857(f234(x80411),x80412),x80414))+P106(f857(f857(f234(x80411),f857(f857(f188(x80411),x80412),x80413)),f857(f857(f188(x80411),x80414),x80415)))
% 15.02/14.80 [8042]~P109(x80421)+~P106(f857(f857(f234(x80421),x80423),x80425))+~P106(f857(f857(f234(x80421),x80422),x80424))+P106(f857(f857(f234(x80421),f857(f857(f233(x80421),x80422),x80423)),f857(f857(f233(x80421),x80424),x80425)))
% 15.02/14.80 [8043]~P84(x80431)+~P106(f857(f857(f234(x80431),x80433),x80435))+~P106(f857(f857(f235(x80431),x80432),x80434))+P106(f857(f857(f235(x80431),f857(f857(f79(x80431),x80432),x80433)),f857(f857(f79(x80431),x80434),x80435)))
% 15.02/14.80 [8044]~P84(x80441)+~P106(f857(f857(f234(x80441),x80442),x80444))+~P106(f857(f857(f235(x80441),x80443),x80445))+P106(f857(f857(f235(x80441),f857(f857(f79(x80441),x80442),x80443)),f857(f857(f79(x80441),x80444),x80445)))
% 15.02/14.80 [8045]~P84(x80451)+~P106(f857(f857(f235(x80451),x80453),x80455))+~P106(f857(f857(f235(x80451),x80452),x80454))+P106(f857(f857(f235(x80451),f857(f857(f79(x80451),x80452),x80453)),f857(f857(f79(x80451),x80454),x80455)))
% 15.02/14.80 [8046]~P113(x80461)+~P106(f857(f857(f286(x80461),x80463),x80465))+~P106(f857(f857(f286(x80461),x80462),x80464))+P106(f857(f857(f286(x80461),f857(f857(f80(x80461),x80462),x80463)),f857(f857(f80(x80461),x80464),x80465)))
% 15.02/14.80 [8183]~P140(x81835)+E(x81831,x81832)+E(x81833,x81834)+~E(f857(f857(f79(x81835),f857(f857(f80(x81835),x81833),x81831)),f857(f857(f80(x81835),x81834),x81832)),f857(f857(f79(x81835),f857(f857(f80(x81835),x81833),x81832)),f857(f857(f80(x81835),x81834),x81831)))
% 15.02/14.80 [8386]~P109(x83864)+~P106(f857(f137(x83861),x83863))+P106(f857(f857(f328(x83861),x83862),f857(f172(x83861),x83863)))+P106(f857(f137(x83861),f857(f857(f148(x83861,x83864,x83865),x83862),x83863)))
% 15.02/14.80 [8531]~P69(x85311)+E(f857(f857(f3(x85311),f857(f857(f8(a919,x85311),x85312),f857(f301(a919,x85313),x85314))),f857(f857(f8(a919,x85311),x85312),f857(f301(a919,x85313),x85315))),f857(f857(f8(a919,x85311),x85312),f857(f301(a919,x85315),x85314)))+~P106(f857(f857(f234(a919),x85315),x85314))+~P106(f857(f857(f234(a919),x85313),x85315))
% 15.02/14.80 [8532]~P72(x85321)+E(f857(f857(f79(x85321),f857(f857(f8(a919,x85321),x85322),f857(f301(a919,x85323),x85324))),f857(f857(f8(a919,x85321),x85322),f857(f301(a919,x85324),x85325))),f857(f857(f8(a919,x85321),x85322),f857(f301(a919,x85323),x85325)))+~P106(f857(f857(f234(a919),x85324),x85325))+~P106(f857(f857(f234(a919),x85323),x85324))
% 15.02/14.80 [8859]~P66(x88592)+E(x88591,f2(x88592))+E(x88593,f2(x88592))+E(f857(f857(f290(x88592),f857(f857(f3(x88592),f857(f857(f80(x88592),x88594),x88591)),f857(f857(f80(x88592),x88595),x88593))),f857(f857(f80(x88592),x88593),x88591)),f857(f857(f3(x88592),f857(f857(f290(x88592),x88594),x88593)),f857(f857(f290(x88592),x88595),x88591)))
% 15.02/14.80 [8860]~P66(x88602)+E(x88601,f2(x88602))+E(x88603,f2(x88602))+E(f857(f857(f290(x88602),f857(f857(f79(x88602),f857(f857(f80(x88602),x88604),x88601)),f857(f857(f80(x88602),x88605),x88603))),f857(f857(f80(x88602),x88603),x88601)),f857(f857(f79(x88602),f857(f857(f290(x88602),x88604),x88603)),f857(f857(f290(x88602),x88605),x88601)))
% 15.02/14.80 [8869]~E(x88692,f857(x88693,x88691))+E(x88691,f502(x88692,x88693,x88694,x88695))+~P26(x88695,x88694,x88693,f241(f927(x88695,a915)))+~P106(f857(f857(f328(x88694),x88692),f857(f309(x88695,x88694,x88693),f241(f927(x88695,a915)))))
% 15.02/14.80 [9086]~P120(x90861)+~P106(f857(f857(f235(x90861),f857(f75(x90861),x90862)),x90864))+P106(f857(f857(f235(x90861),f857(f857(f80(x90861),f857(f75(x90861),x90862)),f857(f75(x90861),x90863))),f857(f857(f80(x90861),x90864),x90865)))+~P106(f857(f857(f235(x90861),f857(f75(x90861),x90863)),x90865))
% 15.02/14.80 [9197]~P26(x91971,x91973,x91975,x91972)+~P106(f857(f60(x91973),x91974))+P106(f857(f857(f234(a919),f857(f34(x91971),x91972)),f857(f34(x91973),x91974)))+~P106(f857(f857(f234(f927(x91973,a915)),f857(f309(x91971,x91973,x91975),x91972)),x91974))
% 15.02/14.80 [9264]~P72(x92642)+~P26(x92641,x92641,x92644,x92645)+~P106(f857(f60(x92641),x92645))+E(f857(f857(f8(x92641,x92642),f857(f72(x92641,x92642,x92641,x92643),x92644)),x92645),f857(f857(f8(x92641,x92642),x92643),f857(f309(x92641,x92641,x92644),x92645)))
% 15.02/14.80 [9265]~P77(x92652)+~P26(x92651,x92651,x92654,x92655)+~P106(f857(f60(x92651),x92655))+E(f857(f857(f11(x92651,x92652),f857(f72(x92651,x92652,x92651,x92653),x92654)),x92655),f857(f857(f11(x92651,x92652),x92653),f857(f309(x92651,x92651,x92654),x92655)))
% 15.02/14.81 [9382]~P39(x93821,x93822)+~P106(f857(f857(f328(x93821),x93823),x93824))+~P106(f857(f857(f328(x93821),x93825),x93824))+~P106(f857(f857(f328(f926(x93821,x93821)),f857(f857(f251(x93821,x93821),x93825),f618(x93822,x93821,x93824))),x93822))
% 15.02/14.81 [9419]~P26(x94192,x94193,x94195,x94191)+E(x94191,f189(f927(x94192,a915)))+E(f857(f309(x94193,x94192,f504(x94194,x94193,x94192,x94191)),x94194),x94191)+~P106(f857(f857(f234(f927(x94193,a915)),f857(f309(x94192,x94193,x94195),x94191)),x94194))
% 15.02/14.81 [9911]~P109(x99115)+~P6(x99115)+P106(f857(f857(f328(x99111),f435(x99112,x99113,x99111,x99114,x99115)),x99113))+~P106(f857(f857(f235(x99115),x99114),f857(f857(f39(x99111,x99115),x99113),x99112)))
% 15.02/14.81 [9916]~P109(x99161)+~P6(x99161)+P106(f857(f857(f235(x99161),x99162),f857(x99163,f435(x99163,x99164,x99165,x99162,x99161))))+~P106(f857(f857(f235(x99161),x99162),f857(f857(f39(x99165,x99161),x99164),x99163)))
% 15.02/14.81 [9994]~P70(x99941)+~P106(f857(f65(x99941,x99941,f80(x99941),x99942,x99943),x99945))+P106(f857(f857(f328(x99941),x99942),x99943))+P106(f857(f65(x99941,x99941,f80(x99941),x99944,f857(f857(f308(x99941),x99942),x99943)),f857(f857(f80(x99941),x99944),x99945)))
% 15.02/14.81 [10209]~P72(x102092)+~P106(f857(f60(x102091),x102095))+E(f857(f857(f8(x102091,x102092),f857(f857(f9(x102091,x102092,x102092),f857(f857(f20(x102091,x102092,f927(x102092,x102092)),f857(f857(f10(a915,f927(x102092,f927(x102092,x102092)),x102091),f96(x102092)),f857(a324,x102093))),x102094)),f2(x102092))),x102095),f2(x102092))+P106(f857(f857(f328(x102091),x102093),x102095))
% 15.02/14.81 [10210]~P77(x102102)+~P106(f857(f60(x102101),x102105))+E(f857(f857(f11(x102101,x102102),f857(f857(f9(x102101,x102102,x102102),f857(f857(f20(x102101,x102102,f927(x102102,x102102)),f857(f857(f10(a915,f927(x102102,f927(x102102,x102102)),x102101),f96(x102102)),f857(a324,x102103))),x102104)),f77(x102102))),x102105),f77(x102102))+P106(f857(f857(f328(x102101),x102103),x102105))
% 15.02/14.81 [10211]~P72(x102112)+~P106(f857(f60(x102111),x102115))+E(f857(f857(f8(x102111,x102112),f857(f857(f9(x102111,x102112,x102112),f857(f857(f20(x102111,x102112,f927(x102112,x102112)),f857(f857(f10(a915,f927(x102112,f927(x102112,x102112)),x102111),f96(x102112)),f857(a324,x102113))),x102114)),f2(x102112))),x102115),f857(x102114,x102113))+~P106(f857(f857(f328(x102111),x102113),x102115))
% 15.02/14.81 [10212]~P77(x102122)+~P106(f857(f60(x102121),x102125))+E(f857(f857(f11(x102121,x102122),f857(f857(f9(x102121,x102122,x102122),f857(f857(f20(x102121,x102122,f927(x102122,x102122)),f857(f857(f10(a915,f927(x102122,f927(x102122,x102122)),x102121),f96(x102122)),f857(a324,x102123))),x102124)),f77(x102122))),x102125),f857(x102124,x102123))+~P106(f857(f857(f328(x102121),x102123),x102125))
% 15.02/14.81 [10269]~P72(x102692)+~P106(f857(f60(x102691),x102695))+E(f857(f857(f8(x102691,x102692),f857(f857(f9(x102691,x102692,x102692),f857(f857(f20(x102691,x102692,f927(x102692,x102692)),f857(f857(f10(a915,f927(x102692,f927(x102692,x102692)),x102691),f96(x102692)),f857(f857(f9(x102691,x102691,a915),a324),x102693))),x102694)),f2(x102692))),x102695),f2(x102692))+P106(f857(f857(f328(x102691),x102693),x102695))
% 15.02/14.81 [10270]~P77(x102702)+~P106(f857(f60(x102701),x102705))+E(f857(f857(f11(x102701,x102702),f857(f857(f9(x102701,x102702,x102702),f857(f857(f20(x102701,x102702,f927(x102702,x102702)),f857(f857(f10(a915,f927(x102702,f927(x102702,x102702)),x102701),f96(x102702)),f857(f857(f9(x102701,x102701,a915),a324),x102703))),x102704)),f77(x102702))),x102705),f77(x102702))+P106(f857(f857(f328(x102701),x102703),x102705))
% 15.02/14.81 [10272]~P72(x102722)+~P106(f857(f60(x102721),x102725))+E(f857(f857(f8(x102721,x102722),f857(f857(f9(x102721,x102722,x102722),f857(f857(f20(x102721,x102722,f927(x102722,x102722)),f857(f857(f10(a915,f927(x102722,f927(x102722,x102722)),x102721),f96(x102722)),f857(f857(f9(x102721,x102721,a915),a324),x102723))),x102724)),f2(x102722))),x102725),f857(x102724,x102723))+~P106(f857(f857(f328(x102721),x102723),x102725))
% 15.02/14.81 [10273]~P77(x102732)+~P106(f857(f60(x102731),x102735))+E(f857(f857(f11(x102731,x102732),f857(f857(f9(x102731,x102732,x102732),f857(f857(f20(x102731,x102732,f927(x102732,x102732)),f857(f857(f10(a915,f927(x102732,f927(x102732,x102732)),x102731),f96(x102732)),f857(f857(f9(x102731,x102731,a915),a324),x102733))),x102734)),f77(x102732))),x102735),f857(x102734,x102733))+~P106(f857(f857(f328(x102731),x102733),x102735))
% 15.02/14.81 [8037]~P69(x80372)+~P106(f857(f60(x80371),x80374))+E(f857(f857(f8(x80371,x80372),x80373),f857(f857(f3(f927(x80371,a915)),x80374),f857(f857(f308(x80371),x80375),f189(f927(x80371,a915))))),f857(f857(f8(x80371,x80372),x80373),x80374))+P106(f857(f857(f328(x80371),x80375),x80374))
% 15.02/14.81 [8539]~P111(x85392)+~P106(f857(f60(x85391),x85394))+E(f857(f857(f8(x85391,x85392),x85393),f857(f857(f3(f927(x85391,a915)),x85394),f857(f857(f308(x85391),x85395),f189(f927(x85391,a915))))),f857(f857(f3(x85392),f857(f857(f8(x85391,x85392),x85393),x85394)),f857(x85393,x85395)))+~P106(f857(f857(f328(x85391),x85395),x85394))
% 15.02/14.81 [8540]~P69(x85402)+~P106(f857(f60(x85401),x85404))+E(f857(f857(f8(x85401,x85402),x85403),f857(f857(f3(f927(x85401,a915)),x85404),f857(f857(f308(x85401),x85405),f189(f927(x85401,a915))))),f857(f857(f3(x85402),f857(f857(f8(x85401,x85402),x85403),x85404)),f857(x85403,x85405)))+~P106(f857(f857(f328(x85401),x85405),x85404))
% 15.02/14.81 [8569]~P69(x85691)+~P106(f857(f60(x85692),x85694))+E(f857(f857(f3(x85691),f857(f857(f8(x85692,x85691),x85693),x85694)),f857(f857(f8(x85692,x85691),x85693),x85695)),f857(f857(f8(x85692,x85691),x85693),f857(f857(f3(f927(x85692,a915)),x85694),x85695)))+~P106(f857(f857(f234(f927(x85692,a915)),x85695),x85694))
% 15.02/14.81 [8588]P106(f857(f60(x85881),f857(x85882,x85883)))+~P106(f857(f60(x85884),x85885))+~P106(f857(f857(f328(x85884),x85883),x85885))+~P106(f857(f60(x85881),f857(f857(f39(x85884,f927(x85881,a915)),x85885),x85882)))
% 15.02/14.81 [9042]~P9(x90421,x90425,x90424)+~E(f857(f284(x90421,x90421,x90424),f857(f857(f308(x90421),x90422),f189(f927(x90421,a915)))),f857(f284(x90421,x90421,x90424),f857(f857(f308(x90421),x90423),f189(f927(x90421,a915)))))+~P106(f857(f857(f328(x90421),x90423),x90425))+P106(f857(f857(f328(f926(x90421,x90421)),f857(f857(f251(x90421,x90421),x90422),x90423)),x90424))
% 15.02/14.81 [9339]~P106(f857(x93391,x93395))+P106(f857(x93391,f358(x93391,x93392,x93393,x93394)))+P106(f857(x93391,f348(x93391,x93392,x93393,x93394)))+~P106(f857(f857(f328(x93394),x93395),f857(f857(f110(f927(x93394,a915)),x93393),x93392)))
% 15.02/14.81 [9525]~P106(f857(x95251,x95255))+P106(f857(x95251,f348(x95251,x95252,x95253,x95254)))+P106(f857(f857(f328(x95254),f358(x95251,x95252,x95253,x95254)),x95252))+~P106(f857(f857(f328(x95254),x95255),f857(f857(f110(f927(x95254,a915)),x95253),x95252)))
% 15.02/14.81 [9526]~P106(f857(x95261,x95265))+P106(f857(x95261,f358(x95261,x95262,x95263,x95264)))+P106(f857(f857(f328(x95264),f348(x95261,x95262,x95263,x95264)),x95263))+~P106(f857(f857(f328(x95264),x95265),f857(f857(f110(f927(x95264,a915)),x95263),x95262)))
% 15.02/14.81 [9530]P106(f857(x95301,x95302))+~P106(f857(x95301,f399(x95301,x95303,x95304,x95305)))+~P106(f857(x95301,f388(x95301,x95303,x95304,x95305)))+~P106(f857(f857(f328(x95305),x95302),f857(f857(f110(f927(x95305,a915)),x95304),x95303)))
% 15.02/14.81 [9535]~P40(x95351,x95354)+~P106(f857(f857(f328(f926(x95351,x95351)),f857(f857(f251(x95351,x95351),x95352),x95355)),x95354))+P106(f857(f857(f328(f926(x95351,x95351)),f857(f857(f251(x95351,x95351),x95352),x95353)),x95354))+~P106(f857(f857(f328(f926(x95351,x95351)),f857(f857(f251(x95351,x95351),x95355),x95353)),x95354))
% 15.02/14.81 [9574]E(x95741,x95742)+~P106(f857(f857(f328(f926(x95743,x95743)),f857(f857(f251(x95743,x95743),x95741),x95742)),f306(x95743,x95745)))+P106(f857(f857(f328(x95743),x95741),x95744))+~P106(f857(f857(f234(f927(f926(x95743,x95743),a915)),x95745),f857(f857(f253(x95743,x95743),x95744),f857(f18(f927(x95743,a915),x95743),x95744))))
% 15.02/14.81 [9592]P106(f857(x95921,x95922))+~P106(f857(x95921,f388(x95921,x95924,x95925,x95923)))+P106(f857(f857(f328(x95923),f399(x95921,x95924,x95925,x95923)),x95924))+~P106(f857(f857(f328(x95923),x95922),f857(f857(f110(f927(x95923,a915)),x95925),x95924)))
% 15.02/14.81 [9593]P106(f857(x95931,x95932))+~P106(f857(x95931,f399(x95931,x95934,x95935,x95933)))+P106(f857(f857(f328(x95933),f388(x95931,x95934,x95935,x95933)),x95935))+~P106(f857(f857(f328(x95933),x95932),f857(f857(f110(f927(x95933,a915)),x95935),x95934)))
% 15.02/14.81 [9661]P106(f857(x96611,x96612))+P106(f857(f857(f328(x96613),f399(x96611,x96614,x96615,x96613)),x96614))+P106(f857(f857(f328(x96613),f388(x96611,x96614,x96615,x96613)),x96615))+~P106(f857(f857(f328(x96613),x96612),f857(f857(f110(f927(x96613,a915)),x96615),x96614)))
% 15.02/14.81 [9663]~P106(f857(x96632,x96635))+P106(f857(f857(f328(x96631),f358(x96632,x96633,x96634,x96631)),x96633))+P106(f857(f857(f328(x96631),f348(x96632,x96633,x96634,x96631)),x96634))+~P106(f857(f857(f328(x96631),x96635),f857(f857(f110(f927(x96631,a915)),x96634),x96633)))
% 15.02/14.81 [9818]~P9(x98181,x98185,x98184)+~P106(f857(f857(f328(x98181),x98183),x98185))+P106(f857(f857(f328(f926(x98181,x98181)),f857(f857(f251(x98181,x98181),x98182),x98183)),x98184))+~P106(f857(f857(f234(f927(x98181,a915)),f857(f284(x98181,x98181,x98184),f857(f857(f308(x98181),x98183),f189(f927(x98181,a915))))),f857(f284(x98181,x98181,x98184),f857(f857(f308(x98181),x98182),f189(f927(x98181,a915))))))
% 15.02/14.81 [9945]~P109(x99455)+~P6(x99455)+P106(f857(f857(f328(x99451),f436(x99452,x99453,x99454,x99451,x99455)),x99454))+~P106(f857(f857(f235(x99455),f857(f857(f38(x99451,x99455),x99454),x99453)),x99452))
% 15.02/14.81 [9977]~P86(x99775)+~P83(x99775)+P106(f857(f857(f328(x99771),f695(x99772,x99773,x99774,x99771,x99775)),f857(f172(x99771),x99774)))+P106(f857(f857(f234(x99775),f857(f165(x99775),f857(f857(f154(x99771,x99775),x99773),x99774))),f857(f165(x99775),f857(f857(f154(x99771,x99775),x99772),x99774))))
% 15.02/14.81 [10086]~P109(x100861)+~P6(x100861)+P106(f857(f857(f235(x100861),f857(x100862,f436(x100863,x100862,x100864,x100865,x100861))),x100863))+~P106(f857(f857(f235(x100861),f857(f857(f38(x100865,x100861),x100864),x100862)),x100863))
% 15.02/14.81 [10227]~P86(x102271)+~P83(x102271)+~P106(f857(f857(f234(x102271),f857(x102273,f695(x102275,x102273,x102274,x102272,x102271))),f857(x102275,f695(x102275,x102273,x102274,x102272,x102271))))+P106(f857(f857(f234(x102271),f857(f165(x102271),f857(f857(f154(x102272,x102271),x102273),x102274))),f857(f165(x102271),f857(f857(f154(x102272,x102271),x102275),x102274))))
% 15.02/14.81 [8882]~P72(x88821)+~P106(f857(f60(x88824),x88825))+~P106(f857(f857(f328(x88824),x88823),x88825))+E(f857(f857(f79(x88821),f857(x88822,x88823)),f857(f857(f8(x88824,x88821),x88822),f857(f857(f3(f927(x88824,a915)),x88825),f857(f857(f308(x88824),x88823),f189(f927(x88824,a915)))))),f857(f857(f8(x88824,x88821),x88822),x88825))
% 15.02/14.81 [8883]~P77(x88831)+~P106(f857(f60(x88834),x88835))+~P106(f857(f857(f328(x88834),x88833),x88835))+E(f857(f857(f80(x88831),f857(x88832,x88833)),f857(f857(f11(x88834,x88831),x88832),f857(f857(f3(f927(x88834,a915)),x88835),f857(f857(f308(x88834),x88833),f189(f927(x88834,a915)))))),f857(f857(f11(x88834,x88831),x88832),x88835))
% 15.02/14.81 [8943]~P19(x89431,x89434,x89435)+~P106(f857(f60(x89431),x89432))+E(f857(f857(f3(f927(x89431,a915)),x89432),f857(f857(f308(x89431),x89433),f189(f927(x89431,a915)))),f189(f927(x89431,a915)))+E(f857(f857(x89434,x89433),f857(x89435,f857(f857(f3(f927(x89431,a915)),x89432),f857(f857(f308(x89431),x89433),f189(f927(x89431,a915)))))),f857(x89435,f857(f857(f308(x89431),x89433),x89432)))
% 15.02/14.81 [9318]~P77(x93181)+~P106(f857(f60(x93182),x93185))+~P106(f857(f60(x93182),x93184))+E(f857(f857(f80(x93181),f857(f857(f11(x93182,x93181),x93183),f857(f857(f110(f927(x93182,a915)),x93184),x93185))),f857(f857(f11(x93182,x93181),x93183),f857(f857(f101(f927(x93182,a915)),x93184),x93185))),f857(f857(f80(x93181),f857(f857(f11(x93182,x93181),x93183),x93184)),f857(f857(f11(x93182,x93181),x93183),x93185)))
% 15.02/14.81 [9319]~P72(x93191)+~P106(f857(f60(x93192),x93195))+~P106(f857(f60(x93192),x93194))+E(f857(f857(f79(x93191),f857(f857(f8(x93192,x93191),x93193),f857(f857(f110(f927(x93192,a915)),x93194),x93195))),f857(f857(f8(x93192,x93191),x93193),f857(f857(f101(f927(x93192,a915)),x93194),x93195))),f857(f857(f79(x93191),f857(f857(f8(x93192,x93191),x93193),x93194)),f857(f857(f8(x93192,x93191),x93193),x93195)))
% 15.02/14.81 [9458]~P69(x94581)+~P106(f857(f60(x94582),x94585))+~P106(f857(f60(x94582),x94584))+E(f857(f857(f3(x94581),f857(f857(f79(x94581),f857(f857(f8(x94582,x94581),x94583),x94584)),f857(f857(f8(x94582,x94581),x94583),x94585))),f857(f857(f8(x94582,x94581),x94583),f857(f857(f101(f927(x94582,a915)),x94584),x94585))),f857(f857(f8(x94582,x94581),x94583),f857(f857(f110(f927(x94582,a915)),x94584),x94585)))
% 15.02/14.81 [9675]~P26(x96751,x96752,x96753,x96755)+~P26(x96751,x96752,x96753,x96754)+P26(x96751,x96752,x96753,f857(f857(f110(f927(x96751,a915)),x96754),x96755))+~E(f857(f857(f101(f927(x96752,a915)),f857(f309(x96751,x96752,x96753),f857(f857(f3(f927(x96751,a915)),x96754),x96755))),f857(f309(x96751,x96752,x96753),f857(f857(f3(f927(x96751,a915)),x96755),x96754))),f189(f927(x96752,a915)))
% 15.02/14.81 [9793]E(x97931,f2(a1))+~P106(f857(f857(f235(a1),f2(a1)),x97933))+~P106(f857(f48(x97932,x97931),f857(f857(f251(a1,a1),x97934),x97935)))+P106(f857(f48(x97932,f857(f857(f80(a1),x97931),x97933)),f857(f857(f251(a1,a1),f857(f857(f35(a1),x97934),x97933)),f857(f857(f79(a1),f857(f857(f80(a1),x97931),f44(a1,x97934,x97933))),x97935))))
% 15.02/14.81 [9801]~P106(f857(f857(f235(a919),f2(a919)),x98013))+~P106(f857(f857(f235(a919),f2(a919)),x98012))+~P106(f857(f47(x98011,x98012),f857(f857(f251(a919,a919),x98014),x98015)))+P106(f857(f47(x98011,f857(f857(f80(a919),x98012),x98013)),f857(f857(f251(a919,a919),f857(f857(f35(a919),x98014),x98013)),f857(f857(f79(a919),f857(f857(f80(a919),x98012),f44(a919,x98014,x98013))),x98015))))
% 15.02/14.81 [9850]~P77(x98501)+~P106(f857(f60(x98502),x98505))+~P106(f857(f60(x98502),x98504))+E(f857(f857(f80(x98501),f857(f857(f857(f64(x98501,x98502,f80(x98501)),x98503),f77(x98501)),f857(f857(f110(f927(x98502,a915)),x98504),x98505))),f857(f857(f857(f64(x98501,x98502,f80(x98501)),x98503),f77(x98501)),f857(f857(f101(f927(x98502,a915)),x98504),x98505))),f857(f857(f80(x98501),f857(f857(f857(f64(x98501,x98502,f80(x98501)),x98503),f77(x98501)),x98504)),f857(f857(f857(f64(x98501,x98502,f80(x98501)),x98503),f77(x98501)),x98505)))
% 15.02/14.81 [9852]~E(f857(f857(f175(x98521),x98525),x98522),f857(f857(f175(x98521),x98525),x98523))+P106(f857(f857(f328(f926(f920(x98521),f920(x98521))),f857(f857(f251(f920(x98521),f920(x98521)),x98522),x98523)),f147(x98521,x98524)))+~P106(f857(f857(f235(a919),x98525),f857(f857(f188(a919),f857(f190(f920(x98521)),x98522)),f857(f190(f920(x98521)),x98523))))+~P106(f857(f857(f328(f926(x98521,x98521)),f857(f857(f251(x98521,x98521),f857(f857(f164(x98521),x98522),x98525)),f857(f857(f164(x98521),x98523),x98525))),x98524))
% 15.02/14.81 [9966]~P86(x99665)+~P146(x99665)+P106(f857(f857(f328(x99661),f354(x99662,x99663,x99664,x99661,x99665)),x99664))+P106(f857(f857(f234(x99665),f857(f857(f8(x99661,x99665),x99663),x99664)),f857(f857(f80(x99665),f857(f100(x99665),f857(f34(x99661),x99664))),x99662)))
% 15.02/14.81 [10145]~P86(x101451)+~P146(x101451)+~P106(f857(f857(f234(x101451),f857(x101453,f354(x101455,x101453,x101454,x101452,x101451))),x101455))+P106(f857(f857(f234(x101451),f857(f857(f8(x101452,x101451),x101453),x101454)),f857(f857(f80(x101451),f857(f100(x101451),f857(f34(x101452),x101454))),x101455)))
% 15.02/14.81 [8911]E(f857(f857(f134(x89111),x89112),x89113),f857(f857(f134(x89111),x89114),x89115))+~E(f857(f857(f175(x89111),f857(f190(f920(x89111)),x89112)),x89114),x89112)+~E(f857(f857(f134(x89111),f857(f857(f138(x89111),f857(f190(f920(x89111)),x89112)),x89114)),x89115),x89113)+P106(f857(f857(f234(a919),f857(f190(f920(x89111)),x89114)),f857(f190(f920(x89111)),x89112)))
% 15.02/14.81 [9041]E(f857(f857(f134(x90411),x90412),x90413),f857(f857(f134(x90411),x90414),x90415))+~E(f857(f857(f175(x90411),f857(f190(f920(x90411)),x90412)),x90414),x90412)+~E(x90413,f857(f857(f134(x90411),f857(f857(f138(x90411),f857(f190(f920(x90411)),x90412)),x90414)),x90415))+~P106(f857(f857(f234(a919),f857(f190(f920(x90411)),x90412)),f857(f190(f920(x90411)),x90414)))
% 15.02/14.81 [10292]~P106(f857(x102925,x102924))+~P106(f857(f60(x102922),f857(f261(x102922),x102925)))+P106(f857(f60(x102921),f857(f261(x102921),f857(f857(f9(x102921,x102922,a915),x102923),x102924))))+~P106(f857(f60(x102921),f857(f261(x102921),f857(f857(f10(f927(x102922,a915),a915,x102921),f86(x102922)),f857(f857(f10(f927(x102922,a915),f927(x102922,a915),x102921),f857(f20(x102922,a915,a915),f857(f857(f10(a915,f927(a915,a915),x102922),a325),x102925))),x102923)))))
% 15.02/14.81 [10365]~P106(f857(f60(x103652),x103655))+~P106(f857(f857(f328(x103652),x103654),x103655))+P106(f857(f60(x103651),f857(f261(x103651),f857(f857(f9(x103651,x103652,a915),x103653),x103654))))+~P106(f857(f60(x103651),f857(f261(x103651),f857(f857(f10(f927(x103652,a915),a915,x103651),f86(x103652)),f857(f857(f10(f927(x103652,a915),f927(x103652,a915),x103651),f857(f20(x103652,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103652),a325),f857(f857(f9(x103652,f927(x103652,a915),a915),f328(x103652)),x103655)))),x103653)))))
% 15.02/14.81 [8697]~P20(x86975,x86971,x86976,x86972)+E(f857(f72(x86971,x86971,x86971,f857(x86972,x86973)),f857(x86972,x86974)),f857(f72(x86971,x86971,x86971,f857(x86972,x86974)),f857(x86972,x86973)))+~P106(f857(f60(x86975),x86974))+~P106(f857(f60(x86975),x86973))
% 15.02/14.81 [8093]~P26(x80931,x80932,x80934,x80933)+~E(f857(x80934,x80936),x80935)+E(f857(f76(x80931,x80932,x80933,x80934),x80935),x80936)+~P106(f857(f857(f328(x80931),x80936),x80933))
% 15.02/14.81 [8094]~P26(x80941,x80942,x80944,x80943)+~E(f857(x80944,x80946),x80945)+E(f857(f91(x80941,x80942,x80943,x80944),x80945),x80946)+~P106(f857(f857(f328(x80941),x80946),x80943))
% 15.02/14.81 [8288]~P21(x82886,x82881,x82884,x82882)+E(f857(f72(x82881,x82881,x82881,f857(x82882,x82883)),f857(x82884,x82885)),f857(x82882,x82883))+~P106(f857(f60(x82886),x82883))+~P106(f857(f857(f328(x82886),x82885),x82883))
% 15.02/14.81 [9410]E(x94101,x94102)+~E(f857(f91(x94103,x94104,x94105,x94106),x94101),f857(f91(x94103,x94104,x94105,x94106),x94102))+~P106(f857(f857(f328(x94104),x94102),f857(f309(x94103,x94104,x94106),x94105)))+~P106(f857(f857(f328(x94104),x94101),f857(f309(x94103,x94104,x94106),x94105)))
% 15.02/14.81 [9509]~P20(x95093,x95091,x95096,x95092)+E(f857(f72(x95091,x95091,x95091,f857(x95092,f857(f857(f3(f927(x95093,a915)),x95094),f857(f857(f308(x95093),x95095),f189(f927(x95093,a915)))))),f857(x95096,x95095)),f857(x95092,x95094))+~P106(f857(f60(x95093),x95094))+~P106(f857(f857(f328(x95093),x95095),x95094))
% 15.02/14.81 [7178]~P63(x71781)+~E(f44(x71781,x71783,x71784),f44(x71781,x71786,x71784))+~E(f44(x71781,x71782,x71784),f44(x71781,x71785,x71784))+E(f44(x71781,f857(f857(f3(x71781),x71782),x71783),x71784),f44(x71781,f857(f857(f3(x71781),x71785),x71786),x71784))
% 15.02/14.81 [7179]~P62(x71791)+~E(f44(x71791,x71793,x71794),f44(x71791,x71796,x71794))+~E(f44(x71791,x71792,x71794),f44(x71791,x71795,x71794))+E(f44(x71791,f857(f857(f80(x71791),x71792),x71793),x71794),f44(x71791,f857(f857(f80(x71791),x71795),x71796),x71794))
% 15.02/14.81 [7180]~P62(x71801)+~E(f44(x71801,x71803,x71804),f44(x71801,x71806,x71804))+~E(f44(x71801,x71802,x71804),f44(x71801,x71805,x71804))+E(f44(x71801,f857(f857(f79(x71801),x71802),x71803),x71804),f44(x71801,f857(f857(f79(x71801),x71805),x71806),x71804))
% 15.02/14.81 [7989]~P17(x79891,x79892,x79893)+~P106(f857(f60(x79891),x79896))+E(f857(f857(f63(x79891,x79892,x79893),x79894),f857(f857(f308(x79891),x79895),x79896)),f857(f857(f63(x79891,x79892,x79893),f857(f857(x79893,x79895),x79894)),x79896))+P106(f857(f857(f328(x79891),x79895),x79896))
% 15.02/14.81 [8052]~P6(x80521)+P106(f857(f857(f234(x80521),x80522),f857(x80523,x80524)))+~P106(f857(f857(f328(x80525),x80524),x80526))+~P106(f857(f857(f234(x80521),x80522),f857(f857(f38(x80525,x80521),x80526),x80523)))
% 15.02/14.81 [8210]~P17(x82101,x82102,x82103)+~P106(f857(f60(x82101),x82106))+E(f857(f857(f63(x82101,x82102,x82103),x82104),f857(f857(f308(x82101),x82105),x82106)),f857(f857(x82103,x82105),f857(f857(f63(x82101,x82102,x82103),x82104),x82106)))+P106(f857(f857(f328(x82101),x82105),x82106))
% 15.02/14.81 [8305]~P109(x83053)+~P106(f857(x83052,x83055))+~P14(x83053,f857(f857(f154(x83051,x83053),x83054),x83056))+E(f857(f136(x83051,x83052),f857(f857(f148(x83051,x83053,x83054),x83055),x83056)),f857(f857(f148(x83051,x83053,x83054),x83055),f857(f136(x83051,x83052),x83056)))
% 15.02/14.81 [8328]E(x83281,x83282)+E(x83283,f2(a1))+~P106(f857(f48(x83284,x83283),f857(f857(f251(a1,a1),x83285),x83282)))+~P106(f857(f48(x83284,x83283),f857(f857(f251(a1,a1),x83286),x83281)))
% 15.02/14.81 [8329]E(x83291,x83292)+E(x83293,f2(a1))+~P106(f857(f48(x83294,x83293),f857(f857(f251(a1,a1),x83292),x83295)))+~P106(f857(f48(x83294,x83293),f857(f857(f251(a1,a1),x83291),x83296)))
% 15.02/14.81 [8352]~P20(x83522,x83525,x83526,x83521)+~P106(f857(f60(x83522),x83524))+E(f857(x83521,f857(f857(f308(x83522),x83523),x83524)),f857(f72(x83525,x83525,x83525,f857(x83521,x83524)),f857(x83526,x83523)))+P106(f857(f857(f328(x83522),x83523),x83524))
% 15.02/14.81 [8572]~P21(x85725,x85721,x85726,x85722)+E(f857(f72(x85721,x85721,x85721,f857(x85722,x85723)),f857(x85722,x85724)),f857(x85722,x85723))+~P106(f857(f60(x85725),x85723))+~P106(f857(f857(f234(f927(x85725,a915)),x85724),x85723))
% 15.02/14.81 [9723]~P26(x97231,x97232,x97234,x97233)+~P106(f857(f857(f328(x97232),x97235),f857(f309(x97231,x97232,x97234),x97233)))+P106(f857(f857(f328(x97231),f857(f76(x97231,x97232,x97233,x97234),x97235)),x97236))+~P106(f857(f857(f234(f927(x97231,a915)),x97233),x97236))
% 15.02/14.81 [10097]~P72(x100972)+~E(f589(x100971,x100973,x100975,x100976,x100974,x100972),f590(x100971,x100973,x100975,x100976,x100974,x100972))+~P106(f857(f60(x100974),x100976))+E(f857(f857(f8(x100971,x100972),x100973),f857(f309(x100974,x100971,x100975),x100976)),f857(f857(f8(x100974,x100972),f857(f72(x100971,x100972,x100974,x100973),x100975)),x100976))
% 15.02/14.81 [10127]~P72(x101276)+E(f857(x101271,f589(x101272,x101273,x101271,x101274,x101275,x101276)),f857(x101271,f590(x101272,x101273,x101271,x101274,x101275,x101276)))+E(f857(f857(f8(x101272,x101276),x101273),f857(f309(x101275,x101272,x101271),x101274)),f857(f857(f8(x101275,x101276),f857(f72(x101272,x101276,x101275,x101273),x101271)),x101274))+~P106(f857(f60(x101275),x101274))
% 15.02/14.81 [10177]~P72(x101772)+~E(f857(x101773,f857(x101775,f590(x101771,x101773,x101775,x101776,x101774,x101772))),f2(x101772))+~P106(f857(f60(x101774),x101776))+E(f857(f857(f8(x101771,x101772),x101773),f857(f309(x101774,x101771,x101775),x101776)),f857(f857(f8(x101774,x101772),f857(f72(x101771,x101772,x101774,x101773),x101775)),x101776))
% 15.02/14.81 [10235]~P72(x102352)+~P106(f857(f60(x102354),x102356))+E(f857(f857(f8(x102351,x102352),x102353),f857(f309(x102354,x102351,x102355),x102356)),f857(f857(f8(x102354,x102352),f857(f72(x102351,x102352,x102354,x102353),x102355)),x102356))+P106(f857(f857(f328(x102354),f590(x102351,x102353,x102355,x102356,x102354,x102352)),x102356))
% 15.02/14.81 [10236]~P72(x102362)+~P106(f857(f60(x102364),x102366))+E(f857(f857(f8(x102361,x102362),x102363),f857(f309(x102364,x102361,x102365),x102366)),f857(f857(f8(x102364,x102362),f857(f72(x102361,x102362,x102364,x102363),x102365)),x102366))+P106(f857(f857(f328(x102364),f589(x102361,x102363,x102365,x102366,x102364,x102362)),x102366))
% 15.02/14.81 [10364]~P77(x103641)+~P106(f857(f60(x103642),x103646))+E(f857(f857(f857(f64(x103641,x103642,f80(x103641)),f857(f857(f20(x103642,f927(x103643,a915),x103641),f857(f857(f9(x103642,x103641,f927(f927(x103643,a915),x103641)),f857(f857(f10(f927(x103643,x103641),f927(x103641,f927(f927(x103643,a915),x103641)),x103642),f64(x103641,x103643,f80(x103641))),x103644)),f77(x103641))),x103645)),f77(x103641)),x103646),f857(f857(f857(f64(x103641,f926(x103642,x103643),f80(x103641)),f857(f256(x103642,x103643,x103641),x103644)),f77(x103641)),f857(f857(f253(x103642,x103643),x103646),x103645)))+P106(f857(f857(f328(x103642),f538(x103644,x103645,x103643,x103646,x103642,x103641)),x103646))
% 15.02/14.81 [10386]~P77(x103861)+~P106(f857(f60(x103862),x103866))+E(f857(f857(f857(f64(x103861,x103862,f80(x103861)),f857(f857(f20(x103862,f927(x103863,a915),x103861),f857(f857(f9(x103862,x103861,f927(f927(x103863,a915),x103861)),f857(f857(f10(f927(x103863,x103861),f927(x103861,f927(f927(x103863,a915),x103861)),x103862),f64(x103861,x103863,f80(x103861))),x103864)),f77(x103861))),x103865)),f77(x103861)),x103866),f857(f857(f857(f64(x103861,f926(x103862,x103863),f80(x103861)),f857(f256(x103862,x103863,x103861),x103864)),f77(x103861)),f857(f857(f253(x103862,x103863),x103866),x103865)))+~P106(f857(f60(x103863),f857(x103865,f538(x103864,x103865,x103863,x103866,x103862,x103861))))
% 15.02/14.81 [8483]~P21(x84832,x84835,x84836,x84831)+~P106(f857(f60(x84832),x84834))+~P106(f857(f60(x84832),x84833))+E(f857(x84831,f857(f857(f110(f927(x84832,a915)),x84833),x84834)),f857(f72(x84835,x84835,x84835,f857(x84831,x84833)),f857(x84831,x84834)))
% 15.02/14.81 [8698]~P6(x86981)+P106(f857(f857(f234(x86981),f857(x86982,x86983)),x86984))+~P106(f857(f857(f328(x86985),x86983),x86986))+~P106(f857(f857(f234(x86981),f857(f857(f39(x86985,x86981),x86986),x86982)),x86984))
% 15.02/14.81 [9127]~P26(x91272,x91271,x91273,x91276)+E(f857(f857(f3(f927(x91271,a915)),f857(f309(x91272,x91271,x91273),x91274)),f857(f309(x91272,x91271,x91273),x91275)),f857(f309(x91272,x91271,x91273),f857(f857(f3(f927(x91272,a915)),x91274),x91275)))+~P106(f857(f857(f234(f927(x91272,a915)),x91275),x91276))+~P106(f857(f857(f234(f927(x91272,a915)),x91274),x91276))
% 15.02/14.81 [9128]~P26(x91282,x91281,x91283,x91286)+E(f857(f857(f101(f927(x91281,a915)),f857(f309(x91282,x91281,x91283),x91284)),f857(f309(x91282,x91281,x91283),x91285)),f857(f309(x91282,x91281,x91283),f857(f857(f101(f927(x91282,a915)),x91284),x91285)))+~P106(f857(f857(f234(f927(x91282,a915)),x91285),x91286))+~P106(f857(f857(f234(f927(x91282,a915)),x91284),x91286))
% 15.02/14.81 [9384]E(x93841,x93842)+~P56(x93843,x93844,x93845)+~P106(f857(f857(f328(f926(x93843,x93844)),f857(f857(f251(x93843,x93844),x93846),x93842)),x93845))+~P106(f857(f857(f328(f926(x93843,x93844)),f857(f857(f251(x93843,x93844),x93846),x93841)),x93845))
% 15.02/14.81 [10173]~P70(x101731)+~E(f857(x101733,f343(x101734,x101736,x101733,x101735,x101732,x101731)),f857(x101736,f343(x101734,x101736,x101733,x101735,x101732,x101731)))+~P106(f857(f60(x101732),x101735))+E(f857(f857(f857(f64(x101731,x101732,f80(x101731)),x101733),x101734),x101735),f857(f857(f857(f64(x101731,x101732,f80(x101731)),x101736),x101734),x101735))
% 15.02/14.81 [10233]~P70(x102331)+~P106(f857(f60(x102332),x102335))+E(f857(f857(f857(f64(x102331,x102332,f80(x102331)),x102333),x102334),x102335),f857(f857(f857(f64(x102331,x102332,f80(x102331)),x102336),x102334),x102335))+P106(f857(f857(f328(x102332),f343(x102334,x102333,x102336,x102335,x102332,x102331)),x102335))
% 15.02/14.81 [8925]~P70(x89251)+~P106(f857(f60(x89252),x89256))+P106(f857(f857(f328(x89252),x89255),x89256))+E(f857(f857(f857(f64(x89251,x89252,f80(x89251)),x89253),x89254),f857(f857(f308(x89252),x89255),x89256)),f857(f857(f80(x89251),f857(x89253,x89255)),f857(f857(f857(f64(x89251,x89252,f80(x89251)),x89253),x89254),x89256)))
% 15.02/14.81 [8978]~P9(x89781,x89786,x89783)+~P12(x89781,f927(x89782,a915),x89783,x89785)+~P106(f857(f857(f328(x89781),x89784),x89786))+E(f857(f857(f39(x89781,f927(x89782,a915)),f857(f284(x89781,x89781,x89783),f857(f857(f308(x89781),x89784),f189(f927(x89781,a915))))),x89785),f857(x89785,x89784))
% 15.02/14.81 [9104]~P17(x91043,x91044,x91041)+~P106(f857(f60(x91043),x91046))+~P106(f857(f857(f328(x91043),x91042),x91046))+E(f857(f857(x91041,x91042),f857(f857(f63(x91043,x91044,x91041),x91045),f857(f857(f3(f927(x91043,a915)),x91046),f857(f857(f308(x91043),x91042),f189(f927(x91043,a915)))))),f857(f857(f63(x91043,x91044,x91041),x91045),x91046))
% 15.02/14.81 [9394]~P20(x93943,x93941,x93946,x93942)+~P106(f857(f60(x93943),x93945))+~P106(f857(f60(x93943),x93944))+E(f857(f72(x93941,x93941,x93941,f857(x93942,f857(f857(f110(f927(x93943,a915)),x93944),x93945))),f857(x93942,f857(f857(f101(f927(x93943,a915)),x93944),x93945))),f857(f72(x93941,x93941,x93941,f857(x93942,x93944)),f857(x93942,x93945)))
% 15.02/14.81 [9746]~E(x97463,f857(f857(f159(x97461,x97462),x97465),x97466))+P106(f857(f857(f328(f926(f920(x97461),f920(x97461))),f857(f857(f251(f920(x97461),f920(x97461)),x97462),x97463)),f157(x97461,x97464)))+~P106(f857(f857(f235(a919),x97465),f857(f190(f920(x97461)),x97462)))+~P106(f857(f857(f328(f926(x97461,x97461)),f857(f857(f251(x97461,x97461),f857(f857(f164(x97461),x97462),x97465)),x97466)),x97464))
% 15.02/14.81 [10249]~P72(x102492)+~P106(f857(f60(x102491),x102496))+P106(f857(f857(f328(x102491),f542(x102494,x102495,x102493,x102496,x102491,x102492)),x102496))+E(f857(f857(f8(x102491,x102492),f857(f857(f20(x102491,f927(x102493,a915),x102492),f857(f857(f10(f927(x102493,x102492),f927(f927(x102493,a915),x102492),x102491),f8(x102493,x102492)),x102494)),x102495)),x102496),f857(f857(f8(f926(x102491,x102493),x102492),f857(f256(x102491,x102493,x102492),x102494)),f857(f857(f253(x102491,x102493),x102496),x102495)))
% 15.02/14.81 [10250]~P77(x102502)+~P106(f857(f60(x102501),x102506))+P106(f857(f857(f328(x102501),f543(x102504,x102505,x102503,x102506,x102501,x102502)),x102506))+E(f857(f857(f11(x102501,x102502),f857(f857(f20(x102501,f927(x102503,a915),x102502),f857(f857(f10(f927(x102503,x102502),f927(f927(x102503,a915),x102502),x102501),f11(x102503,x102502)),x102504)),x102505)),x102506),f857(f857(f11(f926(x102501,x102503),x102502),f857(f256(x102501,x102503,x102502),x102504)),f857(f857(f253(x102501,x102503),x102506),x102505)))
% 15.02/14.81 [10290]~P72(x102902)+~P106(f857(f60(x102901),x102906))+~P106(f857(f60(x102903),f857(x102905,f542(x102904,x102905,x102903,x102906,x102901,x102902))))+E(f857(f857(f8(x102901,x102902),f857(f857(f20(x102901,f927(x102903,a915),x102902),f857(f857(f10(f927(x102903,x102902),f927(f927(x102903,a915),x102902),x102901),f8(x102903,x102902)),x102904)),x102905)),x102906),f857(f857(f8(f926(x102901,x102903),x102902),f857(f256(x102901,x102903,x102902),x102904)),f857(f857(f253(x102901,x102903),x102906),x102905)))
% 15.02/14.81 [10291]~P77(x102912)+~P106(f857(f60(x102911),x102916))+~P106(f857(f60(x102913),f857(x102915,f543(x102914,x102915,x102913,x102916,x102911,x102912))))+E(f857(f857(f11(x102911,x102912),f857(f857(f20(x102911,f927(x102913,a915),x102912),f857(f857(f10(f927(x102913,x102912),f927(f927(x102913,a915),x102912),x102911),f11(x102913,x102912)),x102914)),x102915)),x102916),f857(f857(f11(f926(x102911,x102913),x102912),f857(f256(x102911,x102913,x102912),x102914)),f857(f857(f253(x102911,x102913),x102916),x102915)))
% 15.02/14.81 [10271]~P77(x102712)+~P106(f857(f60(x102711),x102716))+P106(f857(f857(f328(x102711),x102713),x102716))+E(f857(f857(f11(x102711,x102712),f857(f857(f9(x102711,x102712,x102712),f857(f857(f20(x102711,x102712,f927(x102712,x102712)),f857(f857(f10(a915,f927(x102712,f927(x102712,x102712)),x102711),f96(x102712)),f857(f857(f9(x102711,x102711,a915),a324),x102713))),x102714)),x102715)),x102716),f857(f857(f243(x102712),x102715),f857(f34(x102711),x102716)))
% 15.02/14.81 [10276]~P77(x102762)+~P106(f857(f60(x102761),x102766))+~P106(f857(f857(f328(x102761),x102763),x102766))+E(f857(f857(f11(x102761,x102762),f857(f857(f9(x102761,x102762,x102762),f857(f857(f20(x102761,x102762,f927(x102762,x102762)),f857(f857(f10(a915,f927(x102762,f927(x102762,x102762)),x102761),f96(x102762)),f857(f857(f9(x102761,x102761,a915),a324),x102763))),x102764)),x102765)),x102766),f857(f857(f80(x102762),f857(x102764,x102763)),f857(f857(f243(x102762),x102765),f857(f857(f3(a919),f857(f34(x102761),x102766)),f77(a919)))))
% 15.02/14.81 [10355]~P106(f857(f60(x103551),x103555))+~P106(f857(f60(x103552),x103553))+P106(f857(f857(f328(x103552),f560(x103556,x103554,x103553,x103552,x103555,x103551)),x103553))+E(f857(f857(f8(x103551,a919),f857(f857(f10(f927(x103552,a915),a919,x103551),f34(x103552)),f857(f857(f10(f927(x103552,a915),f927(x103552,a915),x103551),f261(x103552)),f857(f857(f10(f927(x103552,a915),f927(x103552,a915),x103551),f857(f20(x103552,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103552),a325),f857(f857(f9(x103552,f927(x103552,a915),a915),f328(x103552)),x103553)))),x103554)))),x103555),f857(f857(f80(a919),x103556),f857(f34(x103552),x103553)))
% 15.02/14.81 [10356]~P106(f857(f60(x103561),x103565))+~P106(f857(f60(x103562),x103563))+P106(f857(f857(f328(x103562),f561(x103566,x103564,x103563,x103562,x103565,x103561)),x103563))+E(f857(f857(f8(x103561,a919),f857(f857(f10(f927(x103562,a915),a919,x103561),f34(x103562)),f857(f857(f10(f927(x103562,a915),f927(x103562,a915),x103561),f261(x103562)),f857(f857(f10(f927(x103562,a915),f927(x103562,a915),x103561),f857(f20(x103562,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103562),a325),f857(f857(f9(x103562,f927(x103562,a915),a915),f328(x103562)),x103563)))),x103564)))),x103565),f857(f857(f8(x103562,a919),x103566),x103563))
% 15.02/14.81 [10400]~P106(f857(f60(x104002),x104003))+~P106(f857(f60(x104001),x104005))+~E(f857(f34(x104001),f857(f261(x104001),f857(f857(f20(x104001,a915,a915),f857(f857(f10(a915,f927(a915,a915),x104001),a325),f857(f857(f9(x104001,f927(x104001,a915),a915),f328(x104001)),x104005))),f857(f857(f9(x104001,x104002,a915),x104004),f560(x104006,x104004,x104003,x104002,x104005,x104001))))),x104006)+E(f857(f857(f8(x104001,a919),f857(f857(f10(f927(x104002,a915),a919,x104001),f34(x104002)),f857(f857(f10(f927(x104002,a915),f927(x104002,a915),x104001),f261(x104002)),f857(f857(f10(f927(x104002,a915),f927(x104002,a915),x104001),f857(f20(x104002,a915,a915),f857(f857(f10(a915,f927(a915,a915),x104002),a325),f857(f857(f9(x104002,f927(x104002,a915),a915),f328(x104002)),x104003)))),x104004)))),x104005),f857(f857(f80(a919),x104006),f857(f34(x104002),x104003)))
% 15.02/14.81 [10402]~P106(f857(f60(x104022),x104023))+~P106(f857(f60(x104021),x104025))+~E(f857(f34(x104021),f857(f261(x104021),f857(f857(f20(x104021,a915,a915),f857(f857(f10(a915,f927(a915,a915),x104021),a325),f857(f857(f9(x104021,f927(x104021,a915),a915),f328(x104021)),x104025))),f857(f857(f9(x104021,x104022,a915),x104024),f561(x104026,x104024,x104023,x104022,x104025,x104021))))),f857(x104026,f561(x104026,x104024,x104023,x104022,x104025,x104021)))+E(f857(f857(f8(x104021,a919),f857(f857(f10(f927(x104022,a915),a919,x104021),f34(x104022)),f857(f857(f10(f927(x104022,a915),f927(x104022,a915),x104021),f261(x104022)),f857(f857(f10(f927(x104022,a915),f927(x104022,a915),x104021),f857(f20(x104022,a915,a915),f857(f857(f10(a915,f927(a915,a915),x104022),a325),f857(f857(f9(x104022,f927(x104022,a915),a915),f328(x104022)),x104023)))),x104024)))),x104025),f857(f857(f8(x104022,a919),x104026),x104023))
% 15.02/14.81 [10022]E(x100221,x100222)+~P17(x100223,x100224,x100225)+~P106(f857(f65(x100223,x100224,x100225,x100226,x100227),x100222))+~P106(f857(f65(x100223,x100224,x100225,x100226,x100227),x100221))
% 15.02/14.81 [9822]P106(f857(x98221,x98222))+~P106(f857(f857(f328(x98227),x98222),f857(x98226,x98224)))+~P106(f857(x98221,f451(x98221,x98226,x98225,x98223,x98227)))+~P106(f857(f857(f328(x98223),x98224),x98225))
% 15.02/14.81 [10263]~P17(x102637,x102636,x102631)+E(f857(f857(x102631,x102632),f808(x102632,x102633,x102634,x102635,x102631,x102636,x102637)),x102633)+~P106(f857(f65(x102637,x102636,x102631,x102635,x102634),x102633))+~P106(f857(f857(f328(x102637),x102632),x102634))
% 15.02/14.81 [10333]~P17(x103331,x103332,x103333)+~P106(f857(f65(x103331,x103332,x103333,x103334,x103335),x103337))+P106(f857(f65(x103331,x103332,x103333,x103334,f857(f857(f3(f927(x103331,a915)),x103335),f857(f857(f308(x103331),x103336),f189(f927(x103331,a915))))),f808(x103336,x103337,x103335,x103334,x103333,x103332,x103331)))+~P106(f857(f857(f328(x103331),x103336),x103335))
% 15.02/14.81 [9465]P27(x94651,x94652,x94653,x94654,x94655)+~P27(x94651,x94652,x94653,x94656,x94657)+~E(f857(f309(x94651,x94652,x94653),x94654),x94655)+~P106(f857(f857(f234(f927(x94651,a915)),x94654),x94656))
% 15.02/14.81 [9714]~P27(x97141,x97142,x97143,x97145,x97147)+~P27(x97141,x97142,x97143,x97144,x97146)+P27(x97141,x97142,x97143,f857(f857(f110(f927(x97141,a915)),x97144),x97145),f857(f857(f110(f927(x97142,a915)),x97146),x97147))+~E(f857(f857(f101(f927(x97142,a915)),x97146),x97147),f189(f927(x97142,a915)))
% 15.02/14.81 [9719]~P70(x97191)+~P26(x97195,x97192,x97196,x97197)+~P106(f857(f60(x97195),x97197))+E(f857(f857(f857(f64(x97191,x97192,f80(x97191)),x97193),x97194),f857(f309(x97195,x97192,x97196),x97197)),f857(f857(f857(f64(x97191,x97195,f80(x97191)),f857(f72(x97192,x97191,x97195,x97193),x97196)),x97194),x97197))
% 15.02/14.81 [9845]~E(f857(f857(f308(x98451),x98455),x98456),f857(f857(f308(x98451),x98452),x98453))+~P106(f857(f65(x98451,x98451,x98454,x98452,x98453),x98457))+P106(f857(f857(f328(x98451),x98452),x98453))+P106(f857(f61(x98451,x98454,f857(f857(f308(x98451),x98455),x98456)),x98457))
% 15.02/14.81 [9929]P106(f857(x99291,x99292))+~P106(f857(f857(f328(x99293),x99292),f857(x99294,x99297)))+~P106(f857(f857(f328(x99296),x99297),x99295))+P106(f857(f857(f328(x99293),f451(x99291,x99294,x99295,x99296,x99293)),f857(f857(f39(x99296,f927(x99293,a915)),x99295),x99294)))
% 15.02/14.81 [9946]~P26(x99462,x99461,x99465,x99464)+~P26(x99461,x99463,x99466,f857(f309(x99462,x99461,x99465),x99464))+E(f857(f857(f72(x99461,x99462,x99463,f76(x99462,x99461,x99464,x99465)),f76(x99461,x99463,f857(f309(x99462,x99461,x99465),x99464),x99466)),x99467),f857(f76(x99462,x99463,x99464,f857(f72(x99461,x99463,x99462,x99466),x99465)),x99467))+~P106(f857(f857(f328(x99463),x99467),f857(f309(x99461,x99463,x99466),f857(f309(x99462,x99461,x99465),x99464))))
% 15.02/14.81 [9947]~P26(x99472,x99471,x99475,x99474)+~P26(x99471,x99473,x99476,f857(f309(x99472,x99471,x99475),x99474))+E(f857(f857(f72(x99471,x99472,x99473,f91(x99472,x99471,x99474,x99475)),f91(x99471,x99473,f857(f309(x99472,x99471,x99475),x99474),x99476)),x99477),f857(f91(x99472,x99473,x99474,f857(f72(x99471,x99473,x99472,x99476),x99475)),x99477))+~P106(f857(f857(f328(x99473),x99477),f857(f309(x99471,x99473,x99476),f857(f309(x99472,x99471,x99475),x99474))))
% 15.02/14.81 [10264]~P17(x102647,x102646,x102641)+E(f857(f857(x102641,x102642),f878(x102643,x102644,x102642,x102645,x102641,x102646,x102647)),x102643)+P106(f857(f857(f328(x102647),x102642),x102644))+~P106(f857(f65(x102647,x102646,x102641,x102645,f857(f857(f308(x102647),x102642),x102644)),x102643))
% 15.02/14.81 [10332]~P17(x103321,x103324,x103325)+P106(f857(f65(x103321,x103324,x103325,x103326,x103323),f878(x103327,x103323,x103322,x103326,x103325,x103324,x103321)))+P106(f857(f857(f328(x103321),x103322),x103323))+~P106(f857(f65(x103321,x103324,x103325,x103326,f857(f857(f308(x103321),x103322),x103323)),x103327))
% 15.02/14.81 [10004]E(x100041,f2(a1))+~P106(f857(f48(x100043,x100041),f857(f857(f251(a1,a1),x100045),x100047)))+~P106(f857(f48(x100042,x100041),f857(f857(f251(a1,a1),x100044),x100046)))+P106(f857(f48(f857(f857(f79(a1),x100042),x100043),x100041),f857(f857(f251(a1,a1),f857(f857(f79(a1),f857(f857(f79(a1),x100044),x100045)),f857(f857(f35(a1),f857(f857(f79(a1),x100046),x100047)),x100041))),f44(a1,f857(f857(f79(a1),x100046),x100047),x100041))))
% 15.02/14.81 [10006]~P106(f857(f857(f235(a919),f2(a919)),x100063))+~P106(f857(f47(x100062,x100063),f857(f857(f251(a919,a919),x100065),x100067)))+~P106(f857(f47(x100061,x100063),f857(f857(f251(a919,a919),x100064),x100066)))+P106(f857(f47(f857(f857(f79(a919),x100061),x100062),x100063),f857(f857(f251(a919,a919),f857(f857(f79(a919),f857(f857(f79(a919),x100064),x100065)),f857(f857(f35(a919),f857(f857(f79(a919),x100066),x100067)),x100063))),f44(a919,f857(f857(f79(a919),x100066),x100067),x100063))))
% 15.02/14.81 [10399]~P72(x103992)+~P106(f857(f60(x103993),x103995))+~P106(f857(f60(x103991),x103997))+E(f857(f857(f8(x103991,x103992),f857(f857(f20(x103991,f927(x103993,a915),x103992),f857(f857(f10(f927(x103993,x103992),f927(f927(x103993,a915),x103992),x103991),f8(x103993,x103992)),x103994)),f857(f857(f10(f927(x103993,a915),f927(x103993,a915),x103991),f261(x103993)),f857(f857(f10(f927(x103993,a915),f927(x103993,a915),x103991),f857(f20(x103993,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103993),a325),f857(f857(f9(x103993,f927(x103993,a915),a915),f328(x103993)),x103995)))),x103996)))),x103997),f857(f857(f8(x103993,x103992),f857(f857(f20(x103993,f927(x103991,a915),x103992),f857(f857(f10(f927(x103991,x103992),f927(f927(x103991,a915),x103992),x103993),f8(x103991,x103992)),f857(f9(x103991,x103993,x103992),x103994))),f857(f857(f10(f927(x103991,a915),f927(x103991,a915),x103993),f261(x103991)),f857(f857(f10(f927(x103991,a915),f927(x103991,a915),x103993),f857(f20(x103991,a915,a915),f857(f857(f10(a915,f927(a915,a915),x103991),a325),f857(f857(f9(x103991,f927(x103991,a915),a915),f328(x103991)),x103997)))),f857(f9(x103991,x103993,a915),x103996))))),x103995))
% 15.02/14.81 [10353]~P22(x103538,x103537,x103536,x103535,x103531)+~E(f857(x103532,f854(x103534,x103532,x103533,x103531,x103535,x103536,x103537)),f857(x103534,f854(x103534,x103532,x103533,x103531,x103535,x103536,x103537)))+E(f857(f857(x103531,x103532),x103533),f857(f857(x103531,x103534),x103533))+~P106(f857(f60(x103537),x103533))
% 15.02/14.81 [9881]~P23(x98817,x98816,x98811,x98818,x98812,x98814)+E(f857(f857(x98811,f857(x98812,x98813)),f857(x98814,x98815)),f857(x98814,x98815))+~P106(f857(f60(x98816),x98815))+~P106(f857(f857(f328(x98816),x98813),x98815))
% 15.02/14.81 [9885]~P13(x98856,x98851,x98852,x98858,x98853,x98854)+~P9(x98856,x98857,x98858)+P12(x98851,x98852,x98853,f857(x98854,x98855))+~P106(f857(f857(f328(x98856),x98855),x98857))
% 15.02/14.81 [10371]~P22(x103718,x103715,x103717,x103716,x103711)+E(f857(f857(x103711,x103712),x103713),f857(f857(x103711,x103714),x103713))+~P106(f857(f60(x103715),x103713))+P106(f857(f857(f328(x103715),f854(x103712,x103714,x103713,x103711,x103716,x103717,x103715)),x103713))
% 15.02/14.81 [10452]~P106(f857(f857(x104521,x104526),x104525))+P106(f857(f857(x104521,f845(x104521,x104524,x104525,x104526,x104523,x104522,x104527,x104528)),f850(x104521,x104524,x104525,x104526,x104523,x104522,x104527,x104528)))+P106(f857(f857(x104521,x104522),x104523))+~P106(f857(f857(f328(f926(f926(x104528,x104527),f926(x104528,x104527))),f857(f857(f251(f926(x104528,x104527),f926(x104528,x104527)),f857(f857(f251(x104528,x104527),x104522),x104523)),f857(f857(f251(x104528,x104527),x104526),x104525))),f306(f926(x104528,x104527),x104524)))
% 15.02/14.81 [10453]~P106(f857(f857(x104531,x104536),x104535))+P106(f857(f857(x104531,f838(x104531,x104534,x104533,x104532,x104535,x104536,x104537,x104538)),f839(x104531,x104534,x104533,x104532,x104535,x104536,x104537,x104538)))+P106(f857(f857(x104531,x104532),x104533))+~P106(f857(f857(f328(f926(f926(x104538,x104537),f926(x104538,x104537))),f857(f857(f251(f926(x104538,x104537),f926(x104538,x104537)),f857(f857(f251(x104538,x104537),x104536),x104535)),f857(f857(f251(x104538,x104537),x104532),x104533))),f306(f926(x104538,x104537),x104534)))
% 15.02/14.81 [10463]~P106(f857(f857(x104631,f846(x104631,x104636,x104635,x104634,x104633,x104632,x104637,x104638)),f849(x104631,x104636,x104635,x104634,x104633,x104632,x104637,x104638)))+P106(f857(f857(x104631,x104632),x104633))+~P106(f857(f857(x104631,x104634),x104635))+~P106(f857(f857(f328(f926(f926(x104638,x104637),f926(x104638,x104637))),f857(f857(f251(f926(x104638,x104637),f926(x104638,x104637)),f857(f857(f251(x104638,x104637),x104632),x104633)),f857(f857(f251(x104638,x104637),x104634),x104635))),f306(f926(x104638,x104637),x104636)))
% 15.02/14.81 [10464]~P106(f857(f857(x104641,f840(x104641,x104646,x104643,x104642,x104645,x104644,x104647,x104648)),f841(x104641,x104646,x104643,x104642,x104645,x104644,x104647,x104648)))+P106(f857(f857(x104641,x104642),x104643))+~P106(f857(f857(x104641,x104644),x104645))+~P106(f857(f857(f328(f926(f926(x104648,x104647),f926(x104648,x104647))),f857(f857(f251(f926(x104648,x104647),f926(x104648,x104647)),f857(f857(f251(x104648,x104647),x104644),x104645)),f857(f857(f251(x104648,x104647),x104642),x104643))),f306(f926(x104648,x104647),x104646)))
% 15.02/14.81 [10477]~P106(f857(f857(x104771,x104776),x104777))+P106(f857(f857(x104771,x104772),x104773))+P106(f857(f857(f328(f926(f926(x104774,x104775),f926(x104774,x104775))),f857(f857(f251(f926(x104774,x104775),f926(x104774,x104775)),f857(f857(f251(x104774,x104775),x104776),x104777)),f857(f857(f251(x104774,x104775),f838(x104771,x104778,x104773,x104772,x104777,x104776,x104775,x104774)),f839(x104771,x104778,x104773,x104772,x104777,x104776,x104775,x104774)))),f306(f926(x104774,x104775),x104778)))+~P106(f857(f857(f328(f926(f926(x104774,x104775),f926(x104774,x104775))),f857(f857(f251(f926(x104774,x104775),f926(x104774,x104775)),f857(f857(f251(x104774,x104775),x104776),x104777)),f857(f857(f251(x104774,x104775),x104772),x104773))),f306(f926(x104774,x104775),x104778)))
% 15.02/14.81 [10479]~P106(f857(f857(x104791,x104798),x104797))+P106(f857(f857(x104791,x104792),x104793))+P106(f857(f857(f328(f926(f926(x104794,x104795),f926(x104794,x104795))),f857(f857(f251(f926(x104794,x104795),f926(x104794,x104795)),f857(f857(f251(x104794,x104795),f845(x104791,x104796,x104797,x104798,x104793,x104792,x104795,x104794)),f850(x104791,x104796,x104797,x104798,x104793,x104792,x104795,x104794))),f857(f857(f251(x104794,x104795),x104798),x104797))),f306(f926(x104794,x104795),x104796)))+~P106(f857(f857(f328(f926(f926(x104794,x104795),f926(x104794,x104795))),f857(f857(f251(f926(x104794,x104795),f926(x104794,x104795)),f857(f857(f251(x104794,x104795),x104792),x104793)),f857(f857(f251(x104794,x104795),x104798),x104797))),f306(f926(x104794,x104795),x104796)))
% 15.02/14.81 [9492]~P20(x94927,x94921,x94928,x94923)+~P106(f857(f60(x94927),x94925))+~P106(f857(f60(x94927),x94924))+E(f857(f72(x94921,x94921,x94922,f857(x94923,x94924)),f857(f72(x94921,x94921,x94922,f857(x94923,x94925)),x94926)),f857(f72(x94921,x94921,x94922,f857(x94923,x94925)),f857(f72(x94921,x94921,x94922,f857(x94923,x94924)),x94926)))
% 15.02/14.81 [9501]~P36(x95011,x95012,x95013,x95014,x95017)+P36(x95011,x95012,x95013,f857(f857(f159(x95011,x95014),x95015),x95016),f857(f857(f159(x95012,x95017),x95015),x95018))+~P106(f857(f857(x95013,x95016),x95018))+~P106(f857(f857(f235(a919),x95015),f857(f190(f920(x95011)),x95014)))
% 15.02/14.81 [9502]~P36(x95021,x95022,x95023,x95024,x95027)+P36(x95021,x95022,x95023,f857(f857(f159(x95021,x95024),x95025),x95026),f857(f857(f159(x95022,x95027),x95025),x95028))+~P106(f857(f857(x95023,x95026),x95028))+~P106(f857(f857(f235(a919),x95025),f857(f190(f920(x95022)),x95027)))
% 15.02/14.81 [9581]~P26(x95812,x95812,x95815,x95816)+~P22(x95813,x95812,x95817,x95818,x95811)+~P106(f857(f60(x95812),x95816))+E(f857(f857(x95811,f857(f72(x95812,x95813,x95812,x95814),x95815)),x95816),f857(f857(x95811,x95814),f857(f309(x95812,x95812,x95815),x95816)))
% 15.02/14.81 [9846]P27(x98461,x98462,x98463,x98464,x98465)+~P27(x98462,x98466,x98467,x98465,x98468)+~P27(x98461,x98466,f857(f72(x98462,x98466,x98461,x98467),x98463),x98464,x98468)+~P106(f857(f857(f234(f927(x98462,a915)),f857(f309(x98461,x98462,x98463),x98464)),x98465))
% 15.02/14.81 [9883]~P24(x98837,x98832,x98835,x98838,x98836,x98831)+~P106(f857(f60(x98832),x98834))+E(f857(x98831,f857(f857(f308(x98832),x98833),x98834)),f857(f857(x98835,f857(x98836,x98833)),f857(x98831,x98834)))+P106(f857(f857(f328(x98832),x98833),x98834))
% 15.02/14.81 [9894]~P23(x98946,x98945,x98941,x98947,x98948,x98942)+E(f857(f857(x98941,f857(x98942,x98943)),f857(x98942,x98944)),f857(x98942,x98944))+~P106(f857(f60(x98945),x98944))+~P106(f857(f857(f234(f927(x98945,a915)),x98943),x98944))
% 15.02/14.81 [10396]P25(x103968,x103967,f857(f857(f308(f918(x103968)),f857(f857(f857(f90(x103968),x103964),x103965),x103963)),f189(f927(f918(x103968),a915))))+~P25(x103968,x103967,f857(f857(f308(f918(x103968)),f857(f857(f857(f90(x103968),x103966),x103965),x103961)),f189(f927(f918(x103968),a915))))+~P106(f857(f857(x103966,x103962),f894(x103963,x103964,x103961,x103965,x103966,x103967,x103968)))+P106(f857(f857(x103961,x103962),f904(x103963,x103964,x103961,x103965,x103966,x103967,x103968)))
% 15.02/14.81 [9479]P106(f857(f857(f328(f926(f920(x94791),f920(x94791))),f857(f857(f251(f920(x94791),f920(x94791)),x94792),x94793)),f157(x94791,x94794)))+~E(x94793,f857(f857(f134(x94791),x94795),f857(f857(f151(x94791),x94796),x94797)))+~E(x94792,f857(f857(f134(x94791),x94795),f857(f857(f151(x94791),x94798),x94797)))+~P106(f857(f857(f328(f926(x94791,x94791)),f857(f857(f251(x94791,x94791),x94798),x94796)),x94794))
% 15.02/14.81 [9888]~P23(x98886,x98882,x98885,x98887,x98888,x98881)+~P106(f857(f60(x98882),x98884))+~P106(f857(f60(x98882),x98883))+E(f857(x98881,f857(f857(f110(f927(x98882,a915)),x98883),x98884)),f857(f857(x98885,f857(x98881,x98883)),f857(x98881,x98884)))
% 15.02/14.81 [10442]~P26(x104424,x104422,x104425,x104428)+E(f857(f857(f38(x104421,f927(x104422,a915)),x104423),f857(f857(f10(f927(x104424,a915),f927(x104422,a915),x104421),f309(x104424,x104422,x104425)),x104426)),f857(f309(x104424,x104422,x104425),f857(f857(f38(x104421,f927(x104424,a915)),x104423),x104426)))+~P106(f857(f857(f328(x104421),x104427),x104423))+P106(f857(f857(f328(x104421),f507(x104427,x104426,x104423,x104421,x104428,x104425,x104422,x104424)),x104423))
% 15.02/14.81 [10468]~P26(x104684,x104682,x104685,x104687)+E(f857(f857(f38(x104681,f927(x104682,a915)),x104683),f857(f857(f10(f927(x104684,a915),f927(x104682,a915),x104681),f309(x104684,x104682,x104685)),x104686)),f857(f309(x104684,x104682,x104685),f857(f857(f38(x104681,f927(x104684,a915)),x104683),x104686)))+~P106(f857(f857(f328(x104681),x104688),x104683))+~P106(f857(f857(f234(f927(x104684,a915)),f857(x104686,f507(x104688,x104686,x104683,x104681,x104687,x104685,x104682,x104684))),x104687))
% 15.02/14.81 [10480]~P106(f857(f857(x104801,x104808),x104807))+P106(f857(f857(x104801,x104802),x104803))+~P106(f857(f857(f328(f926(f926(x104804,x104805),f926(x104804,x104805))),f857(f857(f251(f926(x104804,x104805),f926(x104804,x104805)),f857(f857(f251(x104804,x104805),x104802),x104803)),f857(f857(f251(x104804,x104805),x104808),x104807))),f306(f926(x104804,x104805),x104806)))+P106(f857(f857(f328(f926(f926(x104804,x104805),f926(x104804,x104805))),f857(f857(f251(f926(x104804,x104805),f926(x104804,x104805)),f857(f857(f251(x104804,x104805),f846(x104801,x104806,x104807,x104808,x104803,x104802,x104805,x104804)),f849(x104801,x104806,x104807,x104808,x104803,x104802,x104805,x104804))),f857(f857(f251(x104804,x104805),f845(x104801,x104806,x104807,x104808,x104803,x104802,x104805,x104804)),f850(x104801,x104806,x104807,x104808,x104803,x104802,x104805,x104804)))),x104806))
% 15.02/14.81 [10481]~P106(f857(f857(x104811,x104818),x104817))+P106(f857(f857(x104811,x104812),x104813))+~P106(f857(f857(f328(f926(f926(x104814,x104815),f926(x104814,x104815))),f857(f857(f251(f926(x104814,x104815),f926(x104814,x104815)),f857(f857(f251(x104814,x104815),x104818),x104817)),f857(f857(f251(x104814,x104815),x104812),x104813))),f306(f926(x104814,x104815),x104816)))+P106(f857(f857(f328(f926(f926(x104814,x104815),f926(x104814,x104815))),f857(f857(f251(f926(x104814,x104815),f926(x104814,x104815)),f857(f857(f251(x104814,x104815),f838(x104811,x104816,x104813,x104812,x104817,x104818,x104815,x104814)),f839(x104811,x104816,x104813,x104812,x104817,x104818,x104815,x104814))),f857(f857(f251(x104814,x104815),f840(x104811,x104816,x104813,x104812,x104817,x104818,x104815,x104814)),f841(x104811,x104816,x104813,x104812,x104817,x104818,x104815,x104814)))),x104816))
% 15.02/14.81 [9956]~P24(x99567,x99565,x99561,x99568,x99562,x99564)+~P106(f857(f60(x99565),x99566))+~P106(f857(f857(f328(x99565),x99563),x99566))+E(f857(f857(x99561,f857(x99562,x99563)),f857(x99564,f857(f857(f3(f927(x99565,a915)),x99566),f857(f857(f308(x99565),x99563),f189(f927(x99565,a915)))))),f857(x99564,x99566))
% 15.02/14.81 [9964]~P24(x99646,x99643,x99641,x99647,x99648,x99642)+~P106(f857(f60(x99643),x99645))+~P106(f857(f60(x99643),x99644))+E(f857(f857(x99641,f857(x99642,f857(f857(f110(f927(x99643,a915)),x99644),x99645))),f857(x99642,f857(f857(f101(f927(x99643,a915)),x99644),x99645))),f857(f857(x99641,f857(x99642,x99644)),f857(x99642,x99645)))
% 15.02/14.81 [10047]P44(x100471,x100472,x100473,x100474,x100475,f857(f857(x100473,x100476),x100477))+~P44(x100471,x100472,x100473,x100474,f857(f857(f3(f927(x100471,a915)),x100475),f857(f857(f308(x100471),x100478),f189(f927(x100471,a915)))),x100479)+~E(f857(f857(x100473,x100476),x100477),f857(f857(x100473,x100478),x100479))+~P106(f857(f857(f328(x100471),x100478),x100475))
% 15.02/14.81 [10484]P25(x104841,x104842,f857(f857(f308(f918(x104841)),f857(f857(f857(f90(x104841),f857(x104843,f508(x104844,x104845,x104846,x104847,x104843,x104842,x104841,x104848,x104849))),f857(x104847,f508(x104844,x104845,x104846,x104847,x104843,x104842,x104841,x104848,x104849))),f857(x104846,f508(x104844,x104845,x104846,x104847,x104843,x104842,x104841,x104848,x104849)))),f189(f927(f918(x104841),a915))))+~P106(f857(f60(x104849),x104848))+~P25(x104841,x104842,f857(f309(x104849,f918(x104841),f857(f857(f20(x104849,f927(x104841,f927(a917,a915)),f918(x104841)),f857(f857(f20(x104849,a916,f927(f927(x104841,f927(a917,a915)),f918(x104841))),f857(f857(f10(f927(x104841,f927(a917,a915)),f927(a916,f927(f927(x104841,f927(a917,a915)),f918(x104841))),x104849),f90(x104841)),x104843)),x104847)),x104846)),x104848))+P25(x104841,x104842,f857(f309(x104849,f918(x104841),f857(f857(f20(x104849,f927(x104841,f927(a917,a915)),f918(x104841)),f857(f857(f20(x104849,a916,f927(f927(x104841,f927(a917,a915)),f918(x104841))),f857(f857(f10(f927(x104841,f927(a917,a915)),f927(a916,f927(f927(x104841,f927(a917,a915)),f918(x104841))),x104849),f90(x104841)),x104845)),x104847)),x104844)),x104848))
% 15.02/14.81 [10485]~P25(x104851,x104852,f857(f857(f308(f918(x104851)),f857(f857(f857(f90(x104851),f857(x104854,f508(x104856,x104854,x104858,x104855,x104859,x104852,x104851,x104857,x104853))),f857(x104855,f508(x104856,x104854,x104858,x104855,x104859,x104852,x104851,x104857,x104853))),f857(x104856,f508(x104856,x104854,x104858,x104855,x104859,x104852,x104851,x104857,x104853)))),f189(f927(f918(x104851),a915))))+~P106(f857(f60(x104853),x104857))+~P25(x104851,x104852,f857(f309(x104853,f918(x104851),f857(f857(f20(x104853,f927(x104851,f927(a917,a915)),f918(x104851)),f857(f857(f20(x104853,a916,f927(f927(x104851,f927(a917,a915)),f918(x104851))),f857(f857(f10(f927(x104851,f927(a917,a915)),f927(a916,f927(f927(x104851,f927(a917,a915)),f918(x104851))),x104853),f90(x104851)),x104859)),x104855)),x104858)),x104857))+P25(x104851,x104852,f857(f309(x104853,f918(x104851),f857(f857(f20(x104853,f927(x104851,f927(a917,a915)),f918(x104851)),f857(f857(f20(x104853,a916,f927(f927(x104851,f927(a917,a915)),f918(x104851))),f857(f857(f10(f927(x104851,f927(a917,a915)),f927(a916,f927(f927(x104851,f927(a917,a915)),f918(x104851))),x104853),f90(x104851)),x104854)),x104855)),x104856)),x104857))
% 15.02/14.81 [9988]~P13(x99886,x99887,x99888,x99889,x998810,x99881)+E(f857(f857(x99881,x99882),x99883),f857(f857(x99881,x99884),x99885))+~P106(f857(f857(f328(f926(x99887,x99887)),f857(f857(f251(x99887,x99887),x99883),x99885)),x998810))+~P106(f857(f857(f328(f926(x99886,x99886)),f857(f857(f251(x99886,x99886),x99882),x99884)),x99889))
% 15.02/14.81 [9583]~P2(x95832)+E(x95831,f189(f927(x95832,a915)))+~P106(f857(f60(x95832),x95831))+P106(f857(f857(f328(x95832),f12(x95832,x95831)),x95831))+~P106(f857(f857(f328(x95832),f857(f857(f110(x95832),f526(x95831,x95832)),f541(x95831,x95832))),f857(f857(f308(x95832),f526(x95831,x95832)),f857(f857(f308(x95832),f541(x95831,x95832)),f189(f927(x95832,a915))))))
% 15.02/14.81 [9584]~P2(x95842)+E(x95841,f189(f927(x95842,a915)))+~P106(f857(f60(x95842),x95841))+P106(f857(f857(f328(x95842),f13(x95842,x95841)),x95841))+~P106(f857(f857(f328(x95842),f857(f857(f101(x95842),f650(x95841,x95842)),f663(x95841,x95842))),f857(f857(f308(x95842),f650(x95841,x95842)),f857(f857(f308(x95842),f663(x95841,x95842)),f189(f927(x95842,a915))))))
% 15.02/14.81 [9617]~P70(x96172)+E(x96171,f189(f927(x96172,a915)))+~P106(f857(f60(x96172),x96171))+P106(f857(f857(f328(x96172),f857(f62(x96172,f80(x96172)),x96171)),x96171))+~P106(f857(f857(f328(x96172),f857(f857(f80(x96172),f678(x96171,x96172)),f682(x96171,x96172))),f857(f857(f308(x96172),f678(x96171,x96172)),f857(f857(f308(x96172),f682(x96171,x96172)),f189(f927(x96172,a915))))))
% 15.02/14.81 [9622]~P109(x96222)+E(x96221,f189(f927(x96222,a915)))+~P106(f857(f60(x96222),x96221))+P106(f857(f857(f328(x96222),f14(x96222,f188(x96222),x96221)),x96221))+~P106(f857(f857(f328(x96222),f857(f857(f188(x96222),f818(x96221,x96222)),f831(x96221,x96222))),f857(f857(f308(x96222),f818(x96221,x96222)),f857(f857(f308(x96222),f831(x96221,x96222)),f189(f927(x96222,a915))))))
% 15.02/14.81 [9623]~P109(x96232)+E(x96231,f189(f927(x96232,a915)))+~P106(f857(f60(x96232),x96231))+P106(f857(f857(f328(x96232),f15(x96232,f233(x96232),x96231)),x96231))+~P106(f857(f857(f328(x96232),f857(f857(f233(x96232),f416(x96231,x96232)),f420(x96231,x96232))),f857(f857(f308(x96232),f416(x96231,x96232)),f857(f857(f308(x96232),f420(x96231,x96232)),f189(f927(x96232,a915))))))
% 15.02/14.81 [6742]~P89(x67422)+E(x67421,f2(x67422))+~E(f857(f857(f79(x67422),x67423),x67421),f2(x67422))+~P106(f857(f857(f234(x67422),f2(x67422)),x67423))+~P106(f857(f857(f234(x67422),f2(x67422)),x67421))
% 15.02/14.81 [6743]~P89(x67432)+E(x67431,f2(x67432))+~E(f857(f857(f79(x67432),x67431),x67433),f2(x67432))+~P106(f857(f857(f234(x67432),f2(x67432)),x67433))+~P106(f857(f857(f234(x67432),f2(x67432)),x67431))
% 15.02/14.81 [6940]~P106(f857(f857(f286(a919),x69402),x69401))+~P106(f857(f857(f286(a919),x69401),x69403))+P106(f857(f857(f286(a919),x69402),x69403))+P106(f857(f857(f286(a919),x69401),x69402))+P106(f857(f857(f286(a919),x69403),x69401))
% 15.02/14.81 [7111]~P106(f857(f857(f286(a919),x71111),x71113))+~P106(f857(f857(f286(a919),x71113),x71112))+~P106(f857(f857(f286(a919),x71112),x71111))+P106(f857(f857(f286(a919),x71111),x71112))+P106(f857(f857(f286(a919),x71113),x71111))
% 15.02/14.81 [7279]~P109(x72792)+~P14(x72792,x72791)+E(x72791,f113(x72792))+~P106(f857(f857(f328(x72792),x72793),f857(f172(x72792),f708(x72791,x72792))))+P106(f857(f857(f234(x72792),f728(x72791,x72792)),x72793))
% 15.02/14.81 [7450]~P109(x74501)+E(f16(x74501,x74502),x74503)+~P106(f857(f60(x74501),x74502))+~P106(f857(f857(f234(x74501),x74503),f341(x74503,x74502,x74501)))+~P106(f857(f857(f328(x74501),x74503),x74502))
% 15.02/14.81 [7483]~P109(x74831)+~P14(x74831,x74832)+~P14(x74831,x74833)+P14(x74831,f857(f857(f134(x74831),x74832),x74833))+P106(f857(f857(f328(x74831),f715(x74833,x74832,x74831)),f857(f172(x74831),x74832)))
% 15.02/14.81 [7484]~P109(x74841)+~P14(x74841,x74842)+~P14(x74841,x74843)+P14(x74841,f857(f857(f134(x74841),x74842),x74843))+P106(f857(f857(f328(x74841),f716(x74843,x74842,x74841)),f857(f172(x74841),x74843)))
% 15.02/14.81 [7544]~P109(x75441)+E(f16(x75441,x75442),x75443)+~P106(f857(f60(x75441),x75442))+P106(f857(f857(f328(x75441),f341(x75443,x75442,x75441)),x75442))+~P106(f857(f857(f328(x75441),x75443),x75442))
% 15.02/14.81 [7545]~P109(x75451)+E(f17(x75451,x75452),x75453)+~P106(f857(f60(x75451),x75452))+P106(f857(f857(f328(x75451),f601(x75453,x75452,x75451)),x75452))+~P106(f857(f857(f328(x75451),x75453),x75452))
% 15.02/14.81 [8113]~P109(x81131)+E(f17(x81131,x81132),x81133)+~P106(f857(f60(x81131),x81132))+~P106(f857(f857(f328(x81131),x81133),x81132))+~P106(f857(f857(f234(x81131),f601(x81133,x81132,x81131)),x81133))
% 15.02/14.81 [8431]~P109(x84311)+~P14(x84311,x84312)+~P14(x84311,x84313)+P14(x84311,f857(f857(f134(x84311),x84312),x84313))+~P106(f857(f857(f234(x84311),f715(x84313,x84312,x84311)),f716(x84313,x84312,x84311)))
% 15.02/14.81 [9220]~P2(x92202)+E(x92201,f189(f927(x92202,a915)))+~E(f857(f857(f110(x92202),f857(x92203,f521(x92201,x92203,x92202))),f857(x92203,f523(x92201,x92203,x92202))),f857(x92203,f857(f857(f110(x92202),f521(x92201,x92203,x92202)),f523(x92201,x92203,x92202))))+E(f12(x92202,f857(f309(x92202,x92202,x92203),x92201)),f857(x92203,f12(x92202,x92201)))+~P106(f857(f60(x92202),x92201))
% 15.02/14.81 [9221]~P2(x92212)+E(x92211,f189(f927(x92212,a915)))+~E(f857(f857(f101(x92212),f857(x92213,f511(x92211,x92213,x92212))),f857(x92213,f522(x92211,x92213,x92212))),f857(x92213,f857(f857(f101(x92212),f511(x92211,x92213,x92212)),f522(x92211,x92213,x92212))))+E(f13(x92212,f857(f309(x92212,x92212,x92213),x92211)),f857(x92213,f13(x92212,x92211)))+~P106(f857(f60(x92212),x92211))
% 15.02/14.81 [9222]~P109(x92222)+E(x92221,f189(f927(x92222,a915)))+~E(f857(f857(f188(x92222),f857(x92223,f512(x92221,x92223,x92222))),f857(x92223,f519(x92221,x92223,x92222))),f857(x92223,f857(f857(f188(x92222),f512(x92221,x92223,x92222)),f519(x92221,x92223,x92222))))+E(f16(x92222,f857(f309(x92222,x92222,x92223),x92221)),f857(x92223,f16(x92222,x92221)))+~P106(f857(f60(x92222),x92221))
% 15.02/14.81 [9223]~P109(x92232)+E(x92231,f189(f927(x92232,a915)))+~E(f857(f857(f233(x92232),f857(x92233,f513(x92231,x92233,x92232))),f857(x92233,f518(x92231,x92233,x92232))),f857(x92233,f857(f857(f233(x92232),f513(x92231,x92233,x92232)),f518(x92231,x92233,x92232))))+E(f17(x92232,f857(f309(x92232,x92232,x92233),x92231)),f857(x92233,f17(x92232,x92231)))+~P106(f857(f60(x92232),x92231))
% 15.02/14.81 [9291]~P109(x92912)+E(x92911,f189(f927(x92912,a915)))+~E(f857(f857(f188(x92912),f857(x92913,f514(x92911,x92913,x92912))),f857(x92913,f517(x92911,x92913,x92912))),f857(x92913,f857(f857(f188(x92912),f514(x92911,x92913,x92912)),f517(x92911,x92913,x92912))))+E(f14(x92912,f188(x92912),f857(f309(x92912,x92912,x92913),x92911)),f857(x92913,f14(x92912,f188(x92912),x92911)))+~P106(f857(f60(x92912),x92911))
% 15.02/14.81 [9292]~P109(x92922)+E(x92921,f189(f927(x92922,a915)))+~E(f857(f857(f233(x92922),f857(x92923,f515(x92921,x92923,x92922))),f857(x92923,f516(x92921,x92923,x92922))),f857(x92923,f857(f857(f233(x92922),f515(x92921,x92923,x92922)),f516(x92921,x92923,x92922))))+E(f15(x92922,f233(x92922),f857(f309(x92922,x92922,x92923),x92921)),f857(x92923,f15(x92922,f233(x92922),x92921)))+~P106(f857(f60(x92922),x92921))
% 15.02/14.81 [6759]~P70(x67592)+E(x67591,f189(f927(x67592,a915)))+~P106(f857(f60(x67592),x67591))+E(f857(f62(x67592,f80(x67592)),f857(f857(f308(x67592),x67593),x67591)),f857(f857(f80(x67592),x67593),f857(f62(x67592,f80(x67592)),x67591)))+P106(f857(f857(f328(x67592),x67593),x67591))
% 15.02/14.81 [7285]~P2(x72852)+E(f857(f857(f110(x72852),f12(x72852,x72851)),f12(x72852,x72853)),f12(x72852,x72853))+E(x72851,f189(f927(x72852,a915)))+~P106(f857(f60(x72852),x72853))+~P106(f857(f857(f234(f927(x72852,a915)),x72851),x72853))
% 15.02/14.81 [7286]~P2(x72862)+E(f857(f857(f101(x72862),f13(x72862,x72861)),f13(x72862,x72863)),f13(x72862,x72863))+E(x72861,f189(f927(x72862,a915)))+~P106(f857(f60(x72862),x72863))+~P106(f857(f857(f234(f927(x72862,a915)),x72861),x72863))
% 15.02/14.81 [7287]~P109(x72872)+E(f857(f857(f188(x72872),f16(x72872,x72871)),f16(x72872,x72873)),f16(x72872,x72873))+E(x72871,f189(f927(x72872,a915)))+~P106(f857(f60(x72872),x72873))+~P106(f857(f857(f234(f927(x72872,a915)),x72871),x72873))
% 15.02/14.81 [7288]~P109(x72882)+E(f857(f857(f233(x72882),f17(x72882,x72881)),f17(x72882,x72883)),f17(x72882,x72883))+E(x72881,f189(f927(x72882,a915)))+~P106(f857(f60(x72882),x72883))+~P106(f857(f857(f234(f927(x72882,a915)),x72881),x72883))
% 15.02/14.81 [7592]~P109(x75922)+E(x75921,f189(f927(x75922,a915)))+~P106(f857(f60(x75922),x75923))+P106(f857(f857(f234(x75922),f16(x75922,x75923)),f16(x75922,x75921)))+~P106(f857(f857(f234(f927(x75922,a915)),x75921),x75923))
% 15.02/14.81 [7593]~P109(x75932)+E(x75931,f189(f927(x75932,a915)))+~P106(f857(f60(x75932),x75933))+P106(f857(f857(f234(x75932),f17(x75932,x75931)),f17(x75932,x75933)))+~P106(f857(f857(f234(f927(x75932,a915)),x75931),x75933))
% 15.02/14.81 [7647]~P2(x76471)+E(f12(x76471,x76472),x76473)+~P106(f857(f60(x76471),x76472))+~E(f857(f857(f3(f927(x76471,a915)),x76472),f857(f857(f308(x76471),x76473),f189(f927(x76471,a915)))),f189(f927(x76471,a915)))+~P106(f857(f857(f328(x76471),x76473),x76472))
% 15.02/14.81 [7648]~P2(x76481)+E(f13(x76481,x76482),x76483)+~P106(f857(f60(x76481),x76482))+~E(f857(f857(f3(f927(x76481,a915)),x76482),f857(f857(f308(x76481),x76483),f189(f927(x76481,a915)))),f189(f927(x76481,a915)))+~P106(f857(f857(f328(x76481),x76483),x76482))
% 15.02/14.81 [7649]~P109(x76491)+E(f16(x76491,x76492),x76493)+~P106(f857(f60(x76491),x76492))+~E(f857(f857(f3(f927(x76491,a915)),x76492),f857(f857(f308(x76491),x76493),f189(f927(x76491,a915)))),f189(f927(x76491,a915)))+~P106(f857(f857(f328(x76491),x76493),x76492))
% 15.02/14.81 [7650]~P109(x76501)+E(f17(x76501,x76502),x76503)+~P106(f857(f60(x76501),x76502))+~E(f857(f857(f3(f927(x76501,a915)),x76502),f857(f857(f308(x76501),x76503),f189(f927(x76501,a915)))),f189(f927(x76501,a915)))+~P106(f857(f857(f328(x76501),x76503),x76502))
% 15.02/14.81 [7744]~P109(x77441)+E(f14(x77441,f188(x77441),x77442),x77443)+~P106(f857(f60(x77441),x77442))+~E(f857(f857(f3(f927(x77441,a915)),x77442),f857(f857(f308(x77441),x77443),f189(f927(x77441,a915)))),f189(f927(x77441,a915)))+~P106(f857(f857(f328(x77441),x77443),x77442))
% 15.02/14.81 [7745]~P109(x77451)+E(f15(x77451,f233(x77451),x77452),x77453)+~P106(f857(f60(x77451),x77452))+~E(f857(f857(f3(f927(x77451,a915)),x77452),f857(f857(f308(x77451),x77453),f189(f927(x77451,a915)))),f189(f927(x77451,a915)))+~P106(f857(f857(f328(x77451),x77453),x77452))
% 15.02/14.81 [7780]~P102(x77802)+E(x77801,f189(f927(x77802,a915)))+~P106(f857(f60(x77802),x77801))+~P106(f857(f857(f234(x77802),x77803),f641(x77803,x77801,x77802)))+P106(f857(f857(f234(x77802),x77803),f857(f62(x77802,f101(x77802)),x77801)))
% 15.02/14.81 [7781]~P109(x77812)+E(x77811,f189(f927(x77812,a915)))+~P106(f857(f60(x77812),x77811))+~P106(f857(f857(f234(x77812),x77813),f741(x77813,x77811,x77812)))+P106(f857(f857(f234(x77812),x77813),f857(f62(x77812,f188(x77812)),x77811)))
% 15.02/14.81 [7782]~P109(x77822)+E(x77821,f189(f927(x77822,a915)))+~P106(f857(f60(x77822),x77821))+~P106(f857(f857(f235(x77822),x77823),f767(x77823,x77821,x77822)))+P106(f857(f857(f235(x77822),x77823),f857(f62(x77822,f188(x77822)),x77821)))
% 15.02/14.81 [7869]~P102(x78692)+E(x78691,f189(f927(x78692,a915)))+~P106(f857(f60(x78692),x78691))+P106(f857(f857(f328(x78692),f641(x78693,x78691,x78692)),x78691))+P106(f857(f857(f234(x78692),x78693),f857(f62(x78692,f101(x78692)),x78691)))
% 15.02/14.81 [7870]~P109(x78702)+E(x78701,f189(f927(x78702,a915)))+~P106(f857(f60(x78702),x78701))+P106(f857(f857(f328(x78702),f741(x78703,x78701,x78702)),x78701))+P106(f857(f857(f234(x78702),x78703),f857(f62(x78702,f188(x78702)),x78701)))
% 15.02/14.81 [7871]~P109(x78712)+E(x78711,f189(f927(x78712,a915)))+~P106(f857(f60(x78712),x78711))+P106(f857(f857(f328(x78712),f767(x78713,x78711,x78712)),x78711))+P106(f857(f857(f235(x78712),x78713),f857(f62(x78712,f188(x78712)),x78711)))
% 15.02/14.81 [7991]~P109(x79912)+E(x79911,f189(f927(x79912,a915)))+E(f857(f857(f188(x79912),f14(x79912,f188(x79912),x79911)),f14(x79912,f188(x79912),x79913)),f14(x79912,f188(x79912),x79913))+~P106(f857(f60(x79912),x79913))+~P106(f857(f857(f234(f927(x79912,a915)),x79911),x79913))
% 15.02/14.81 [7992]~P109(x79922)+E(x79921,f189(f927(x79922,a915)))+E(f857(f857(f233(x79922),f15(x79922,f233(x79922),x79921)),f15(x79922,f233(x79922),x79923)),f15(x79922,f233(x79922),x79923))+~P106(f857(f60(x79922),x79923))+~P106(f857(f857(f234(f927(x79922,a915)),x79921),x79923))
% 15.02/14.81 [8191]~E(f884(x81911,x81913,x81912),f885(x81911,x81913,x81912))+~E(f857(f34(x81912),f886(x81911,x81913,x81912)),x81911)+E(f857(f857(f80(a919),x81911),f857(f34(f927(x81912,a915)),x81913)),f857(f34(x81912),f36(f927(x81912,a915),x81913)))+~P106(f857(f60(x81912),f36(f927(x81912,a915),x81913)))+~P106(f857(f60(f927(x81912,a915)),x81913))
% 15.02/14.81 [8371]~P109(x83712)+E(x83711,f189(f927(x83712,a915)))+~P106(f857(f60(x83712),x83713))+P106(f857(f857(f234(x83712),f857(f62(x83712,f188(x83712)),x83713)),f857(f62(x83712,f188(x83712)),x83711)))+~P106(f857(f857(f234(f927(x83712,a915)),x83711),x83713))
% 15.02/14.81 [8668]~E(f884(x86681,x86683,x86682),f885(x86681,x86683,x86682))+E(f857(f857(f80(a919),x86681),f857(f34(f927(x86682,a915)),x86683)),f857(f34(x86682),f36(f927(x86682,a915),x86683)))+P106(f857(f857(f328(f927(x86682,a915)),f886(x86681,x86683,x86682)),x86683))+~P106(f857(f60(x86682),f36(f927(x86682,a915),x86683)))+~P106(f857(f60(f927(x86682,a915)),x86683))
% 15.02/14.81 [8694]~E(f857(f34(x86942),f886(x86941,x86943,x86942)),x86941)+E(f857(f857(f80(a919),x86941),f857(f34(f927(x86942,a915)),x86943)),f857(f34(x86942),f36(f927(x86942,a915),x86943)))+P106(f857(f857(f328(f927(x86942,a915)),f885(x86941,x86943,x86942)),x86943))+~P106(f857(f60(x86942),f36(f927(x86942,a915),x86943)))+~P106(f857(f60(f927(x86942,a915)),x86943))
% 15.02/14.81 [8695]~E(f857(f34(x86952),f886(x86951,x86953,x86952)),x86951)+E(f857(f857(f80(a919),x86951),f857(f34(f927(x86952,a915)),x86953)),f857(f34(x86952),f36(f927(x86952,a915),x86953)))+P106(f857(f857(f328(f927(x86952,a915)),f884(x86951,x86953,x86952)),x86953))+~P106(f857(f60(x86952),f36(f927(x86952,a915),x86953)))+~P106(f857(f60(f927(x86952,a915)),x86953))
% 15.02/14.81 [8720]~E(f857(f34(x87202),f886(x87201,x87203,x87202)),x87201)+~E(f857(f857(f101(f927(x87202,a915)),f885(x87201,x87203,x87202)),f884(x87201,x87203,x87202)),f189(f927(x87202,a915)))+E(f857(f857(f80(a919),x87201),f857(f34(f927(x87202,a915)),x87203)),f857(f34(x87202),f36(f927(x87202,a915),x87203)))+~P106(f857(f60(f927(x87202,a915)),x87203))+~P106(f857(f60(x87202),f36(f927(x87202,a915),x87203)))
% 15.02/14.81 [8984]E(f857(f857(f80(a919),x89841),f857(f34(f927(x89842,a915)),x89843)),f857(f34(x89842),f36(f927(x89842,a915),x89843)))+P106(f857(f857(f328(f927(x89842,a915)),f886(x89841,x89843,x89842)),x89843))+P106(f857(f857(f328(f927(x89842,a915)),f885(x89841,x89843,x89842)),x89843))+~P106(f857(f60(f927(x89842,a915)),x89843))+~P106(f857(f60(x89842),f36(f927(x89842,a915),x89843)))
% 15.02/14.81 [8985]E(f857(f857(f80(a919),x89851),f857(f34(f927(x89852,a915)),x89853)),f857(f34(x89852),f36(f927(x89852,a915),x89853)))+P106(f857(f857(f328(f927(x89852,a915)),f886(x89851,x89853,x89852)),x89853))+P106(f857(f857(f328(f927(x89852,a915)),f884(x89851,x89853,x89852)),x89853))+~P106(f857(f60(f927(x89852,a915)),x89853))+~P106(f857(f60(x89852),f36(f927(x89852,a915),x89853)))
% 15.02/14.81 [9011]~E(f857(f857(f101(f927(x90112,a915)),f885(x90111,x90113,x90112)),f884(x90111,x90113,x90112)),f189(f927(x90112,a915)))+E(f857(f857(f80(a919),x90111),f857(f34(f927(x90112,a915)),x90113)),f857(f34(x90112),f36(f927(x90112,a915),x90113)))+~P106(f857(f60(f927(x90112,a915)),x90113))+P106(f857(f857(f328(f927(x90112,a915)),f886(x90111,x90113,x90112)),x90113))+~P106(f857(f60(x90112),f36(f927(x90112,a915),x90113)))
% 15.02/14.81 [9266]~P97(x92662)+E(x92661,f189(f927(x92662,a915)))+~E(f857(f857(f80(x92662),f857(x92663,f524(x92661,x92663,x92662))),f857(x92663,f525(x92661,x92663,x92662))),f857(x92663,f857(f857(f80(x92662),f524(x92661,x92663,x92662)),f525(x92661,x92663,x92662))))+~P106(f857(f60(x92662),x92661))+E(f857(f62(x92662,f80(x92662)),f857(f309(x92662,x92662,x92663),x92661)),f857(x92663,f857(f62(x92662,f80(x92662)),x92661)))
% 15.02/14.81 [10207]P106(f857(f857(x102071,x102072),x102073))+P106(f857(f857(f235(a1),f389(x102071,x102073,x102072)),f390(x102071,x102073,x102072)))+P106(f857(f857(f234(a1),f390(x102071,x102073,x102072)),f2(a1)))+P106(f857(f857(x102071,f389(x102071,x102073,x102072)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f390(x102071,x102073,x102072))))+~P106(f857(f314(f926(a1,a1),a57),f857(f857(f251(a1,a1),x102072),x102073)))
% 15.02/14.81 [10213]P106(f857(f857(x102131,x102132),x102133))+P106(f857(f857(f234(a1),f387(x102131,x102133,x102132)),f2(a1)))+P106(f857(f857(x102131,f385(x102131,x102133,x102132)),f857(f857(f80(a1),f857(f103(a1),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f387(x102131,x102133,x102132))))+P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),f385(x102131,x102133,x102132)),f387(x102131,x102133,x102132))))+~P106(f857(f314(f926(a1,a1),a51),f857(f857(f251(a1,a1),x102132),x102133)))
% 15.02/14.81 [8162]~P120(x81621)+~P106(f857(f857(f234(x81621),x81622),f77(x81621)))+~P106(f857(f857(f234(x81621),f2(x81621)),x81622))+~P106(f857(f857(f234(x81621),f2(x81621)),x81623))+P106(f857(f857(f234(x81621),f857(f857(f80(x81621),x81622),x81623)),x81623))
% 15.02/14.81 [8163]~P120(x81631)+~P106(f857(f857(f234(x81631),x81633),f77(x81631)))+~P106(f857(f857(f234(x81631),f2(x81631)),x81633))+~P106(f857(f857(f234(x81631),f2(x81631)),x81632))+P106(f857(f857(f234(x81631),f857(f857(f80(x81631),x81632),x81633)),x81632))
% 15.02/14.81 [8516]~P109(x85162)+E(x85161,f189(f927(x85162,a915)))+~P106(f857(f60(x85162),x85161))+P106(f857(f857(f234(x85162),f729(x85163,x85161,x85162)),x85163))+~P106(f857(f857(f234(x85162),f857(f62(x85162,f188(x85162)),x85161)),x85163))
% 15.02/14.81 [8517]~P109(x85172)+E(x85171,f189(f927(x85172,a915)))+~P106(f857(f60(x85172),x85171))+P106(f857(f857(f328(x85172),f729(x85173,x85171,x85172)),x85171))+~P106(f857(f857(f234(x85172),f857(f62(x85172,f188(x85172)),x85171)),x85173))
% 15.02/14.81 [8518]~P109(x85182)+E(x85181,f189(f927(x85182,a915)))+~P106(f857(f60(x85182),x85181))+P106(f857(f857(f328(x85182),f756(x85183,x85181,x85182)),x85181))+~P106(f857(f857(f235(x85182),f857(f62(x85182,f188(x85182)),x85181)),x85183))
% 15.02/14.81 [8519]~P109(x85192)+E(x85191,f189(f927(x85192,a915)))+~P106(f857(f60(x85192),x85191))+P106(f857(f857(f235(x85192),f756(x85193,x85191,x85192)),x85193))+~P106(f857(f857(f235(x85192),f857(f62(x85192,f188(x85192)),x85191)),x85193))
% 15.02/14.81 [8604]~P106(f857(x86041,x86043))+P106(f857(x86041,f472(x86041,x86042)))+P106(f857(x86041,f466(x86041,x86042)))+~P106(f857(f857(f235(a1),f2(a1)),x86042))+P106(f857(x86041,f857(f857(f3(a1),f466(x86041,x86042)),f857(f857(f80(a1),f473(x86041,x86042)),x86042))))
% 15.02/14.81 [8821]~P106(f857(x88211,x88213))+P106(f857(x88211,f466(x88211,x88212)))+~P106(f857(f857(f235(a1),f2(a1)),x88212))+P106(f857(f857(f328(a1),f472(x88211,x88212)),f302(a1,f77(a1),x88212)))+P106(f857(x88211,f857(f857(f3(a1),f466(x88211,x88212)),f857(f857(f80(a1),f473(x88211,x88212)),x88212))))
% 15.02/14.81 [9033]~P106(f857(x90331,x90333))+~P106(f857(x90331,f466(x90331,x90332)))+P106(f857(x90331,f472(x90331,x90332)))+~P106(f857(f857(f235(a1),f2(a1)),x90332))+~P106(f857(x90331,f857(f857(f3(a1),f466(x90331,x90332)),f857(f857(f80(a1),f473(x90331,x90332)),x90332))))
% 15.02/14.81 [9157]~P106(f857(x91571,x91573))+~P106(f857(x91571,f466(x91571,x91572)))+~P106(f857(f857(f235(a1),f2(a1)),x91572))+P106(f857(f857(f328(a1),f472(x91571,x91572)),f302(a1,f77(a1),x91572)))+~P106(f857(x91571,f857(f857(f3(a1),f466(x91571,x91572)),f857(f857(f80(a1),f473(x91571,x91572)),x91572))))
% 15.02/14.81 [8939]~P2(x89391)+~P106(f857(f60(x89391),x89392))+E(f857(f857(f3(f927(x89391,a915)),x89392),f857(f857(f308(x89391),x89393),f189(f927(x89391,a915)))),f189(f927(x89391,a915)))+~P106(f857(f857(f328(x89391),x89393),x89392))+E(f857(f857(f110(x89391),x89393),f12(x89391,f857(f857(f3(f927(x89391,a915)),x89392),f857(f857(f308(x89391),x89393),f189(f927(x89391,a915)))))),f12(x89391,x89392))
% 15.02/14.81 [8940]~P2(x89401)+~P106(f857(f60(x89401),x89402))+E(f857(f857(f3(f927(x89401,a915)),x89402),f857(f857(f308(x89401),x89403),f189(f927(x89401,a915)))),f189(f927(x89401,a915)))+~P106(f857(f857(f328(x89401),x89403),x89402))+E(f857(f857(f101(x89401),x89403),f13(x89401,f857(f857(f3(f927(x89401,a915)),x89402),f857(f857(f308(x89401),x89403),f189(f927(x89401,a915)))))),f13(x89401,x89402))
% 15.02/14.81 [8941]~P109(x89411)+~P106(f857(f60(x89411),x89412))+E(f857(f857(f3(f927(x89411,a915)),x89412),f857(f857(f308(x89411),x89413),f189(f927(x89411,a915)))),f189(f927(x89411,a915)))+~P106(f857(f857(f328(x89411),x89413),x89412))+E(f857(f857(f188(x89411),x89413),f16(x89411,f857(f857(f3(f927(x89411,a915)),x89412),f857(f857(f308(x89411),x89413),f189(f927(x89411,a915)))))),f16(x89411,x89412))
% 15.02/14.81 [8942]~P109(x89421)+~P106(f857(f60(x89421),x89422))+E(f857(f857(f3(f927(x89421,a915)),x89422),f857(f857(f308(x89421),x89423),f189(f927(x89421,a915)))),f189(f927(x89421,a915)))+~P106(f857(f857(f328(x89421),x89423),x89422))+E(f857(f857(f233(x89421),x89423),f17(x89421,f857(f857(f3(f927(x89421,a915)),x89422),f857(f857(f308(x89421),x89423),f189(f927(x89421,a915)))))),f17(x89421,x89422))
% 15.02/14.81 [9004]~P109(x90041)+~P106(f857(f60(x90041),x90042))+E(f857(f857(f3(f927(x90041,a915)),x90042),f857(f857(f308(x90041),x90043),f189(f927(x90041,a915)))),f189(f927(x90041,a915)))+~P106(f857(f857(f328(x90041),x90043),x90042))+E(f857(f857(f188(x90041),x90043),f14(x90041,f188(x90041),f857(f857(f3(f927(x90041,a915)),x90042),f857(f857(f308(x90041),x90043),f189(f927(x90041,a915)))))),f14(x90041,f188(x90041),x90042))
% 15.02/14.81 [9005]~P109(x90051)+~P106(f857(f60(x90051),x90052))+E(f857(f857(f3(f927(x90051,a915)),x90052),f857(f857(f308(x90051),x90053),f189(f927(x90051,a915)))),f189(f927(x90051,a915)))+~P106(f857(f857(f328(x90051),x90053),x90052))+E(f857(f857(f233(x90051),x90053),f15(x90051,f233(x90051),f857(f857(f3(f927(x90051,a915)),x90052),f857(f857(f308(x90051),x90053),f189(f927(x90051,a915)))))),f15(x90051,f233(x90051),x90052))
% 15.02/14.81 [9020]~P2(x90201)+~P106(f857(f60(x90201),x90203))+~P106(f857(f60(x90201),x90202))+E(f857(f857(f101(f927(x90201,a915)),x90202),x90203),f189(f927(x90201,a915)))+E(f857(f857(f110(x90201),f12(x90201,f857(f857(f110(f927(x90201,a915)),x90202),x90203))),f12(x90201,f857(f857(f101(f927(x90201,a915)),x90202),x90203))),f857(f857(f110(x90201),f12(x90201,x90202)),f12(x90201,x90203)))
% 15.02/14.81 [9021]~P2(x90211)+~P106(f857(f60(x90211),x90213))+~P106(f857(f60(x90211),x90212))+E(f857(f857(f101(f927(x90211,a915)),x90212),x90213),f189(f927(x90211,a915)))+E(f857(f857(f101(x90211),f13(x90211,f857(f857(f110(f927(x90211,a915)),x90212),x90213))),f13(x90211,f857(f857(f101(f927(x90211,a915)),x90212),x90213))),f857(f857(f101(x90211),f13(x90211,x90212)),f13(x90211,x90213)))
% 15.02/14.81 [9022]~P109(x90221)+~P106(f857(f60(x90221),x90223))+~P106(f857(f60(x90221),x90222))+E(f857(f857(f101(f927(x90221,a915)),x90222),x90223),f189(f927(x90221,a915)))+E(f857(f857(f188(x90221),f16(x90221,f857(f857(f110(f927(x90221,a915)),x90222),x90223))),f16(x90221,f857(f857(f101(f927(x90221,a915)),x90222),x90223))),f857(f857(f188(x90221),f16(x90221,x90222)),f16(x90221,x90223)))
% 15.02/14.81 [9023]~P109(x90231)+~P106(f857(f60(x90231),x90233))+~P106(f857(f60(x90231),x90232))+E(f857(f857(f101(f927(x90231,a915)),x90232),x90233),f189(f927(x90231,a915)))+E(f857(f857(f233(x90231),f17(x90231,f857(f857(f110(f927(x90231,a915)),x90232),x90233))),f17(x90231,f857(f857(f101(f927(x90231,a915)),x90232),x90233))),f857(f857(f233(x90231),f17(x90231,x90232)),f17(x90231,x90233)))
% 15.02/14.81 [9238]~P109(x92381)+~P106(f857(f60(x92381),x92383))+~P106(f857(f60(x92381),x92382))+E(f857(f857(f101(f927(x92381,a915)),x92382),x92383),f189(f927(x92381,a915)))+E(f857(f857(f188(x92381),f14(x92381,f188(x92381),f857(f857(f110(f927(x92381,a915)),x92382),x92383))),f14(x92381,f188(x92381),f857(f857(f101(f927(x92381,a915)),x92382),x92383))),f857(f857(f188(x92381),f14(x92381,f188(x92381),x92382)),f14(x92381,f188(x92381),x92383)))
% 15.02/14.81 [9239]~P109(x92391)+~P106(f857(f60(x92391),x92393))+~P106(f857(f60(x92391),x92392))+E(f857(f857(f101(f927(x92391,a915)),x92392),x92393),f189(f927(x92391,a915)))+E(f857(f857(f233(x92391),f15(x92391,f233(x92391),f857(f857(f110(f927(x92391,a915)),x92392),x92393))),f15(x92391,f233(x92391),f857(f857(f101(f927(x92391,a915)),x92392),x92393))),f857(f857(f233(x92391),f15(x92391,f233(x92391),x92392)),f15(x92391,f233(x92391),x92393)))
% 15.02/14.81 [10044]~P127(x100443)+E(x100441,x100442)+~P106(f857(f857(f234(x100443),f2(x100443)),x100442))+~P106(f857(f857(f234(x100443),f2(x100443)),x100441))+~E(f857(f857(f243(x100443),x100441),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))),f857(f857(f243(x100443),x100442),f857(f103(a919),f857(f857(f79(a1),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)),f857(f857(f3(a1),f857(f857(f79(a1),a82),a82)),a97)))))
% 15.02/14.81 [6082]~P62(x60822)+E(x60821,f2(x60822))+~E(f857(f857(f35(x60822),x60823),x60821),x60824)+E(x60823,f857(f857(f80(x60822),x60824),x60821))+~P106(f857(f857(f286(x60822),x60821),x60823))
% 15.02/14.81 [6083]~P62(x60832)+E(x60831,f2(x60832))+~E(x60833,f857(f857(f80(x60832),x60834),x60831))+E(f857(f857(f35(x60832),x60833),x60831),x60834)+~P106(f857(f857(f286(x60832),x60831),x60833))
% 15.02/14.81 [6557]E(f889(x65571,x65572,x65573),x65574)+E(f857(x65571,x65574),f2(a919))+~E(f857(f857(f8(x65573,a919),x65571),x65572),f77(a919))+~P106(f857(f60(x65573),x65572))+~P106(f857(f857(f328(x65573),x65574),x65572))
% 15.02/14.81 [6619]E(f891(x66191,x66192,x66193),x66194)+E(f857(x66191,x66194),f2(a919))+~E(f857(f857(f8(x66193,a919),x66191),x66192),f857(a112,f2(a919)))+~P106(f857(f60(x66193),x66192))+~P106(f857(f857(f328(x66193),x66194),x66192))
% 15.02/14.81 [6728]~P109(x67281)+~P6(x67281)+P106(f857(f857(f235(x67281),x67282),f36(x67281,x67283)))+~P106(f857(f857(f235(x67281),x67282),x67284))+~P106(f857(f857(f328(x67281),x67284),x67283))
% 15.02/14.81 [6902]~P109(x69021)+~P6(x69021)+~P106(f857(f857(f235(x69021),x69024),x69023))+P106(f857(f857(f235(x69021),f37(x69021,x69022)),x69023))+~P106(f857(f857(f328(x69021),x69024),x69022))
% 15.02/14.81 [7164]~P127(x71643)+E(x71641,x71642)+~E(f857(f857(f243(x71643),x71641),f857(a112,x71644)),f857(f857(f243(x71643),x71642),f857(a112,x71644)))+~P106(f857(f857(f234(x71643),f2(x71643)),x71642))+~P106(f857(f857(f234(x71643),f2(x71643)),x71641))
% 15.02/14.81 [7376]~E(f897(x73762,x73763,x73761,x73764),x73764)+~E(f857(x73762,x73764),f77(a919))+E(f857(f857(f8(x73761,a919),x73762),x73763),f77(a919))+~P106(f857(f60(x73761),x73763))+~P106(f857(f857(f328(x73761),x73764),x73763))
% 15.02/14.81 [7383]~P113(x73834)+~P133(x73834)+E(f857(x73831,f883(x73831,x73832,x73833,x73834)),f2(x73834))+~E(f857(f857(f11(x73833,x73834),x73831),x73832),f2(x73834))+~P106(f857(f60(x73833),x73832))
% 15.02/14.81 [7473]~E(f895(x74732,x74733,x74731,x74734),x74734)+~E(f857(x74732,x74734),f857(a112,f2(a919)))+E(f857(f857(f8(x74731,a919),x74732),x74733),f857(a112,f2(a919)))+~P106(f857(f60(x74731),x74733))+~P106(f857(f857(f328(x74731),x74734),x74733))
% 15.02/14.81 [8203]~E(f857(x82032,x82034),f77(a919))+~E(f857(x82032,f897(x82032,x82033,x82031,x82034)),f2(a919))+E(f857(f857(f8(x82031,a919),x82032),x82033),f77(a919))+~P106(f857(f60(x82031),x82033))+~P106(f857(f857(f328(x82031),x82034),x82033))
% 15.02/14.81 [8241]~E(f857(x82412,x82414),f857(a112,f2(a919)))+~E(f857(x82412,f895(x82412,x82413,x82411,x82414)),f2(a919))+E(f857(f857(f8(x82411,a919),x82412),x82413),f857(a112,f2(a919)))+~P106(f857(f60(x82411),x82413))+~P106(f857(f857(f328(x82411),x82414),x82413))
% 15.02/14.81 [8326]~P147(x83262)+~P123(x83262)+~P106(f857(x83261,x83264))+~P106(f857(f857(f286(x83262),x83263),f857(f857(f79(x83262),x83264),f2(x83262))))+P106(f857(x83261,f857(f857(f80(x83262),x83263),f855(x83263,x83261,x83262))))
% 15.02/14.81 [8788]~P109(x87881)+~P14(x87881,x87884)+P14(x87881,x87882)+~E(x87882,f857(f857(f151(x87881),x87883),x87884))+~P106(f857(f857(f234(x87881),x87883),f730(x87882,x87881,x87884,x87883)))
% 15.02/14.81 [8825]E(x88251,x88252)+E(f857(f857(f3(a1),f458(x88253,x88252,x88254,x88251)),f459(x88253,x88252,x88254,x88251)),x88251)+~E(f857(f857(f79(a1),x88251),x88254),x88252)+~P106(f857(f857(f235(a1),f2(a1)),x88254))+~P106(f857(f857(f328(a1),x88252),x88253))
% 15.02/14.81 [8826]E(x88261,x88262)+E(f857(f857(f79(a1),f460(x88263,x88262,x88264,x88261)),f461(x88263,x88262,x88264,x88261)),x88261)+~E(f857(f857(f3(a1),x88261),x88264),x88262)+~P106(f857(f857(f235(a1),f2(a1)),x88264))+~P106(f857(f857(f328(a1),x88262),x88263))
% 15.02/14.81 [9018]E(f857(x90181,f361(x90182,x90181,x90183,x90184)),x90182)+P106(f857(f857(f234(a919),x90184),f362(x90182,x90181,x90183,x90184)))+~P106(f857(f857(f234(a1),x90182),f857(x90181,x90183)))+~P106(f857(f857(f235(a919),x90184),x90183))+~P106(f857(f857(f234(a1),f857(x90181,x90184)),x90182))
% 15.02/14.81 [9019]~P109(x90191)+~P14(x90191,x90193)+P14(x90191,x90192)+~E(x90192,f857(f857(f151(x90191),x90194),x90193))+P106(f857(f857(f328(x90191),f730(x90192,x90191,x90193,x90194)),f857(f172(x90191),x90193)))
% 15.02/14.81 [9037]~P113(x90374)+~P133(x90374)+~E(f857(f857(f11(x90371,x90374),x90372),x90373),f2(x90374))+~P106(f857(f60(x90371),x90373))+P106(f857(f857(f328(x90371),f883(x90372,x90373,x90371,x90374)),x90373))
% 15.02/14.81 [9075]~E(f857(x90752,x90754),f77(a919))+E(f857(f857(f8(x90751,a919),x90752),x90753),f77(a919))+~P106(f857(f60(x90751),x90753))+~P106(f857(f857(f328(x90751),x90754),x90753))+P106(f857(f857(f328(x90751),f897(x90752,x90753,x90751,x90754)),x90753))
% 15.02/14.81 [9087]E(x90871,x90872)+~E(f857(f857(f79(a1),x90872),x90874),x90871)+~P106(f857(f857(f235(a1),f2(a1)),x90874))+~P106(f857(f857(f328(a1),x90871),x90873))+P106(f857(f857(f328(a1),f458(x90873,x90871,x90874,x90872)),x90873))
% 15.02/14.81 [9088]E(x90881,x90882)+~E(f857(f857(f3(a1),x90882),x90884),x90881)+~P106(f857(f857(f235(a1),f2(a1)),x90884))+~P106(f857(f857(f328(a1),x90881),x90883))+P106(f857(f857(f328(a1),f460(x90883,x90881,x90884,x90882)),x90883))
% 15.02/14.81 [9090]~E(f857(x90902,x90904),f857(a112,f2(a919)))+E(f857(f857(f8(x90901,a919),x90902),x90903),f857(a112,f2(a919)))+~P106(f857(f60(x90901),x90903))+~P106(f857(f857(f328(x90901),x90904),x90903))+P106(f857(f857(f328(x90901),f895(x90902,x90903,x90901,x90904)),x90903))
% 15.02/14.81 [9095]P60(x90952,x90953,x90954,x90951)+E(x90951,f189(f927(x90952,a915)))+~P106(f857(f60(x90952),x90954))+~P106(f857(f60(x90952),x90951))+P106(f857(f857(f328(x90952),f798(x90953,x90951,x90954,x90952)),x90954))
% 15.02/14.81 [9096]P60(x90962,x90963,x90964,x90961)+E(x90961,f189(f927(x90962,a915)))+~P106(f857(f60(x90962),x90964))+~P106(f857(f60(x90962),x90961))+P106(f857(f857(f328(x90962),f520(x90961,x90964,x90963,x90962)),x90964))
% 15.02/14.81 [9097]P60(x90972,x90973,x90974,x90971)+E(x90971,f189(f927(x90972,a915)))+~P106(f857(f60(x90972),x90974))+~P106(f857(f60(x90972),x90971))+P106(f857(f857(f328(x90972),f799(x90971,x90974,x90973,x90972)),x90974))
% 15.02/14.81 [9170]E(x91701,x91702)+~E(f857(f857(f79(a1),x91702),x91704),x91701)+~P106(f857(f857(f235(a1),f2(a1)),x91704))+~P106(f857(f857(f328(a1),x91701),x91703))+P106(f857(f857(f328(a1),f459(x91703,x91701,x91704,x91702)),f302(a1,f77(a1),x91704)))
% 15.02/14.81 [9171]E(x91711,x91712)+~E(f857(f857(f3(a1),x91712),x91714),x91711)+~P106(f857(f857(f235(a1),f2(a1)),x91714))+~P106(f857(f857(f328(a1),x91711),x91713))+P106(f857(f857(f328(a1),f461(x91713,x91711,x91714,x91712)),f302(a1,f77(a1),x91714)))
% 15.02/14.81 [9244]P106(f857(f857(f234(a919),x92441),f361(x92442,x92443,x92444,x92441)))+~P106(f857(f857(f234(a1),x92442),f857(x92443,x92444)))+P106(f857(f857(f234(a919),x92441),f362(x92442,x92443,x92444,x92441)))+~P106(f857(f857(f235(a919),x92441),x92444))+~P106(f857(f857(f234(a1),f857(x92443,x92441)),x92442))
% 15.02/14.81 [9358]E(f857(x93581,f361(x93582,x93581,x93583,x93584)),x93582)+~P106(f857(f857(f234(a1),x93582),f857(x93581,x93583)))+P106(f857(f857(f235(a919),f362(x93582,x93581,x93583,x93584)),x93583))+~P106(f857(f857(f235(a919),x93584),x93583))+~P106(f857(f857(f234(a1),f857(x93581,x93584)),x93582))
% 15.02/14.81 [9471]~P106(f857(f857(f286(a919),x94714),x94711))+~P106(f857(f857(f286(a919),x94714),x94713))+~P106(f857(f857(f286(a919),x94712),x94711))+P106(f857(f857(f286(a919),x94711),x94712))+P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x94713,x94712)),f289(a919,f286(a919),x94714,x94711)))
% 15.02/14.81 [9472]~P106(f857(f857(f286(a919),x94722),x94721))+~P106(f857(f857(f286(a919),x94723),x94724))+~P106(f857(f857(f286(a919),x94722),x94724))+P106(f857(f857(f286(a919),x94721),x94722))+P106(f857(f857(f235(f927(a919,a915)),f289(a919,f286(a919),x94721,x94723)),f289(a919,f286(a919),x94722,x94724)))
% 15.02/14.81 [9489]~P106(f857(f857(f234(a1),x94892),f857(x94893,x94894)))+P106(f857(f857(f234(a919),x94891),f362(x94892,x94893,x94894,x94891)))+P106(f857(f857(f234(a919),f361(x94892,x94893,x94894,x94891)),x94894))+~P106(f857(f857(f235(a919),x94891),x94894))+~P106(f857(f857(f234(a1),f857(x94893,x94891)),x94892))
% 15.02/14.81 [9490]~P106(f857(f857(f234(a1),x94902),f857(x94903,x94904)))+P106(f857(f857(f234(a919),x94901),f361(x94902,x94903,x94904,x94901)))+P106(f857(f857(f235(a919),f362(x94902,x94903,x94904,x94901)),x94904))+~P106(f857(f857(f235(a919),x94901),x94904))+~P106(f857(f857(f234(a1),f857(x94903,x94901)),x94902))
% 15.02/14.81 [9598]~P106(f857(f857(f234(a1),x95981),f857(x95982,x95983)))+P106(f857(f857(f235(a919),f362(x95981,x95982,x95983,x95984)),x95983))+~P106(f857(f857(f235(a919),x95984),x95983))+~P106(f857(f857(f234(a1),f857(x95982,x95984)),x95981))+P106(f857(f857(f234(a919),f361(x95981,x95982,x95983,x95984)),x95983))
% 15.02/14.81 [9690]E(x96901,f189(f927(x96902,a915)))+~P106(f857(f60(x96902),x96904))+~P106(f857(f60(x96902),x96901))+P106(f857(f857(f328(f926(f927(x96902,a915),f927(x96902,a915))),f857(f857(f251(f927(x96902,a915),f927(x96902,a915)),x96904),x96901)),f317(x96902,x96903)))+P106(f857(f857(f328(x96902),f400(x96903,x96901,x96904,x96902)),x96904))
% 15.02/14.81 [9691]E(x96911,f189(f927(x96912,a915)))+~P106(f857(f60(x96912),x96914))+~P106(f857(f60(x96912),x96911))+P106(f857(f857(f328(f926(f927(x96912,a915),f927(x96912,a915))),f857(f857(f251(f927(x96912,a915),f927(x96912,a915)),x96914),x96911)),f317(x96912,x96913)))+P106(f857(f857(f328(x96912),f606(x96913,x96911,x96914,x96912)),x96914))
% 15.02/14.81 [10366]E(f857(x103661,f361(x103662,x103661,x103663,x103664)),x103662)+~P106(f857(f857(f234(a1),x103662),f857(x103661,x103663)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x103661,f857(f857(f79(a919),f362(x103662,x103661,x103663,x103664)),f77(a919)))),f857(x103661,f362(x103662,x103661,x103663,x103664))))),f77(a1)))+~P106(f857(f857(f235(a919),x103664),x103663))+~P106(f857(f857(f234(a1),f857(x103661,x103664)),x103662))
% 15.02/14.81 [10367]~P106(f857(f857(f234(a1),x103672),f857(x103673,x103674)))+P106(f857(f857(f234(a919),x103671),f361(x103672,x103673,x103674,x103671)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x103673,f857(f857(f79(a919),f362(x103672,x103673,x103674,x103671)),f77(a919)))),f857(x103673,f362(x103672,x103673,x103674,x103671))))),f77(a1)))+~P106(f857(f857(f235(a919),x103671),x103674))+~P106(f857(f857(f234(a1),f857(x103673,x103671)),x103672))
% 15.02/14.81 [10368]~P106(f857(f857(f234(a1),x103681),f857(x103682,x103683)))+~P106(f857(f857(f234(a1),f857(f75(a1),f857(f857(f3(a1),f857(x103682,f857(f857(f79(a919),f362(x103681,x103682,x103683,x103684)),f77(a919)))),f857(x103682,f362(x103681,x103682,x103683,x103684))))),f77(a1)))+~P106(f857(f857(f235(a919),x103684),x103683))+~P106(f857(f857(f234(a1),f857(x103682,x103684)),x103681))+P106(f857(f857(f234(a919),f361(x103681,x103682,x103683,x103684)),x103683))
% 15.02/14.81 [7436]~P67(x74361)+P106(f857(f857(f235(x74361),x74362),f2(x74361)))+~P106(f857(f857(f234(x74361),x74363),f2(x74361)))+P106(f857(f857(f235(x74361),f2(x74361)),x74362))+P106(f857(f857(f234(x74361),x74363),f857(f857(f290(x74361),x74364),x74362)))
% 15.02/14.81 [7437]~P67(x74371)+P106(f857(f857(f235(x74371),x74372),f2(x74371)))+~P106(f857(f857(f235(x74371),x74373),f2(x74371)))+P106(f857(f857(f235(x74371),f2(x74371)),x74372))+P106(f857(f857(f235(x74371),x74373),f857(f857(f290(x74371),x74374),x74372)))
% 15.02/14.81 [7684]~P67(x76841)+P106(f857(f857(f234(x76841),x76842),f2(x76841)))+P106(f857(f857(f235(x76841),x76843),f2(x76841)))+P106(f857(f857(f235(x76841),f2(x76841)),x76843))+~P106(f857(f857(f234(x76841),x76842),f857(f857(f290(x76841),x76844),x76843)))
% 15.02/14.81 [7685]~P67(x76851)+P106(f857(f857(f235(x76851),x76852),f2(x76851)))+P106(f857(f857(f235(x76851),x76853),f2(x76851)))+P106(f857(f857(f235(x76851),f2(x76851)),x76853))+~P106(f857(f857(f235(x76851),x76852),f857(f857(f290(x76851),x76854),x76853)))
% 15.02/14.81 [7801]E(x78011,x78012)+~E(f857(f857(f164(x78013),x78014),x78011),f857(f857(f164(x78013),x78014),x78012))+~P106(f857(f137(x78013),x78014))+~P106(f857(f857(f235(a919),x78012),f857(f190(f920(x78013)),x78014)))+~P106(f857(f857(f235(a919),x78011),f857(f190(f920(x78013)),x78014)))
% 15.02/14.81 [8164]~P67(x81641)+~P106(f857(f857(f234(x81641),x81643),f2(x81641)))+P106(f857(f857(f235(x81641),f2(x81641)),x81642))+~P106(f857(f857(f234(x81641),x81644),f857(f857(f80(x81641),x81643),x81642)))+P106(f857(f857(f234(x81641),x81643),f857(f857(f290(x81641),x81644),x81642)))
% 15.02/14.81 [8165]~P67(x81651)+~P106(f857(f857(f235(x81651),x81653),f2(x81651)))+P106(f857(f857(f235(x81651),f2(x81651)),x81652))+~P106(f857(f857(f235(x81651),x81654),f857(f857(f80(x81651),x81653),x81652)))+P106(f857(f857(f235(x81651),x81653),f857(f857(f290(x81651),x81654),x81652)))
% 15.02/14.81 [8166]~P67(x81661)+~P106(f857(f857(f235(x81661),x81662),f2(x81661)))+P106(f857(f857(f235(x81661),f2(x81661)),x81662))+~P106(f857(f857(f234(x81661),x81664),f857(f857(f80(x81661),x81663),x81662)))+P106(f857(f857(f234(x81661),x81663),f857(f857(f290(x81661),x81664),x81662)))
% 15.02/14.81 [8167]~P67(x81671)+~P106(f857(f857(f235(x81671),x81672),f2(x81671)))+P106(f857(f857(f235(x81671),f2(x81671)),x81672))+~P106(f857(f857(f234(x81671),x81674),f857(f857(f290(x81671),x81673),x81672)))+P106(f857(f857(f234(x81671),x81673),f857(f857(f80(x81671),x81674),x81672)))
% 15.02/14.81 [8168]~P67(x81681)+~P106(f857(f857(f235(x81681),x81682),f2(x81681)))+P106(f857(f857(f235(x81681),f2(x81681)),x81682))+~P106(f857(f857(f235(x81681),x81684),f857(f857(f80(x81681),x81683),x81682)))+P106(f857(f857(f235(x81681),x81683),f857(f857(f290(x81681),x81684),x81682)))
% 15.02/14.81 [8169]~P67(x81691)+~P106(f857(f857(f235(x81691),x81692),f2(x81691)))+P106(f857(f857(f235(x81691),f2(x81691)),x81692))+~P106(f857(f857(f235(x81691),x81694),f857(f857(f290(x81691),x81693),x81692)))+P106(f857(f857(f235(x81691),x81693),f857(f857(f80(x81691),x81694),x81692)))
% 15.02/14.81 [8309]~P109(x83091)+~P14(x83091,x83092)+~P106(f857(f857(f234(a919),x83093),x83094))+P106(f857(f857(f234(x83091),f857(f857(f164(x83091),x83092),x83093)),f857(f857(f164(x83091),x83092),x83094)))+~P106(f857(f857(f235(a919),x83094),f857(f190(f920(x83091)),x83092)))
% 15.02/14.81 [8362]~P127(x83621)+~P106(f857(f857(f234(x83621),x83622),f77(x83621)))+~P106(f857(f857(f234(x83621),f2(x83621)),x83622))+~P106(f857(f857(f234(a919),x83624),x83623))+P106(f857(f857(f234(x83621),f857(f857(f243(x83621),x83622),x83623)),f857(f857(f243(x83621),x83622),x83624)))
% 15.02/14.81 [8363]~P127(x83631)+~P106(f857(f857(f235(x83631),x83632),f77(x83631)))+~P106(f857(f857(f235(x83631),f2(x83631)),x83632))+~P106(f857(f857(f235(a919),x83634),x83633))+P106(f857(f857(f235(x83631),f857(f857(f243(x83631),x83632),x83633)),f857(f857(f243(x83631),x83632),x83634)))
% 15.02/14.81 [8364]~P127(x83641)+~P106(f857(f857(f234(x83641),f2(x83641)),x83642))+~P106(f857(f857(f235(a919),f2(a919)),x83643))+~P106(f857(f857(f235(x83641),x83642),x83644))+P106(f857(f857(f235(x83641),f857(f857(f243(x83641),x83642),x83643)),f857(f857(f243(x83641),x83644),x83643)))
% 15.02/14.81 [8382]~P109(x83821)+~P14(x83821,f857(f168(x83821),x83822))+~P106(f857(f857(f234(a919),x83824),x83823))+P106(f857(f857(f234(x83821),f857(f857(f164(x83821),x83822),x83823)),f857(f857(f164(x83821),x83822),x83824)))+~P106(f857(f857(f235(a919),x83823),f857(f190(f920(x83821)),x83822)))
% 15.02/14.81 [8625]~P67(x86251)+~P106(f857(f857(f234(x86251),x86252),f2(x86251)))+~P106(f857(f857(f234(x86251),x86253),x86254))+~P106(f857(f857(f235(x86251),f2(x86251)),f857(f857(f80(x86251),x86253),x86254)))+P106(f857(f857(f234(x86251),f857(f857(f290(x86251),x86252),x86253)),f857(f857(f290(x86251),x86252),x86254)))
% 15.02/14.81 [8626]~P68(x86261)+~P106(f857(f857(f235(x86261),x86262),f2(x86261)))+~P106(f857(f857(f235(x86261),x86263),x86264))+~P106(f857(f857(f235(x86261),f2(x86261)),f857(f857(f80(x86261),x86263),x86264)))+P106(f857(f857(f235(x86261),f857(f857(f290(x86261),x86262),x86263)),f857(f857(f290(x86261),x86262),x86264)))
% 15.02/14.81 [8635]~P68(x86351)+~P106(f857(f857(f234(x86351),x86354),x86353))+~P106(f857(f857(f234(x86351),f2(x86351)),x86352))+~P106(f857(f857(f235(x86351),f2(x86351)),f857(f857(f80(x86351),x86353),x86354)))+P106(f857(f857(f234(x86351),f857(f857(f290(x86351),x86352),x86353)),f857(f857(f290(x86351),x86352),x86354)))
% 15.02/14.81 [8636]~P68(x86361)+~P106(f857(f857(f235(x86361),x86364),x86363))+~P106(f857(f857(f235(x86361),f2(x86361)),x86362))+~P106(f857(f857(f235(x86361),f2(x86361)),f857(f857(f80(x86361),x86363),x86364)))+P106(f857(f857(f235(x86361),f857(f857(f290(x86361),x86362),x86363)),f857(f857(f290(x86361),x86362),x86364)))
% 15.02/14.81 [8736]P106(f857(x87361,x87362))+~P106(f857(f60(x87364),x87362))+P106(f857(x87361,f510(x87361,x87363,x87362,x87364)))+~P106(f857(x87361,f189(f927(x87364,a915))))+~P106(f857(f857(f234(f927(x87364,a915)),x87362),x87363))
% 15.02/14.81 [8745]P106(f857(x87451,x87452))+P106(f857(f60(x87453),f510(x87451,x87454,x87452,x87453)))+~P106(f857(f60(x87453),x87452))+~P106(f857(x87451,f189(f927(x87453,a915))))+~P106(f857(f857(f234(f927(x87453,a915)),x87452),x87454))
% 15.02/14.81 [9013]E(f857(f857(f79(a1),f462(x90131,x90132,x90133,x90134)),f463(x90131,x90132,x90133,x90134)),x90134)+~P106(f857(f857(f235(a1),f2(a1)),x90133))+~P106(f857(f857(f235(a1),x90132),x90134))+~P106(f857(f857(f328(a1),x90132),x90131))+P106(f857(f857(f235(a1),x90132),f857(f857(f3(a1),x90134),x90133)))
% 15.02/14.81 [9226]~P106(f857(f857(f235(a1),f2(a1)),x92263))+~P106(f857(f857(f235(a1),x92262),x92264))+~P106(f857(f857(f328(a1),x92262),x92261))+P106(f857(f857(f328(a1),f462(x92261,x92262,x92263,x92264)),x92261))+P106(f857(f857(f235(a1),x92262),f857(f857(f3(a1),x92264),x92263)))
% 15.02/14.81 [9237]P106(f857(x92371,x92372))+~P106(f857(f60(x92373),x92372))+P106(f857(f857(f328(x92373),f506(x92371,x92374,x92372,x92373)),x92374))+~P106(f857(x92371,f189(f927(x92373,a915))))+~P106(f857(f857(f234(f927(x92373,a915)),x92372),x92374))
% 15.02/14.81 [9254]E(f857(f857(f79(a1),f447(x92541,x92542,x92543,x92544)),f448(x92541,x92542,x92543,x92544)),x92544)+~P106(f857(f857(f235(a1),f2(a1)),x92543))+~P106(f857(f857(f234(a1),x92542),x92544))+P106(f857(f857(f234(a1),x92542),f857(f857(f3(a1),x92544),x92543)))+~P106(f857(f857(f328(a1),f857(f857(f3(a1),x92542),f77(a1))),x92541))
% 15.02/14.81 [9308]~P106(f857(f857(f235(a1),f2(a1)),x93083))+~P106(f857(f857(f235(a1),x93081),x93082))+~P106(f857(f857(f328(a1),x93081),x93084))+P106(f857(f857(f328(a1),f463(x93084,x93081,x93083,x93082)),f302(a1,f77(a1),x93083)))+P106(f857(f857(f235(a1),x93081),f857(f857(f3(a1),x93082),x93083)))
% 15.02/14.81 [9334]~P72(x93342)+~E(f777(x93343,x93344,x93341,x93342),f778(x93343,x93344,x93341,x93342))+~P106(f857(f60(x93341),f779(x93343,x93344,x93341,x93342)))+E(f857(f857(f8(f927(x93341,a915),x93342),f857(f8(x93341,x93342),x93343)),x93344),f857(f857(f8(x93341,x93342),x93343),f36(f927(x93341,a915),x93344)))+~P106(f857(f60(f927(x93341,a915)),x93344))
% 15.02/14.81 [9338]~P72(x93382)+~E(f857(x93383,f782(x93383,x93384,x93381,x93382)),f2(x93382))+~P106(f857(f60(x93381),f779(x93383,x93384,x93381,x93382)))+E(f857(f857(f8(f927(x93381,a915),x93382),f857(f8(x93381,x93382),x93383)),x93384),f857(f857(f8(x93381,x93382),x93383),f36(f927(x93381,a915),x93384)))+~P106(f857(f60(f927(x93381,a915)),x93384))
% 15.02/14.81 [9401]~P106(f857(f857(f235(a1),f2(a1)),x94013))+~P106(f857(f857(f234(a1),x94012),x94014))+P106(f857(f857(f328(a1),f447(x94011,x94012,x94013,x94014)),x94011))+P106(f857(f857(f234(a1),x94012),f857(f857(f3(a1),x94014),x94013)))+~P106(f857(f857(f328(a1),f857(f857(f3(a1),x94012),f77(a1))),x94011))
% 15.02/14.81 [9446]~P106(f857(f857(f235(a1),f2(a1)),x94463))+~P106(f857(f857(f234(a1),x94461),x94462))+P106(f857(f857(f328(a1),f448(x94464,x94461,x94463,x94462)),f302(a1,f77(a1),x94463)))+P106(f857(f857(f234(a1),x94461),f857(f857(f3(a1),x94462),x94463)))+~P106(f857(f857(f328(a1),f857(f857(f3(a1),x94461),f77(a1))),x94464))
% 15.02/14.81 [9467]~P72(x94672)+~E(f777(x94673,x94674,x94671,x94672),f778(x94673,x94674,x94671,x94672))+E(f857(f857(f8(f927(x94671,a915),x94672),f857(f8(x94671,x94672),x94673)),x94674),f857(f857(f8(x94671,x94672),x94673),f36(f927(x94671,a915),x94674)))+P106(f857(f857(f328(f927(x94671,a915)),f779(x94673,x94674,x94671,x94672)),x94674))+~P106(f857(f60(f927(x94671,a915)),x94674))
% 15.02/14.81 [9474]~P72(x94742)+~E(f857(x94743,f782(x94743,x94744,x94741,x94742)),f2(x94742))+E(f857(f857(f8(f927(x94741,a915),x94742),f857(f8(x94741,x94742),x94743)),x94744),f857(f857(f8(x94741,x94742),x94743),f36(f927(x94741,a915),x94744)))+P106(f857(f857(f328(f927(x94741,a915)),f779(x94743,x94744,x94741,x94742)),x94744))+~P106(f857(f60(f927(x94741,a915)),x94744))
% 15.02/14.81 [9575]~P72(x95752)+~P106(f857(f60(x95751),f779(x95753,x95754,x95751,x95752)))+E(f857(f857(f8(f927(x95751,a915),x95752),f857(f8(x95751,x95752),x95753)),x95754),f857(f857(f8(x95751,x95752),x95753),f36(f927(x95751,a915),x95754)))+P106(f857(f857(f328(f927(x95751,a915)),f778(x95753,x95754,x95751,x95752)),x95754))+~P106(f857(f60(f927(x95751,a915)),x95754))
% 15.02/14.81 [9576]~P72(x95762)+~P106(f857(f60(x95761),f779(x95763,x95764,x95761,x95762)))+E(f857(f857(f8(f927(x95761,a915),x95762),f857(f8(x95761,x95762),x95763)),x95764),f857(f857(f8(x95761,x95762),x95763),f36(f927(x95761,a915),x95764)))+P106(f857(f857(f328(f927(x95761,a915)),f777(x95763,x95764,x95761,x95762)),x95764))+~P106(f857(f60(f927(x95761,a915)),x95764))
% 15.02/14.81 [9656]~P72(x96562)+E(f857(f857(f8(f927(x96561,a915),x96562),f857(f8(x96561,x96562),x96563)),x96564),f857(f857(f8(x96561,x96562),x96563),f36(f927(x96561,a915),x96564)))+P106(f857(f857(f328(f927(x96561,a915)),f779(x96563,x96564,x96561,x96562)),x96564))+P106(f857(f857(f328(f927(x96561,a915)),f778(x96563,x96564,x96561,x96562)),x96564))+~P106(f857(f60(f927(x96561,a915)),x96564))
% 15.02/14.81 [9657]~P72(x96572)+E(f857(f857(f8(f927(x96571,a915),x96572),f857(f8(x96571,x96572),x96573)),x96574),f857(f857(f8(x96571,x96572),x96573),f36(f927(x96571,a915),x96574)))+P106(f857(f857(f328(f927(x96571,a915)),f779(x96573,x96574,x96571,x96572)),x96574))+P106(f857(f857(f328(f927(x96571,a915)),f777(x96573,x96574,x96571,x96572)),x96574))+~P106(f857(f60(f927(x96571,a915)),x96574))
% 15.02/14.81 [9676]~P72(x96762)+P106(f857(f857(f328(x96761),f782(x96763,x96764,x96761,x96762)),f778(x96763,x96764,x96761,x96762)))+~P106(f857(f60(x96761),f779(x96763,x96764,x96761,x96762)))+E(f857(f857(f8(f927(x96761,a915),x96762),f857(f8(x96761,x96762),x96763)),x96764),f857(f857(f8(x96761,x96762),x96763),f36(f927(x96761,a915),x96764)))+~P106(f857(f60(f927(x96761,a915)),x96764))
% 15.02/14.81 [9677]~P72(x96772)+P106(f857(f857(f328(x96771),f782(x96773,x96774,x96771,x96772)),f777(x96773,x96774,x96771,x96772)))+~P106(f857(f60(x96771),f779(x96773,x96774,x96771,x96772)))+E(f857(f857(f8(f927(x96771,a915),x96772),f857(f8(x96771,x96772),x96773)),x96774),f857(f857(f8(x96771,x96772),x96773),f36(f927(x96771,a915),x96774)))+~P106(f857(f60(f927(x96771,a915)),x96774))
% 15.02/14.81 [9694]P106(f857(x96941,x96942))+~P106(f857(f857(f328(x96943),f506(x96941,x96944,x96942,x96943)),f510(x96941,x96944,x96942,x96943)))+~P106(f857(f60(x96943),x96942))+~P106(f857(x96941,f189(f927(x96943,a915))))+~P106(f857(f857(f234(f927(x96943,a915)),x96942),x96944))
% 15.02/14.81 [9732]~P72(x97322)+P106(f857(f857(f328(x97321),f782(x97323,x97324,x97321,x97322)),f778(x97323,x97324,x97321,x97322)))+E(f857(f857(f8(f927(x97321,a915),x97322),f857(f8(x97321,x97322),x97323)),x97324),f857(f857(f8(x97321,x97322),x97323),f36(f927(x97321,a915),x97324)))+P106(f857(f857(f328(f927(x97321,a915)),f779(x97323,x97324,x97321,x97322)),x97324))+~P106(f857(f60(f927(x97321,a915)),x97324))
% 15.02/14.81 [9733]~P72(x97332)+P106(f857(f857(f328(x97331),f782(x97333,x97334,x97331,x97332)),f777(x97333,x97334,x97331,x97332)))+E(f857(f857(f8(f927(x97331,a915),x97332),f857(f8(x97331,x97332),x97333)),x97334),f857(f857(f8(x97331,x97332),x97333),f36(f927(x97331,a915),x97334)))+P106(f857(f857(f328(f927(x97331,a915)),f779(x97333,x97334,x97331,x97332)),x97334))+~P106(f857(f60(f927(x97331,a915)),x97334))
% 15.02/14.81 [9908]P106(f857(x99081,x99082))+~P106(f857(f60(x99083),x99082))+~P106(f857(x99081,f857(f857(f308(x99083),f506(x99081,x99084,x99082,x99083)),f510(x99081,x99084,x99082,x99083))))+~P106(f857(x99081,f189(f927(x99083,a915))))+~P106(f857(f857(f234(f927(x99083,a915)),x99082),x99084))
% 15.02/14.81 [7936]~P67(x79361)+P106(f857(f857(f235(x79361),x79362),f2(x79361)))+~P106(f857(f857(f234(x79361),f2(x79361)),x79364))+P106(f857(f857(f235(x79361),f2(x79361)),x79362))+P106(f857(f857(f234(x79361),f857(f857(f290(x79361),x79363),x79362)),x79364))
% 15.02/14.81 [7937]~P67(x79371)+P106(f857(f857(f235(x79371),x79372),f2(x79371)))+P106(f857(f857(f235(x79371),f2(x79371)),x79372))+~P106(f857(f857(f235(x79371),f2(x79371)),x79374))+P106(f857(f857(f235(x79371),f857(f857(f290(x79371),x79373),x79372)),x79374))
% 15.02/14.81 [8216]~P106(f857(f857(f234(a1),x82164),f2(a1)))+~E(x82162,f857(f857(f79(a1),f857(f857(f80(a1),x82161),x82163)),x82164))+P106(f857(f857(f235(a1),f2(a1)),x82161))+~P106(f857(f857(f235(a1),x82161),x82164))+P106(f857(f48(x82162,x82161),f857(f857(f251(a1,a1),x82163),x82164)))
% 15.02/14.81 [8250]~P106(f857(x82501,x82504))+P106(f857(x82501,f353(x82502,x82501,x82503)))+~P106(f857(f857(f234(a1),f2(a1)),x82502))+~P106(f857(f857(f235(a1),f2(a1)),x82503))+P106(f857(x82501,f857(f857(f3(a1),x82504),f857(f857(f80(a1),x82502),x82503))))
% 15.02/14.81 [8251]~P106(f857(x82511,x82514))+P106(f857(x82511,f355(x82512,x82511,x82513)))+~P106(f857(f857(f234(a1),f2(a1)),x82512))+~P106(f857(f857(f235(a1),f2(a1)),x82513))+P106(f857(x82511,f857(f857(f79(a1),x82514),f857(f857(f80(a1),x82512),x82513))))
% 15.02/14.81 [8252]~P67(x82521)+P106(f857(f857(f235(x82521),x82522),f2(x82521)))+P106(f857(f857(f235(x82521),f2(x82521)),x82522))+P106(f857(f857(f234(x82521),f2(x82521)),x82523))+~P106(f857(f857(f234(x82521),f857(f857(f290(x82521),x82524),x82522)),x82523))
% 15.02/14.81 [8253]~P67(x82531)+P106(f857(f857(f235(x82531),x82532),f2(x82531)))+P106(f857(f857(f235(x82531),f2(x82531)),x82532))+P106(f857(f857(f235(x82531),f2(x82531)),x82533))+~P106(f857(f857(f235(x82531),f857(f857(f290(x82531),x82534),x82532)),x82533))
% 15.02/14.81 [8304]~E(x83041,f857(f857(f79(a1),f857(f857(f80(a1),x83042),x83043)),x83044))+~P106(f857(f857(f234(a1),f2(a1)),x83044))+~P106(f857(f857(f235(a1),f2(a1)),x83042))+~P106(f857(f857(f235(a1),x83044),x83042))+P106(f857(f48(x83041,x83042),f857(f857(f251(a1,a1),x83043),x83044)))
% 15.02/14.81 [8421]~P67(x84211)+P106(f857(f857(f235(x84211),x84212),f2(x84211)))+~P106(f857(f857(f234(x84211),f2(x84211)),x84214))+~P106(f857(f857(f234(x84211),x84213),f857(f857(f80(x84211),x84214),x84212)))+P106(f857(f857(f234(x84211),f857(f857(f290(x84211),x84213),x84212)),x84214))
% 15.02/14.81 [8422]~P67(x84221)+P106(f857(f857(f235(x84221),x84222),f2(x84221)))+~P106(f857(f857(f235(x84221),f2(x84221)),x84224))+~P106(f857(f857(f235(x84221),x84223),f857(f857(f80(x84221),x84224),x84222)))+P106(f857(f857(f235(x84221),f857(f857(f290(x84221),x84223),x84222)),x84224))
% 15.02/14.81 [8506]~P67(x85061)+P106(f857(f857(f235(x85061),x85062),f2(x85061)))+~P106(f857(f857(f234(x85061),x85063),f2(x85061)))+P106(f857(f857(f234(x85061),x85063),f857(f857(f290(x85061),x85064),x85062)))+~P106(f857(f857(f234(x85061),f857(f857(f80(x85061),x85063),x85062)),x85064))
% 15.02/14.81 [8507]~P67(x85071)+P106(f857(f857(f235(x85071),x85072),f2(x85071)))+~P106(f857(f857(f235(x85071),x85073),f2(x85071)))+P106(f857(f857(f235(x85071),x85073),f857(f857(f290(x85071),x85074),x85072)))+~P106(f857(f857(f235(x85071),f857(f857(f80(x85071),x85073),x85072)),x85074))
% 15.02/14.81 [8657]~P67(x86571)+~P106(f857(f857(f235(x86571),x86572),f2(x86571)))+P106(f857(f857(f235(x86571),f2(x86571)),x86572))+~P106(f857(f857(f234(x86571),f857(f857(f290(x86571),x86574),x86572)),x86573))+P106(f857(f857(f234(x86571),f857(f857(f80(x86571),x86573),x86572)),x86574))
% 15.02/14.81 [8658]~P67(x86581)+~P106(f857(f857(f235(x86581),x86582),f2(x86581)))+P106(f857(f857(f235(x86581),f2(x86581)),x86582))+~P106(f857(f857(f234(x86581),f857(f857(f80(x86581),x86584),x86582)),x86583))+P106(f857(f857(f234(x86581),f857(f857(f290(x86581),x86583),x86582)),x86584))
% 15.02/14.81 [8659]~P67(x86591)+~P106(f857(f857(f235(x86591),x86592),f2(x86591)))+P106(f857(f857(f235(x86591),f2(x86591)),x86592))+~P106(f857(f857(f235(x86591),f857(f857(f290(x86591),x86594),x86592)),x86593))+P106(f857(f857(f235(x86591),f857(f857(f80(x86591),x86593),x86592)),x86594))
% 15.02/14.81 [8660]~P67(x86601)+~P106(f857(f857(f235(x86601),x86602),f2(x86601)))+P106(f857(f857(f235(x86601),f2(x86601)),x86602))+~P106(f857(f857(f235(x86601),f857(f857(f80(x86601),x86604),x86602)),x86603))+P106(f857(f857(f235(x86601),f857(f857(f290(x86601),x86603),x86602)),x86604))
% 15.02/14.81 [8676]~P67(x86761)+~P106(f857(f857(f234(x86761),f2(x86761)),x86764))+P106(f857(f857(f235(x86761),f2(x86761)),x86762))+~P106(f857(f857(f234(x86761),f857(f857(f80(x86761),x86764),x86762)),x86763))+P106(f857(f857(f234(x86761),f857(f857(f290(x86761),x86763),x86762)),x86764))
% 15.02/14.81 [8677]~P67(x86771)+~P106(f857(f857(f235(x86771),f2(x86771)),x86774))+P106(f857(f857(f235(x86771),f2(x86771)),x86772))+~P106(f857(f857(f235(x86771),f857(f857(f80(x86771),x86774),x86772)),x86773))+P106(f857(f857(f235(x86771),f857(f857(f290(x86771),x86773),x86772)),x86774))
% 15.02/14.81 [8753]~P67(x87531)+~P106(f857(f857(f235(x87531),x87534),f2(x87531)))+~P106(f857(f857(f234(x87531),x87533),f857(f857(f80(x87531),x87532),x87534)))+P106(f857(f857(f234(x87531),x87532),f857(f857(f290(x87531),x87533),x87534)))+~P106(f857(f857(f234(x87531),f857(f857(f80(x87531),x87532),x87534)),x87533))
% 15.02/14.81 [8754]~P67(x87541)+~P106(f857(f857(f234(x87541),x87542),f2(x87541)))+~P106(f857(f857(f234(x87541),x87543),f857(f857(f80(x87541),x87542),x87544)))+P106(f857(f857(f234(x87541),x87542),f857(f857(f290(x87541),x87543),x87544)))+~P106(f857(f857(f234(x87541),f857(f857(f80(x87541),x87542),x87544)),x87543))
% 15.02/14.81 [8755]~P67(x87551)+~P106(f857(f857(f235(x87551),x87554),f2(x87551)))+~P106(f857(f857(f235(x87551),x87553),f857(f857(f80(x87551),x87552),x87554)))+P106(f857(f857(f235(x87551),x87552),f857(f857(f290(x87551),x87553),x87554)))+~P106(f857(f857(f235(x87551),f857(f857(f80(x87551),x87552),x87554)),x87553))
% 15.02/14.81 [8756]~P67(x87561)+~P106(f857(f857(f235(x87561),x87562),f2(x87561)))+~P106(f857(f857(f235(x87561),x87563),f857(f857(f80(x87561),x87562),x87564)))+P106(f857(f857(f235(x87561),x87562),f857(f857(f290(x87561),x87563),x87564)))+~P106(f857(f857(f235(x87561),f857(f857(f80(x87561),x87562),x87564)),x87563))
% 15.02/14.81 [8878]~P67(x88781)+~P106(f857(f857(f235(x88781),x88783),f2(x88781)))+~P106(f857(f857(f234(x88781),x88782),f857(f857(f80(x88781),x88784),x88783)))+~P106(f857(f857(f234(x88781),f857(f857(f80(x88781),x88784),x88783)),x88782))+P106(f857(f857(f234(x88781),f857(f857(f290(x88781),x88782),x88783)),x88784))
% 15.02/14.81 [8879]~P67(x88791)+~P106(f857(f857(f235(x88791),x88793),f2(x88791)))+~P106(f857(f857(f235(x88791),x88792),f857(f857(f80(x88791),x88794),x88793)))+~P106(f857(f857(f235(x88791),f857(f857(f80(x88791),x88794),x88793)),x88792))+P106(f857(f857(f235(x88791),f857(f857(f290(x88791),x88792),x88793)),x88794))
% 15.02/14.81 [8896]~P67(x88961)+~P106(f857(f857(f234(x88961),f2(x88961)),x88964))+~P106(f857(f857(f234(x88961),x88962),f857(f857(f80(x88961),x88964),x88963)))+~P106(f857(f857(f234(x88961),f857(f857(f80(x88961),x88964),x88963)),x88962))+P106(f857(f857(f234(x88961),f857(f857(f290(x88961),x88962),x88963)),x88964))
% 15.02/14.81 [8897]~P67(x88971)+~P106(f857(f857(f235(x88971),f2(x88971)),x88974))+~P106(f857(f857(f235(x88971),x88972),f857(f857(f80(x88971),x88974),x88973)))+~P106(f857(f857(f235(x88971),f857(f857(f80(x88971),x88974),x88973)),x88972))+P106(f857(f857(f235(x88971),f857(f857(f290(x88971),x88972),x88973)),x88974))
% 15.02/14.81 [9080]E(f857(f857(f3(a1),f469(x90801,x90802,x90803,x90804)),f470(x90801,x90802,x90803,x90804)),x90804)+~P106(f857(f857(f235(a1),f2(a1)),x90803))+~P106(f857(f857(f328(a1),x90802),x90801))+~P106(f857(f857(f235(a1),x90804),x90802))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x90804),x90803)),x90802))
% 15.02/14.81 [9151]~P106(f857(x91511,x91512))+~P106(f857(f857(f234(a1),f2(a1)),x91513))+~P106(f857(f857(f235(a1),f2(a1)),x91514))+~P106(f857(x91511,f857(f857(f3(a1),f353(x91513,x91511,x91514)),x91514)))+P106(f857(x91511,f857(f857(f3(a1),x91512),f857(f857(f80(a1),x91513),x91514))))
% 15.02/14.81 [9152]~P106(f857(x91521,x91522))+~P106(f857(f857(f234(a1),f2(a1)),x91523))+~P106(f857(f857(f235(a1),f2(a1)),x91524))+~P106(f857(x91521,f857(f857(f79(a1),f355(x91523,x91521,x91524)),x91524)))+P106(f857(x91521,f857(f857(f79(a1),x91522),f857(f857(f80(a1),x91523),x91524))))
% 15.02/14.81 [9302]~P106(f857(f857(f235(a1),f2(a1)),x93023))+~P106(f857(f857(f328(a1),x93022),x93021))+~P106(f857(f857(f235(a1),x93024),x93022))+P106(f857(f857(f328(a1),f469(x93021,x93022,x93023,x93024)),x93021))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x93024),x93023)),x93022))
% 15.02/14.81 [9321]E(f857(f857(f3(a1),f449(x93211,x93212,x93213,x93214)),f450(x93211,x93212,x93213,x93214)),x93214)+~P106(f857(f857(f235(a1),f2(a1)),x93213))+~P106(f857(f857(f234(a1),x93214),x93212))+~P106(f857(f857(f328(a1),f857(f857(f79(a1),x93212),f77(a1))),x93211))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x93214),x93213)),x93212))
% 15.02/14.81 [9349]~P106(f857(f857(f235(a1),f2(a1)),x93492))+~P106(f857(f857(f328(a1),x93493),x93494))+~P106(f857(f857(f235(a1),x93491),x93493))+P106(f857(f857(f328(a1),f470(x93494,x93493,x93492,x93491)),f302(a1,f77(a1),x93492)))+P106(f857(f857(f235(a1),f857(f857(f79(a1),x93491),x93492)),x93493))
% 15.02/14.81 [9438]~P106(f857(f857(f235(a1),f2(a1)),x94383))+~P106(f857(f857(f234(a1),x94384),x94382))+P106(f857(f857(f328(a1),f449(x94381,x94382,x94383,x94384)),x94381))+~P106(f857(f857(f328(a1),f857(f857(f79(a1),x94382),f77(a1))),x94381))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x94384),x94383)),x94382))
% 15.02/14.81 [9485]~P106(f857(f857(f235(a1),f2(a1)),x94852))+~P106(f857(f857(f234(a1),x94851),x94853))+P106(f857(f857(f328(a1),f450(x94854,x94853,x94852,x94851)),f302(a1,f77(a1),x94852)))+~P106(f857(f857(f328(a1),f857(f857(f79(a1),x94853),f77(a1))),x94854))+P106(f857(f857(f234(a1),f857(f857(f79(a1),x94851),x94852)),x94853))
% 15.02/14.81 [9786]~P39(x97861,x97863)+~P28(x97861,x97864)+P39(x97861,f857(f857(f110(f927(f926(x97861,x97861),a915)),x97862),x97863))+~P106(f857(f857(f234(f927(f926(x97861,x97861),a915)),x97862),f857(f250(f927(f926(x97861,x97861),a915),f927(f926(x97861,x97861),a915)),x97864)))+~P106(f857(f857(f234(f927(f926(x97861,x97861),a915)),x97863),f857(f255(f927(f926(x97861,x97861),a915),f927(f926(x97861,x97861),a915)),x97864)))
% 15.02/14.81 [10176]~P19(x101762,x101764,x101763)+E(x101761,f189(f927(x101762,a915)))+~P106(f857(f60(x101762),x101761))+P106(f857(f857(f328(x101762),f857(x101763,x101761)),x101761))+~P106(f857(f857(f328(x101762),f857(f857(x101764,f471(x101761,x101763,x101764,x101762)),f479(x101761,x101763,x101764,x101762))),f857(f857(f308(x101762),f471(x101761,x101763,x101764,x101762)),f857(f857(f308(x101762),f479(x101761,x101763,x101764,x101762)),f189(f927(x101762,a915))))))
% 15.02/14.81 [10099]~P110(x100992)+~P64(x100991)+~P106(f857(f857(f234(f927(x100991,x100992)),x100993),x100994))+P106(f857(f857(f235(f927(x100991,x100992)),x100993),x100994))+~P106(f857(f55(x100991),f857(f857(f10(a915,a915,x100991),a321),f857(f857(f20(x100991,x100992,a915),f857(f857(f10(x100992,f927(x100992,a915),x100991),a324),x100993)),x100994))))
% 15.02/14.81 [9700]~P56(x97001,x97001,x97004)+P106(f857(f857(f328(f926(x97001,x97001)),f857(f857(f251(x97001,x97001),x97002),x97003)),f306(x97001,x97004)))+P106(f857(f857(f328(f926(x97001,x97001)),f857(f857(f251(x97001,x97001),x97003),x97002)),f306(x97001,x97004)))+~P106(f857(f857(f328(f926(x97001,x97001)),f857(f857(f251(x97001,x97001),x97005),x97002)),f306(x97001,x97004)))+~P106(f857(f857(f328(f926(x97001,x97001)),f857(f857(f251(x97001,x97001),x97005),x97003)),f306(x97001,x97004)))
% 15.02/14.81 [5821]E(x58211,f2(a919))+~E(f857(f34(x58212),x58215),x58211)+E(f857(f34(x58212),x58213),f857(a112,x58211))+~E(x58213,f857(f857(f308(x58212),x58214),x58215))+P106(f857(f857(f328(x58212),x58214),x58215))
% 15.02/14.81 [5943]~P66(x59432)+E(x59431,f2(x59432))+E(x59433,f2(x59432))+~E(f857(f857(f290(x59432),x59434),x59433),f857(f857(f290(x59432),x59435),x59431))+E(f857(f857(f80(x59432),x59434),x59431),f857(f857(f80(x59432),x59435),x59433))
% 15.02/14.81 [5944]~P66(x59442)+E(x59441,f2(x59442))+E(x59443,f2(x59442))+~E(f857(f857(f80(x59442),x59444),x59443),f857(f857(f80(x59442),x59445),x59441))+E(f857(f857(f290(x59442),x59444),x59441),f857(f857(f290(x59442),x59445),x59443))
% 15.02/14.81 [6013]~E(f857(f34(x60131),x60135),x60133)+~E(x60135,f189(f927(x60131,a915)))+E(f857(f34(x60131),x60132),f857(a112,x60133))+~E(x60132,f857(f857(f308(x60131),x60134),x60135))+P106(f857(f857(f328(x60131),x60134),x60135))
% 15.02/14.81 [6253]~P113(x62532)+~E(f857(x62533,x62535),f2(x62532))+E(f857(f857(f11(x62531,x62532),x62533),x62534),f2(x62532))+~P106(f857(f60(x62531),x62534))+~P106(f857(f857(f328(x62531),x62535),x62534))
% 15.02/14.81 [6632]~P109(x66323)+E(x66321,x66322)+~E(f857(f301(x66323,x66324),x66321),f857(f301(x66323,x66325),x66322))+~P106(f857(f857(f235(x66323),x66325),x66322))+~P106(f857(f857(f235(x66323),x66324),x66321))
% 15.02/14.81 [6633]~P109(x66333)+E(x66331,x66332)+~E(f857(f301(x66333,x66331),x66334),f857(f301(x66333,x66332),x66335))+~P106(f857(f857(f235(x66333),x66332),x66335))+~P106(f857(f857(f235(x66333),x66331),x66334))
% 15.02/14.81 [7701]~P109(x77011)+~P14(x77011,f857(f857(f134(x77011),x77014),x77015))+~P106(f857(f857(f328(x77011),x77013),f857(f172(x77011),x77015)))+~P106(f857(f857(f328(x77011),x77012),f857(f172(x77011),x77014)))+P106(f857(f857(f234(x77011),x77012),x77013))
% 15.02/14.81 [8790]~P110(x87901)+~P106(f857(f857(f235(f927(x87901,a915)),f302(x87901,x87905,x87902)),f302(x87901,x87904,x87903)))+~P106(f857(f857(f234(x87901),x87905),x87902))+P106(f857(f857(f235(x87901),x87902),x87903))+P106(f857(f857(f235(x87901),x87904),x87905))
% 15.02/14.81 [10219]~P18(x102192,x102195,x102193)+E(x102191,f189(f927(x102192,a915)))+~E(f857(f857(x102195,f857(x102194,f533(x102191,x102194,x102193,x102195,x102192))),f857(x102194,f534(x102191,x102194,x102193,x102195,x102192))),f857(x102194,f857(f857(x102195,f533(x102191,x102194,x102193,x102195,x102192)),f534(x102191,x102194,x102193,x102195,x102192))))+E(f857(x102193,f857(f309(x102192,x102192,x102194),x102191)),f857(x102194,f857(x102193,x102191)))+~P106(f857(f60(x102192),x102191))
% 15.02/14.81 [6629]~P19(x66292,x66295,x66293)+E(x66291,f189(f927(x66292,a915)))+~P106(f857(f60(x66292),x66291))+E(f857(x66293,f857(f857(f308(x66292),x66294),x66291)),f857(f857(x66295,x66294),f857(x66293,x66291)))+P106(f857(f857(f328(x66292),x66294),x66291))
% 15.02/14.81 [7464]~P18(x74642,x74643,x74644)+E(f857(f857(x74643,f857(x74644,x74641)),f857(x74644,x74645)),f857(x74644,x74645))+E(x74641,f189(f927(x74642,a915)))+~P106(f857(f60(x74642),x74645))+~P106(f857(f857(f234(f927(x74642,a915)),x74641),x74645))
% 15.02/14.81 [7836]~P19(x78364,x78365,x78361)+E(f857(x78361,x78362),x78363)+~P106(f857(f60(x78364),x78362))+~E(f857(f857(f3(f927(x78364,a915)),x78362),f857(f857(f308(x78364),x78363),f189(f927(x78364,a915)))),f189(f927(x78364,a915)))+~P106(f857(f857(f328(x78364),x78363),x78362))
% 15.02/14.81 [8711]~P77(x87111)+~P123(x87111)+~P106(f857(f60(x87112),x87115))+P106(f857(f857(f286(x87111),f857(f857(f11(x87112,x87111),x87113),x87114)),f857(f857(f11(x87112,x87111),x87113),x87115)))+~P106(f857(f857(f234(f927(x87112,a915)),x87114),x87115))
% 15.02/14.81 [8760]E(x87601,x87602)+~P9(x87603,x87604,x87605)+E(f857(f857(f101(f927(x87603,a915)),x87601),x87602),f189(f927(x87603,a915)))+~P106(f857(f857(f328(f927(x87603,a915)),x87602),f857(f857(f59(x87603),x87604),x87605)))+~P106(f857(f857(f328(f927(x87603,a915)),x87601),f857(f857(f59(x87603),x87604),x87605)))
% 15.02/14.81 [9568]~P72(x95682)+~E(f857(x95683,f908(x95683,x95684,x95685,x95681,x95682)),f2(x95682))+E(f857(f857(f8(x95681,x95682),x95683),x95684),f857(f857(f8(x95681,x95682),x95683),x95685))+~P106(f857(f60(x95681),x95685))+~P106(f857(f857(f234(f927(x95681,a915)),x95684),x95685))
% 15.02/14.81 [9569]~P72(x95692)+~E(f857(x95693,f910(x95693,x95694,x95695,x95691,x95692)),f2(x95692))+E(f857(f857(f8(x95691,x95692),x95693),x95694),f857(f857(f8(x95691,x95692),x95693),x95695))+~P106(f857(f60(x95691),x95695))+~P106(f857(f857(f234(f927(x95691,a915)),x95694),x95695))
% 15.02/14.81 [9570]~P77(x95702)+~E(f857(x95703,f871(x95703,x95704,x95705,x95701,x95702)),f77(x95702))+E(f857(f857(f11(x95701,x95702),x95703),x95704),f857(f857(f11(x95701,x95702),x95703),x95705))+~P106(f857(f60(x95701),x95705))+~P106(f857(f857(f234(f927(x95701,a915)),x95704),x95705))
% 15.02/14.81 [9571]~P77(x95712)+~E(f857(x95713,f873(x95713,x95714,x95715,x95711,x95712)),f77(x95712))+E(f857(f857(f11(x95711,x95712),x95713),x95714),f857(f857(f11(x95711,x95712),x95713),x95715))+~P106(f857(f60(x95711),x95715))+~P106(f857(f857(f234(f927(x95711,a915)),x95714),x95715))
% 15.02/14.81 [10052]~P89(x100521)+~P106(f857(f60(x100522),x100525))+~P106(f857(f857(f234(x100521),f2(x100521)),f857(x100523,f900(x100523,x100524,x100525,x100522,x100521))))+P106(f857(f857(f234(x100521),f857(f857(f8(x100522,x100521),x100523),x100524)),f857(f857(f8(x100522,x100521),x100523),x100525)))+~P106(f857(f857(f234(f927(x100522,a915)),x100524),x100525))
% 15.02/14.81 [7698]E(x76981,f2(a919))+P106(f857(x76982,x76983))+~E(x76984,f857(f857(f79(a919),f857(f857(f80(a919),x76981),x76983)),x76985))+~P106(f857(f857(f235(a919),x76985),x76981))+~P106(f857(x76982,f857(f857(f35(a919),x76984),x76981)))
% 15.02/14.81 [7774]E(x77741,f2(a919))+P106(f857(x77742,x77743))+~P106(f857(x77742,f44(a919,x77744,x77741)))+~E(x77744,f857(f857(f79(a919),f857(f857(f80(a919),x77741),x77745)),x77743))+~P106(f857(f857(f235(a919),x77743),x77741))
% 15.02/14.81 [8065]~P66(x80653)+E(f857(x80651,x80652),f2(x80653))+~P106(f857(f60(x80654),x80655))+E(f857(f857(f11(x80654,x80653),x80651),f857(f857(f3(f927(x80654,a915)),x80655),f857(f857(f308(x80654),x80652),f189(f927(x80654,a915))))),f857(f857(f11(x80654,x80653),x80651),x80655))+P106(f857(f857(f328(x80654),x80652),x80655))
% 15.02/14.81 [8461]~P72(x84611)+~P106(f857(f60(x84612),x84615))+~P106(f857(f60(x84612),x84614))+~E(f857(f857(f101(f927(x84612,a915)),x84614),x84615),f189(f927(x84612,a915)))+E(f857(f857(f79(x84611),f857(f857(f8(x84612,x84611),x84613),x84614)),f857(f857(f8(x84612,x84611),x84613),x84615)),f857(f857(f8(x84612,x84611),x84613),f857(f857(f110(f927(x84612,a915)),x84614),x84615)))
% 15.02/14.81 [8463]~P77(x84631)+~P106(f857(f60(x84632),x84635))+~P106(f857(f60(x84632),x84634))+~E(f857(f857(f101(f927(x84632,a915)),x84634),x84635),f189(f927(x84632,a915)))+E(f857(f857(f80(x84631),f857(f857(f11(x84632,x84631),x84633),x84634)),f857(f857(f11(x84632,x84631),x84633),x84635)),f857(f857(f11(x84632,x84631),x84633),f857(f857(f110(f927(x84632,a915)),x84634),x84635)))
% 15.02/14.81 [8561]~P66(x85613)+E(f857(x85611,x85612),f2(x85613))+~P106(f857(f60(x85614),x85615))+E(f857(f857(f11(x85614,x85613),x85611),f857(f857(f3(f927(x85614,a915)),x85615),f857(f857(f308(x85614),x85612),f189(f927(x85614,a915))))),f857(f857(f290(x85613),f857(f857(f11(x85614,x85613),x85611),x85615)),f857(x85611,x85612)))+~P106(f857(f857(f328(x85614),x85612),x85615))
% 15.02/14.81 [9279]~P9(x92791,x92795,x92794)+~E(f857(f857(f59(x92791),f857(f857(f308(x92791),x92792),f189(f927(x92791,a915)))),x92794),f857(f857(f59(x92791),f857(f857(f308(x92791),x92793),f189(f927(x92791,a915)))),x92794))+~P106(f857(f857(f328(x92791),x92793),x92795))+~P106(f857(f857(f328(x92791),x92792),x92795))+P106(f857(f857(f328(f926(x92791,x92791)),f857(f857(f251(x92791,x92791),x92792),x92793)),x92794))
% 15.02/14.81 [9301]~P9(x93011,x93015,x93013)+E(f857(f857(f59(x93011),f857(f857(f308(x93011),x93012),f189(f927(x93011,a915)))),x93013),f857(f857(f59(x93011),f857(f857(f308(x93011),x93014),f189(f927(x93011,a915)))),x93013))+~P106(f857(f857(f328(x93011),x93014),x93015))+~P106(f857(f857(f328(x93011),x93012),x93015))+~P106(f857(f857(f328(f926(x93011,x93011)),f857(f857(f251(x93011,x93011),x93012),x93014)),x93013))
% 15.02/14.81 [9597]~P77(x95971)+~P106(f857(f60(x95972),x95975))+~P106(f857(f60(x95972),x95974))+~E(f857(f857(f101(f927(x95972,a915)),x95974),x95975),f189(f927(x95972,a915)))+E(f857(f857(f80(x95971),f857(f857(f857(f64(x95971,x95972,f80(x95971)),x95973),f77(x95971)),x95974)),f857(f857(f857(f64(x95971,x95972,f80(x95971)),x95973),f77(x95971)),x95975)),f857(f857(f857(f64(x95971,x95972,f80(x95971)),x95973),f77(x95971)),f857(f857(f110(f927(x95972,a915)),x95974),x95975)))
% 15.02/14.81 [9608]~P72(x96081)+~E(f857(x96083,f901(x96083,x96085,x96084,x96082,x96081)),f2(x96081))+~P106(f857(f60(x96082),x96084))+~P106(f857(f60(x96082),x96085))+E(f857(f857(f79(x96081),f857(f857(f8(x96082,x96081),x96083),x96084)),f857(f857(f8(x96082,x96081),x96083),x96085)),f857(f857(f8(x96082,x96081),x96083),f857(f857(f110(f927(x96082,a915)),x96084),x96085)))
% 15.02/14.81 [9609]~P72(x96091)+~E(f857(x96093,f902(x96093,x96095,x96094,x96092,x96091)),f2(x96091))+~P106(f857(f60(x96092),x96094))+~P106(f857(f60(x96092),x96095))+E(f857(f857(f79(x96091),f857(f857(f8(x96092,x96091),x96093),x96094)),f857(f857(f8(x96092,x96091),x96093),x96095)),f857(f857(f8(x96092,x96091),x96093),f857(f857(f110(f927(x96092,a915)),x96094),x96095)))
% 15.02/14.81 [9610]~P77(x96101)+~E(f857(x96103,f866(x96103,x96105,x96104,x96102,x96101)),f77(x96101))+~P106(f857(f60(x96102),x96104))+~P106(f857(f60(x96102),x96105))+E(f857(f857(f80(x96101),f857(f857(f11(x96102,x96101),x96103),x96104)),f857(f857(f11(x96102,x96101),x96103),x96105)),f857(f857(f11(x96102,x96101),x96103),f857(f857(f110(f927(x96102,a915)),x96104),x96105)))
% 15.02/14.81 [9611]~P77(x96111)+~E(f857(x96113,f872(x96113,x96115,x96114,x96112,x96111)),f77(x96111))+~P106(f857(f60(x96112),x96114))+~P106(f857(f60(x96112),x96115))+E(f857(f857(f80(x96111),f857(f857(f11(x96112,x96111),x96113),x96114)),f857(f857(f11(x96112,x96111),x96113),x96115)),f857(f857(f11(x96112,x96111),x96113),f857(f857(f110(f927(x96112,a915)),x96114),x96115)))
% 15.02/14.81 [9829]~P77(x98291)+~E(f857(x98293,f877(x98293,x98295,x98294,x98292,x98291)),f77(x98291))+~P106(f857(f60(x98292),x98294))+~P106(f857(f60(x98292),x98295))+E(f857(f857(f80(x98291),f857(f857(f857(f64(x98291,x98292,f80(x98291)),x98293),f77(x98291)),x98294)),f857(f857(f857(f64(x98291,x98292,f80(x98291)),x98293),f77(x98291)),x98295)),f857(f857(f857(f64(x98291,x98292,f80(x98291)),x98293),f77(x98291)),f857(f857(f110(f927(x98292,a915)),x98294),x98295)))
% 15.02/14.81 [9939]~P72(x99392)+E(f857(f857(f8(x99391,x99392),x99393),x99394),f857(f857(f8(x99391,x99392),x99393),x99395))+~P106(f857(f60(x99391),x99395))+~P106(f857(f857(f234(f927(x99391,a915)),x99394),x99395))+P106(f857(f857(f328(x99391),f908(x99393,x99394,x99395,x99391,x99392)),f857(f857(f3(f927(x99391,a915)),x99395),x99394)))
% 15.02/14.81 [9940]~P72(x99402)+E(f857(f857(f8(x99401,x99402),x99403),x99404),f857(f857(f8(x99401,x99402),x99403),x99405))+~P106(f857(f60(x99401),x99405))+~P106(f857(f857(f234(f927(x99401,a915)),x99404),x99405))+P106(f857(f857(f328(x99401),f910(x99403,x99404,x99405,x99401,x99402)),f857(f857(f3(f927(x99401,a915)),x99405),x99404)))
% 15.02/14.81 [9941]~P77(x99412)+E(f857(f857(f11(x99411,x99412),x99413),x99414),f857(f857(f11(x99411,x99412),x99413),x99415))+~P106(f857(f60(x99411),x99415))+~P106(f857(f857(f234(f927(x99411,a915)),x99414),x99415))+P106(f857(f857(f328(x99411),f871(x99413,x99414,x99415,x99411,x99412)),f857(f857(f3(f927(x99411,a915)),x99415),x99414)))
% 15.02/14.81 [9942]~P77(x99422)+E(f857(f857(f11(x99421,x99422),x99423),x99424),f857(f857(f11(x99421,x99422),x99423),x99425))+~P106(f857(f60(x99421),x99425))+~P106(f857(f857(f234(f927(x99421,a915)),x99424),x99425))+P106(f857(f857(f328(x99421),f873(x99423,x99424,x99425,x99421,x99422)),f857(f857(f3(f927(x99421,a915)),x99425),x99424)))
% 15.02/14.81 [9960]~P72(x99601)+~P106(f857(f60(x99602),x99604))+~P106(f857(f60(x99602),x99605))+E(f857(f857(f79(x99601),f857(f857(f8(x99602,x99601),x99603),x99604)),f857(f857(f8(x99602,x99601),x99603),x99605)),f857(f857(f8(x99602,x99601),x99603),f857(f857(f110(f927(x99602,a915)),x99604),x99605)))+P106(f857(f857(f328(x99602),f901(x99603,x99605,x99604,x99602,x99601)),f857(f857(f101(f927(x99602,a915)),x99604),x99605)))
% 15.02/14.81 [9961]~P72(x99611)+~P106(f857(f60(x99612),x99614))+~P106(f857(f60(x99612),x99615))+E(f857(f857(f79(x99611),f857(f857(f8(x99612,x99611),x99613),x99614)),f857(f857(f8(x99612,x99611),x99613),x99615)),f857(f857(f8(x99612,x99611),x99613),f857(f857(f110(f927(x99612,a915)),x99614),x99615)))+P106(f857(f857(f328(x99612),f902(x99613,x99615,x99614,x99612,x99611)),f857(f857(f101(f927(x99612,a915)),x99614),x99615)))
% 15.02/14.81 [9962]~P77(x99621)+~P106(f857(f60(x99622),x99624))+~P106(f857(f60(x99622),x99625))+E(f857(f857(f80(x99621),f857(f857(f11(x99622,x99621),x99623),x99624)),f857(f857(f11(x99622,x99621),x99623),x99625)),f857(f857(f11(x99622,x99621),x99623),f857(f857(f110(f927(x99622,a915)),x99624),x99625)))+P106(f857(f857(f328(x99622),f866(x99623,x99625,x99624,x99622,x99621)),f857(f857(f101(f927(x99622,a915)),x99624),x99625)))
% 15.02/14.81 [9963]~P77(x99631)+~P106(f857(f60(x99632),x99634))+~P106(f857(f60(x99632),x99635))+E(f857(f857(f80(x99631),f857(f857(f11(x99632,x99631),x99633),x99634)),f857(f857(f11(x99632,x99631),x99633),x99635)),f857(f857(f11(x99632,x99631),x99633),f857(f857(f110(f927(x99632,a915)),x99634),x99635)))+P106(f857(f857(f328(x99632),f872(x99633,x99635,x99634,x99632,x99631)),f857(f857(f101(f927(x99632,a915)),x99634),x99635)))
% 15.02/14.81 [9969]~P89(x99695)+~P106(f857(f60(x99691),x99694))+P106(f857(f857(f234(x99695),f857(f857(f8(x99691,x99695),x99692),x99693)),f857(f857(f8(x99691,x99695),x99692),x99694)))+~P106(f857(f857(f234(f927(x99691,a915)),x99693),x99694))+P106(f857(f857(f328(x99691),f900(x99692,x99693,x99694,x99691,x99695)),f857(f857(f3(f927(x99691,a915)),x99694),x99693)))
% 15.02/14.81 [10013]~P77(x100131)+~P106(f857(f60(x100132),x100134))+~P106(f857(f60(x100132),x100135))+E(f857(f857(f80(x100131),f857(f857(f857(f64(x100131,x100132,f80(x100131)),x100133),f77(x100131)),x100134)),f857(f857(f857(f64(x100131,x100132,f80(x100131)),x100133),f77(x100131)),x100135)),f857(f857(f857(f64(x100131,x100132,f80(x100131)),x100133),f77(x100131)),f857(f857(f110(f927(x100132,a915)),x100134),x100135)))+P106(f857(f857(f328(x100132),f877(x100133,x100135,x100134,x100132,x100131)),f857(f857(f101(f927(x100132,a915)),x100134),x100135)))
% 15.02/14.81 [8969]~P19(x89691,x89694,x89695)+~P106(f857(f60(x89691),x89692))+E(f857(f857(f3(f927(x89691,a915)),x89692),f857(f857(f308(x89691),x89693),f189(f927(x89691,a915)))),f189(f927(x89691,a915)))+~P106(f857(f857(f328(x89691),x89693),x89692))+E(f857(f857(x89694,x89693),f857(x89695,f857(f857(f3(f927(x89691,a915)),x89692),f857(f857(f308(x89691),x89693),f189(f927(x89691,a915)))))),f857(x89695,x89692))
% 15.02/14.81 [9047]~P19(x90471,x90474,x90475)+~P106(f857(f60(x90471),x90473))+~P106(f857(f60(x90471),x90472))+E(f857(f857(f101(f927(x90471,a915)),x90472),x90473),f189(f927(x90471,a915)))+E(f857(f857(x90474,f857(x90475,f857(f857(f110(f927(x90471,a915)),x90472),x90473))),f857(x90475,f857(f857(f101(f927(x90471,a915)),x90472),x90473))),f857(f857(x90474,f857(x90475,x90472)),f857(x90475,x90473)))
% 15.02/14.81 [9613]~P106(f857(f857(f234(a1),x96134),f2(a1)))+~P106(f857(f857(f235(a1),x96133),x96135))+P106(f857(f857(f234(a1),x96131),x96132))+~P106(f857(f857(f235(a1),x96133),x96134))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),f857(f857(f80(a1),x96133),x96132)),x96135)),f857(f857(f79(a1),f857(f857(f80(a1),x96133),x96131)),x96134)))
% 15.02/14.81 [9615]~P106(f857(f857(f234(a1),f2(a1)),x96155))+P106(f857(f857(f234(a1),x96151),x96152))+~P106(f857(f857(f235(a1),x96153),x96154))+~P106(f857(f857(f235(a1),x96155),x96154))+~P106(f857(f857(f234(a1),f857(f857(f79(a1),f857(f857(f80(a1),x96154),x96151)),x96155)),f857(f857(f79(a1),f857(f857(f80(a1),x96154),x96152)),x96153)))
% 15.02/14.81 [9738]~P66(x97385)+E(f857(x97381,f909(x97381,x97382,x97383,x97384,x97385)),f2(x97385))+~P106(f857(f60(x97384),x97383))+~P106(f857(f60(x97384),x97382))+E(f857(f857(f290(x97385),f857(f857(f80(x97385),f857(f857(f11(x97384,x97385),x97381),x97383)),f857(f857(f11(x97384,x97385),x97381),x97382))),f857(f857(f11(x97384,x97385),x97381),f857(f857(f101(f927(x97384,a915)),x97383),x97382))),f857(f857(f11(x97384,x97385),x97381),f857(f857(f110(f927(x97384,a915)),x97383),x97382)))
% 15.02/14.81 [10005]~P66(x100051)+~P106(f857(f60(x100052),x100054))+~P106(f857(f60(x100052),x100055))+E(f857(f857(f290(x100051),f857(f857(f80(x100051),f857(f857(f11(x100052,x100051),x100053),x100054)),f857(f857(f11(x100052,x100051),x100053),x100055))),f857(f857(f11(x100052,x100051),x100053),f857(f857(f101(f927(x100052,a915)),x100054),x100055))),f857(f857(f11(x100052,x100051),x100053),f857(f857(f110(f927(x100052,a915)),x100054),x100055)))+P106(f857(f857(f328(x100052),f909(x100053,x100055,x100054,x100052,x100051)),f857(f857(f101(f927(x100052,a915)),x100054),x100055)))
% 15.02/14.81 [9320]E(f857(f857(f134(x93201),x93202),x93203),f857(f857(f134(x93201),x93204),x93205))+~E(f857(f857(f175(x93201),f857(f190(f920(x93201)),x93204)),x93202),x93204)+~E(f857(f857(f175(x93201),f857(f190(f920(x93201)),x93202)),x93204),x93202)+~E(x93205,f857(f857(f134(x93201),f857(f857(f138(x93201),f857(f190(f920(x93201)),x93204)),x93202)),x93203))+~E(f857(f857(f134(x93201),f857(f857(f138(x93201),f857(f190(f920(x93201)),x93202)),x93204)),x93205),x93203)
% 15.02/14.81 [9736]~P109(x97362)+E(f857(f857(f148(x97361,x97362,x97363),x97364),f170(x97361,x97364,x97365)),x97365)+~P14(x97362,f857(f857(f154(x97361,x97362),x97363),x97365))+~P106(f857(f857(f328(x97361),x97364),f857(f172(x97361),x97365)))+~E(f857(f141(x97361),f857(f136(x97361,f857(f857(f10(x97362,a915,x97361),f857(a324,f857(x97363,x97364))),x97363)),x97365)),x97364)
% 15.02/14.81 [10070]~P70(x100701)+~P106(f857(f65(x100701,x100701,f80(x100701),x100702,x100703),x100705))+~P106(f857(f857(f328(x100701),x100704),x100703))+P106(f857(f857(f328(x100701),x100702),x100703))+P106(f857(f65(x100701,x100701,f80(x100701),x100704,f857(f857(f308(x100701),x100702),f857(f857(f3(f927(x100701,a915)),x100703),f857(f857(f308(x100701),x100704),f189(f927(x100701,a915)))))),x100705))
% 15.02/14.81 [7472]E(x74721,x74722)+~P26(x74724,x74725,x74723,x74726)+~E(f857(x74723,x74721),f857(x74723,x74722))+~P106(f857(f857(f328(x74724),x74722),x74726))+~P106(f857(f857(f328(x74724),x74721),x74726))
% 15.02/14.81 [6722]~P140(x67224)+E(x67221,x67222)+~E(x67225,x67226)+E(x67223,f2(x67224))+~E(f857(f857(f79(x67224),x67225),f857(f857(f80(x67224),x67223),x67221)),f857(f857(f79(x67224),x67226),f857(f857(f80(x67224),x67223),x67222)))
% 15.02/14.81 [7754]~P109(x77541)+~P6(x77541)+~P106(f857(f857(f235(x77541),x77542),f857(x77545,x77546)))+~P106(f857(f857(f328(x77543),x77546),x77544))+P106(f857(f857(f235(x77541),x77542),f857(f857(f39(x77543,x77541),x77544),x77545)))
% 15.02/14.81 [10066]~P26(x100662,x100661,x100663,x100664)+~P26(x100661,x100662,x100666,x100665)+P27(x100661,x100662,f825(x100663,x100664,x100665,x100666,x100662,x100661),x100665,x100664)+~P106(f857(f857(f234(f927(x100662,a915)),f857(f309(x100661,x100662,x100666),x100665)),x100664))+~P106(f857(f857(f234(f927(x100661,a915)),f857(f309(x100662,x100661,x100663),x100664)),x100665))
% 15.02/14.81 [8432]~P109(x84321)+~P6(x84321)+~P106(f857(f857(f235(x84321),f857(x84324,x84326)),x84325))+~P106(f857(f857(f328(x84322),x84326),x84323))+P106(f857(f857(f235(x84321),f857(f857(f38(x84322,x84321),x84323),x84324)),x84325))
% 15.02/14.81 [8683]~P20(x86832,x86835,x86836,x86831)+~P106(f857(f60(x86832),x86834))+~P106(f857(f60(x86832),x86833))+~E(f857(f857(f101(f927(x86832,a915)),x86833),x86834),f189(f927(x86832,a915)))+E(f857(x86831,f857(f857(f110(f927(x86832,a915)),x86833),x86834)),f857(f72(x86835,x86835,x86835,f857(x86831,x86833)),f857(x86831,x86834)))
% 15.02/14.81 [10280]~P77(x102801)+~E(f815(x102804,x102805,x102803,x102806,x102802,x102801),f816(x102804,x102805,x102803,x102806,x102802,x102801))+~P106(f857(f60(x102802),x102806))+E(f857(f857(f857(f64(x102801,x102802,f80(x102801)),f857(f857(f10(f927(x102803,a915),x102801,x102802),f857(f857(f64(x102801,x102803,f80(x102801)),x102804),f77(x102801))),x102805)),f77(x102801)),x102806),f857(f857(f857(f64(x102801,x102803,f80(x102801)),x102804),f77(x102801)),f857(f857(f39(x102802,f927(x102803,a915)),x102806),x102805)))+P106(f857(f857(f328(x102802),f814(x102804,x102805,x102803,x102806,x102802,x102801)),x102806))
% 15.02/14.81 [10310]~P77(x103101)+~E(f815(x103104,x103105,x103103,x103106,x103102,x103101),f816(x103104,x103105,x103103,x103106,x103102,x103101))+~P106(f857(f60(x103102),x103106))+E(f857(f857(f857(f64(x103101,x103102,f80(x103101)),f857(f857(f10(f927(x103103,a915),x103101,x103102),f857(f857(f64(x103101,x103103,f80(x103101)),x103104),f77(x103101))),x103105)),f77(x103101)),x103106),f857(f857(f857(f64(x103101,x103103,f80(x103101)),x103104),f77(x103101)),f857(f857(f39(x103102,f927(x103103,a915)),x103106),x103105)))+~P106(f857(f60(x103103),f857(x103105,f814(x103104,x103105,x103103,x103106,x103102,x103101))))
% 15.02/14.81 [10313]~P77(x103131)+~P106(f857(f60(x103132),x103136))+E(f857(f857(f857(f64(x103131,x103132,f80(x103131)),f857(f857(f10(f927(x103133,a915),x103131,x103132),f857(f857(f64(x103131,x103133,f80(x103131)),x103134),f77(x103131))),x103135)),f77(x103131)),x103136),f857(f857(f857(f64(x103131,x103133,f80(x103131)),x103134),f77(x103131)),f857(f857(f39(x103132,f927(x103133,a915)),x103136),x103135)))+P106(f857(f857(f328(x103132),f814(x103134,x103135,x103133,x103136,x103132,x103131)),x103136))+P106(f857(f857(f328(x103132),f816(x103134,x103135,x103133,x103136,x103132,x103131)),x103136))
% 15.02/14.81 [10314]~P77(x103141)+~P106(f857(f60(x103142),x103146))+E(f857(f857(f857(f64(x103141,x103142,f80(x103141)),f857(f857(f10(f927(x103143,a915),x103141,x103142),f857(f857(f64(x103141,x103143,f80(x103141)),x103144),f77(x103141))),x103145)),f77(x103141)),x103146),f857(f857(f857(f64(x103141,x103143,f80(x103141)),x103144),f77(x103141)),f857(f857(f39(x103142,f927(x103143,a915)),x103146),x103145)))+P106(f857(f857(f328(x103142),f814(x103144,x103145,x103143,x103146,x103142,x103141)),x103146))+P106(f857(f857(f328(x103142),f815(x103144,x103145,x103143,x103146,x103142,x103141)),x103146))
% 15.02/14.81 [10334]~P77(x103341)+~P106(f857(f60(x103342),x103346))+E(f857(f857(f857(f64(x103341,x103342,f80(x103341)),f857(f857(f10(f927(x103343,a915),x103341,x103342),f857(f857(f64(x103341,x103343,f80(x103341)),x103344),f77(x103341))),x103345)),f77(x103341)),x103346),f857(f857(f857(f64(x103341,x103343,f80(x103341)),x103344),f77(x103341)),f857(f857(f39(x103342,f927(x103343,a915)),x103346),x103345)))+P106(f857(f857(f328(x103342),f816(x103344,x103345,x103343,x103346,x103342,x103341)),x103346))+~P106(f857(f60(x103343),f857(x103345,f814(x103344,x103345,x103343,x103346,x103342,x103341))))
% 15.02/14.81 [10335]~P77(x103351)+~P106(f857(f60(x103352),x103356))+E(f857(f857(f857(f64(x103351,x103352,f80(x103351)),f857(f857(f10(f927(x103353,a915),x103351,x103352),f857(f857(f64(x103351,x103353,f80(x103351)),x103354),f77(x103351))),x103355)),f77(x103351)),x103356),f857(f857(f857(f64(x103351,x103353,f80(x103351)),x103354),f77(x103351)),f857(f857(f39(x103352,f927(x103353,a915)),x103356),x103355)))+P106(f857(f857(f328(x103352),f815(x103354,x103355,x103353,x103356,x103352,x103351)),x103356))+~P106(f857(f60(x103353),f857(x103355,f814(x103354,x103355,x103353,x103356,x103352,x103351))))
% 15.02/14.81 [10346]~P77(x103461)+~E(f857(f857(f101(f927(x103463,a915)),f857(x103465,f816(x103464,x103465,x103463,x103466,x103462,x103461))),f857(x103465,f815(x103464,x103465,x103463,x103466,x103462,x103461))),f189(f927(x103463,a915)))+~P106(f857(f60(x103462),x103466))+E(f857(f857(f857(f64(x103461,x103462,f80(x103461)),f857(f857(f10(f927(x103463,a915),x103461,x103462),f857(f857(f64(x103461,x103463,f80(x103461)),x103464),f77(x103461))),x103465)),f77(x103461)),x103466),f857(f857(f857(f64(x103461,x103463,f80(x103461)),x103464),f77(x103461)),f857(f857(f39(x103462,f927(x103463,a915)),x103466),x103465)))+P106(f857(f857(f328(x103462),f814(x103464,x103465,x103463,x103466,x103462,x103461)),x103466))
% 15.02/14.81 [10357]~P77(x103571)+~E(f857(f857(f101(f927(x103573,a915)),f857(x103575,f816(x103574,x103575,x103573,x103576,x103572,x103571))),f857(x103575,f815(x103574,x103575,x103573,x103576,x103572,x103571))),f189(f927(x103573,a915)))+~P106(f857(f60(x103572),x103576))+E(f857(f857(f857(f64(x103571,x103572,f80(x103571)),f857(f857(f10(f927(x103573,a915),x103571,x103572),f857(f857(f64(x103571,x103573,f80(x103571)),x103574),f77(x103571))),x103575)),f77(x103571)),x103576),f857(f857(f857(f64(x103571,x103573,f80(x103571)),x103574),f77(x103571)),f857(f857(f39(x103572,f927(x103573,a915)),x103576),x103575)))+~P106(f857(f60(x103573),f857(x103575,f814(x103574,x103575,x103573,x103576,x103572,x103571))))
% 15.02/14.81 [9409]~P123(x94091)+~P119(x94091)+~P106(f857(f857(f286(x94091),x94092),x94095))+~P106(f857(f857(f286(x94091),x94092),f857(f857(f79(x94091),x94093),x94096)))+P106(f857(f857(f286(x94091),x94092),f857(f857(f79(x94091),f857(f857(f3(x94091),x94093),f857(f857(f80(x94091),x94094),x94095))),x94096)))
% 15.02/14.81 [9602]~P123(x96021)+~P119(x96021)+~P106(f857(f857(f286(x96021),x96022),x96025))+P106(f857(f857(f286(x96021),x96022),f857(f857(f79(x96021),x96023),x96024)))+~P106(f857(f857(f286(x96021),x96022),f857(f857(f79(x96021),f857(f857(f3(x96021),x96023),f857(f857(f80(x96021),x96026),x96025))),x96024)))
% 15.02/14.81 [9017]E(x90171,x90172)+~P58(x90174,x90175,x90176,x90173,x90177)+~E(f857(x90173,x90171),f857(x90173,x90172))+~P106(f857(f857(f328(x90175),x90172),x90177))+~P106(f857(f857(f328(x90175),x90171),x90177))
% 15.02/14.81 [10324]~P106(f857(x103242,x103244))+~E(x103245,f857(f136(x103241,x103242),x103247))+E(f857(f136(x103241,x103242),x103243),f857(f857(f151(x103241),x103244),x103245))+~E(x103243,f857(f857(f134(x103241),x103246),f857(f857(f151(x103241),x103244),x103247)))+P106(f857(x103242,f749(x103245,x103244,x103243,x103242,x103241,x103246,x103247)))
% 15.02/14.81 [10325]~P106(f857(x103254,x103252))+~E(x103253,f857(f136(x103251,x103254),x103257))+E(f857(f857(f151(x103251),x103252),x103253),f857(f136(x103251,x103254),x103255))+~E(x103255,f857(f857(f134(x103251),x103256),f857(f857(f151(x103251),x103252),x103257)))+P106(f857(x103254,f748(x103255,x103254,x103253,x103252,x103251,x103256,x103257)))
% 15.02/14.81 [10369]~P106(f857(x103692,x103694))+~E(x103695,f857(f136(x103691,x103692),x103697))+E(f857(f136(x103691,x103692),x103693),f857(f857(f151(x103691),x103694),x103695))+~E(x103693,f857(f857(f134(x103691),x103696),f857(f857(f151(x103691),x103694),x103697)))+P106(f857(f857(f328(x103691),f749(x103695,x103694,x103693,x103692,x103691,x103696,x103697)),f857(f172(x103691),x103696)))
% 15.02/14.81 [10370]~P106(f857(x103704,x103702))+~E(x103703,f857(f136(x103701,x103704),x103707))+E(f857(f857(f151(x103701),x103702),x103703),f857(f136(x103701,x103704),x103705))+~E(x103705,f857(f857(f134(x103701),x103706),f857(f857(f151(x103701),x103702),x103707)))+P106(f857(f857(f328(x103701),f748(x103705,x103704,x103703,x103702,x103701,x103706,x103707)),f857(f172(x103701),x103706)))
% 15.02/14.81 [10374]~P9(x103741,x103747,x103746)+~P12(x103741,f927(x103745,a915),x103746,x103744)+P106(f857(f857(f328(x103741),f488(x103742,x103743,x103744,x103745,x103746,x103747,x103741)),x103747))+~P106(f857(f857(f328(f927(x103741,a915)),x103743),f857(f857(f59(x103741),x103747),x103746)))+P106(f857(f857(f328(f927(x103745,a915)),f857(f857(f39(x103741,f927(x103745,a915)),x103743),x103744)),x103742))
% 15.02/14.81 [10433]~P9(x104332,x104336,x104337)+~P12(x104332,f927(x104331,a915),x104337,x104334)+~P106(f857(f857(f328(f927(x104332,a915)),x104333),f857(f857(f59(x104332),x104336),x104337)))+~P106(f857(f857(f328(f927(x104331,a915)),f857(x104334,f488(x104335,x104333,x104334,x104331,x104337,x104336,x104332))),x104335))+P106(f857(f857(f328(f927(x104331,a915)),f857(f857(f39(x104332,f927(x104331,a915)),x104333),x104334)),x104335))
% 15.02/14.81 [8603]~P77(x86032)+~P26(x86031,x86035,x86038,x86034)+~E(x86033,f857(f72(x86035,x86032,x86031,x86036),x86038))+~E(x86037,f857(f309(x86031,x86035,x86038),x86034))+E(f857(f857(f11(x86031,x86032),x86033),x86034),f857(f857(f11(x86035,x86032),x86036),x86037))
% 15.02/14.81 [10437]~P77(x104372)+~P26(x104375,x104371,x104378,x104377)+~E(f857(x104376,f595(x104373,x104376,x104374,x104377,x104378,x104371,x104375,x104372)),f857(f857(f72(x104371,x104372,x104375,x104373),x104378),f595(x104373,x104376,x104374,x104377,x104378,x104371,x104375,x104372)))+~E(x104374,f857(f309(x104375,x104371,x104378),x104377))+E(f857(f857(f11(x104371,x104372),x104373),x104374),f857(f857(f11(x104375,x104372),x104376),x104377))
% 15.02/14.81 [10440]~P72(x104402)+~P26(x104401,x104405,x104408,x104404)+~E(x104407,f857(f309(x104401,x104405,x104408),x104404))+E(f857(f857(f8(x104401,x104402),x104403),x104404),f857(f857(f8(x104405,x104402),x104406),x104407))+P106(f857(f857(f328(x104401),f609(x104406,x104403,x104407,x104404,x104408,x104405,x104401,x104402)),x104404))
% 15.02/14.81 [10441]~P77(x104412)+~P26(x104411,x104415,x104418,x104414)+~E(x104417,f857(f309(x104411,x104415,x104418),x104414))+E(f857(f857(f11(x104411,x104412),x104413),x104414),f857(f857(f11(x104415,x104412),x104416),x104417))+P106(f857(f857(f328(x104411),f595(x104416,x104413,x104417,x104414,x104418,x104415,x104411,x104412)),x104414))
% 15.02/14.81 [10446]~P72(x104462)+~P26(x104465,x104461,x104468,x104467)+~E(x104464,f857(f309(x104465,x104461,x104468),x104467))+~E(f857(x104466,f609(x104463,x104466,x104464,x104467,x104468,x104461,x104465,x104462)),f857(x104463,f857(x104468,f609(x104463,x104466,x104464,x104467,x104468,x104461,x104465,x104462))))+E(f857(f857(f8(x104461,x104462),x104463),x104464),f857(f857(f8(x104465,x104462),x104466),x104467))
% 15.02/14.81 [9902]~P24(x99026,x99022,x99025,x99027,x99028,x99021)+~P106(f857(f60(x99022),x99024))+~P106(f857(f60(x99022),x99023))+~E(f857(f857(f101(f927(x99022,a915)),x99023),x99024),f189(f927(x99022,a915)))+E(f857(x99021,f857(f857(f110(f927(x99022,a915)),x99023),x99024)),f857(f857(x99025,f857(x99021,x99023)),f857(x99021,x99024)))
% 15.02/14.81 [10307]~P24(x103078,x103072,x103075,x103077,x103076,x103071)+~E(f857(x103076,f636(x103074,x103073,x103071,x103076,x103077,x103075,x103072)),x103077)+~P106(f857(f60(x103072),x103073))+~P106(f857(f60(x103072),x103074))+E(f857(x103071,f857(f857(f110(f927(x103072,a915)),x103073),x103074)),f857(f857(x103075,f857(x103071,x103073)),f857(x103071,x103074)))
% 15.02/14.81 [10381]~P24(x103818,x103812,x103815,x103817,x103816,x103811)+~P106(f857(f60(x103812),x103813))+~P106(f857(f60(x103812),x103814))+E(f857(x103811,f857(f857(f110(f927(x103812,a915)),x103813),x103814)),f857(f857(x103815,f857(x103811,x103813)),f857(x103811,x103814)))+P106(f857(f857(f328(x103812),f636(x103814,x103813,x103811,x103816,x103817,x103815,x103812)),f857(f857(f101(f927(x103812,a915)),x103813),x103814)))
% 15.02/14.81 [10057]~P9(x100574,x100578,x100575)+~P9(x100571,x100579,x100573)+~P13(x100571,x100574,f927(x100572,a915),x100573,x100575,x100577)+P12(x100571,f927(x100572,a915),x100573,f857(f857(f10(f927(x100574,f927(x100572,a915)),f927(x100572,a915),x100571),f857(f39(x100574,f927(x100572,a915)),f857(f284(x100574,x100574,x100575),f857(f857(f308(x100574),x100576),f189(f927(x100574,a915)))))),x100577))+~P106(f857(f857(f328(x100574),x100576),x100578))
% 15.02/14.81 [5618]~P109(x56183)+~P14(x56183,x56181)+E(x56181,f726(x56182,x56183))+~E(f857(f172(x56183),x56181),x56182)+~P106(f857(f60(x56183),x56182))+~P106(f857(f137(x56183),x56181))
% 15.02/14.81 [7463]P16(x74631,x74632)+~E(f857(x74632,f806(x74632)),f857(x74632,f807(x74632)))+~P106(f857(f857(x74632,f806(x74632)),f806(x74632)))+~P106(f857(f857(x74632,f806(x74632)),f807(x74632)))+~P106(f857(f857(x74632,f807(x74632)),f807(x74632)))+~P106(f857(f857(x74632,x74633),x74633))
% 15.02/14.81 [5240]~P133(x52402)+~P134(x52402)+~P145(x52402)+~P116(x52402)+E(x52401,f2(x52402))+~E(f857(f857(f243(x52402),x52401),x52403),f2(x52402))
% 15.02/14.81 [5241]~P133(x52412)+~P134(x52412)+~P145(x52412)+~P116(x52412)+~E(x52411,f2(a919))+~E(f857(f857(f243(x52412),x52413),x52411),f2(x52412))
% 15.02/14.81 [6704]~P89(x67041)+~E(x67043,f2(x67041))+~E(x67042,f2(x67041))+E(f857(f857(f79(x67041),x67042),x67043),f2(x67041))+~P106(f857(f857(f234(x67041),f2(x67041)),x67043))+~P106(f857(f857(f234(x67041),f2(x67041)),x67042))
% 15.02/14.81 [9085]~E(f857(f250(a919,a919),x90853),f2(a919))+~E(x90851,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x90853)),x90852)),f857(f255(a919,a919),x90853)))+P106(f857(f47(x90851,x90852),x90853))+~P106(f857(f857(f234(a919),f857(f255(a919,a919),x90853)),f2(a919)))+P106(f857(f857(f235(a919),f2(a919)),x90852))+~P106(f857(f857(f235(a919),x90852),f857(f255(a919,a919),x90853)))
% 15.02/14.81 [9093]E(x90931,f2(a919))+~E(x90932,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x90933)),x90931)),f857(f255(a919,a919),x90933)))+P106(f857(f47(x90932,x90931),x90933))+~P106(f857(f857(f235(a919),f2(a919)),x90931))+~P106(f857(f857(f234(a919),f2(a919)),f857(f255(a919,a919),x90933)))+~P106(f857(f857(f235(a919),f857(f255(a919,a919),x90933)),x90931))
% 15.02/14.81 [9111]~E(f857(f250(a919,a919),x91113),f2(a919))+~E(x91111,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x91113)),x91112)),f857(f255(a919,a919),x91113)))+P106(f857(f47(x91111,x91112),x91113))+~P106(f857(f857(f235(a919),f2(a919)),x91112))+~P106(f857(f857(f234(a919),f2(a919)),f857(f255(a919,a919),x91113)))+~P106(f857(f857(f235(a919),f857(f255(a919,a919),x91113)),x91112))
% 15.02/14.81 [7088]~P2(x70882)+E(x70881,f189(f927(x70882,a915)))+E(x70883,f189(f927(x70882,a915)))+~P106(f857(f60(x70882),x70881))+~P106(f857(f60(x70882),x70883))+E(f12(x70882,f857(f857(f110(f927(x70882,a915)),x70883),x70881)),f857(f857(f110(x70882),f12(x70882,x70883)),f12(x70882,x70881)))
% 15.02/14.81 [7089]~P2(x70892)+E(x70891,f189(f927(x70892,a915)))+E(x70893,f189(f927(x70892,a915)))+~P106(f857(f60(x70892),x70891))+~P106(f857(f60(x70892),x70893))+E(f13(x70892,f857(f857(f110(f927(x70892,a915)),x70893),x70891)),f857(f857(f101(x70892),f13(x70892,x70893)),f13(x70892,x70891)))
% 15.02/14.81 [7090]~P109(x70902)+E(x70901,f189(f927(x70902,a915)))+E(x70903,f189(f927(x70902,a915)))+~P106(f857(f60(x70902),x70901))+~P106(f857(f60(x70902),x70903))+E(f16(x70902,f857(f857(f110(f927(x70902,a915)),x70903),x70901)),f857(f857(f188(x70902),f16(x70902,x70903)),f16(x70902,x70901)))
% 15.02/14.81 [7091]~P109(x70912)+E(x70911,f189(f927(x70912,a915)))+E(x70913,f189(f927(x70912,a915)))+~P106(f857(f60(x70912),x70911))+~P106(f857(f60(x70912),x70913))+E(f17(x70912,f857(f857(f110(f927(x70912,a915)),x70913),x70911)),f857(f857(f233(x70912),f17(x70912,x70913)),f17(x70912,x70911)))
% 15.02/14.81 [7729]~P97(x77292)+E(x77291,f189(f927(x77292,a915)))+E(x77293,f189(f927(x77292,a915)))+~P106(f857(f60(x77292),x77291))+~P106(f857(f60(x77292),x77293))+E(f857(f857(f80(x77292),f857(f62(x77292,f80(x77292)),x77293)),f857(f62(x77292,f80(x77292)),x77291)),f857(f62(x77292,f80(x77292)),f857(f857(f110(f927(x77292,a915)),x77293),x77291)))
% 15.02/14.81 [7890]~P109(x78902)+E(x78901,f189(f927(x78902,a915)))+E(x78903,f189(f927(x78902,a915)))+~P106(f857(f60(x78902),x78901))+~P106(f857(f60(x78902),x78903))+E(f857(f857(f188(x78902),f14(x78902,f188(x78902),x78903)),f14(x78902,f188(x78902),x78901)),f14(x78902,f188(x78902),f857(f857(f110(f927(x78902,a915)),x78903),x78901)))
% 15.02/14.81 [7891]~P109(x78912)+E(x78911,f189(f927(x78912,a915)))+E(x78913,f189(f927(x78912,a915)))+~P106(f857(f60(x78912),x78911))+~P106(f857(f60(x78912),x78913))+E(f857(f857(f233(x78912),f15(x78912,f233(x78912),x78913)),f15(x78912,f233(x78912),x78911)),f15(x78912,f233(x78912),f857(f857(f110(f927(x78912,a915)),x78913),x78911)))
% 15.02/14.81 [8918]~P106(f857(x89181,x89183))+P106(f857(x89181,f474(x89181,x89182)))+P106(f857(x89181,f466(x89181,x89182)))+~P106(f857(f857(f235(a1),f2(a1)),x89182))+~P106(f857(f857(f328(a1),x89183),f302(a1,f77(a1),x89182)))+P106(f857(x89181,f857(f857(f3(a1),f466(x89181,x89182)),f857(f857(f80(a1),f473(x89181,x89182)),x89182))))
% 15.02/14.81 [9219]~P106(f857(x92191,x92193))+~P106(f857(x92191,f466(x92191,x92192)))+P106(f857(x92191,f474(x92191,x92192)))+~P106(f857(f857(f235(a1),f2(a1)),x92192))+~P106(f857(f857(f328(a1),x92193),f302(a1,f77(a1),x92192)))+~P106(f857(x92191,f857(f857(f3(a1),f466(x92191,x92192)),f857(f857(f80(a1),f473(x92191,x92192)),x92192))))
% 15.02/14.81 [10473]~P99(x104732)+E(x104731,f189(f927(x104732,a915)))+E(x104733,f189(f927(x104732,a915)))+~P106(f857(f60(x104732),x104731))+~P106(f857(f60(x104732),x104733))+E(f13(x104732,f857(f261(x104732),f857(f857(f10(f927(x104732,a915),a915,x104732),f86(x104732)),f857(f857(f10(f927(x104732,f927(x104732,a915)),f927(x104732,a915),x104732),f857(f10(f927(x104732,a915),a915,x104732),f86(x104732))),f857(f857(f9(x104732,f927(x104732,f927(x104732,a915)),f927(x104732,f927(x104732,a915))),f857(f857(f10(f927(x104732,f927(f927(x104732,a915),f927(x104732,a915))),f927(f927(x104732,f927(x104732,a915)),f927(x104732,f927(x104732,a915))),x104732),f20(x104732,f927(x104732,a915),f927(x104732,a915))),f857(f857(f10(f927(x104732,f927(x104732,f927(a915,a915))),f927(x104732,f927(f927(x104732,a915),f927(x104732,a915))),x104732),f857(f10(f927(x104732,f927(a915,a915)),f927(f927(x104732,a915),f927(x104732,a915)),x104732),f20(x104732,a915,a915))),f857(f857(f10(f927(x104732,f927(x104732,a915)),f927(x104732,f927(x104732,f927(a915,a915))),x104732),f857(f10(f927(x104732,a915),f927(x104732,f927(a915,a915)),x104732),f857(f10(a915,f927(a915,a915),x104732),a325))),f857(f857(f9(x104732,f927(x104732,f927(x104732,x104732)),f927(x104732,f927(x104732,a915))),f857(f857(f10(f927(f927(x104732,x104732),f927(x104732,a915)),f927(f927(x104732,f927(x104732,x104732)),f927(x104732,f927(x104732,a915))),x104732),f10(f927(x104732,x104732),f927(x104732,a915),x104732)),f857(f857(f10(f927(x104732,a915),f927(f927(x104732,x104732),f927(x104732,a915)),x104732),f10(x104732,a915,x104732)),a324))),f110(x104732)))))),f857(f857(f9(x104732,f927(x104732,a915),f927(x104732,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x104732,a915),f927(x104732,a915)),x104732),f10(a915,a915,x104732)),f857(f857(f10(a915,f927(a915,a915),x104732),a325),f857(f857(f9(x104732,f927(x104732,a915),a915),f328(x104732)),x104733)))),f857(f857(f9(x104732,f927(x104732,a915),a915),f328(x104732)),x104731))))))),f857(f857(f110(x104732),f13(x104732,x104733)),f13(x104732,x104731)))
% 15.02/14.81 [10474]~P99(x104742)+E(x104741,f189(f927(x104742,a915)))+E(x104743,f189(f927(x104742,a915)))+~P106(f857(f60(x104742),x104741))+~P106(f857(f60(x104742),x104743))+E(f12(x104742,f857(f261(x104742),f857(f857(f10(f927(x104742,a915),a915,x104742),f86(x104742)),f857(f857(f10(f927(x104742,f927(x104742,a915)),f927(x104742,a915),x104742),f857(f10(f927(x104742,a915),a915,x104742),f86(x104742))),f857(f857(f9(x104742,f927(x104742,f927(x104742,a915)),f927(x104742,f927(x104742,a915))),f857(f857(f10(f927(x104742,f927(f927(x104742,a915),f927(x104742,a915))),f927(f927(x104742,f927(x104742,a915)),f927(x104742,f927(x104742,a915))),x104742),f20(x104742,f927(x104742,a915),f927(x104742,a915))),f857(f857(f10(f927(x104742,f927(x104742,f927(a915,a915))),f927(x104742,f927(f927(x104742,a915),f927(x104742,a915))),x104742),f857(f10(f927(x104742,f927(a915,a915)),f927(f927(x104742,a915),f927(x104742,a915)),x104742),f20(x104742,a915,a915))),f857(f857(f10(f927(x104742,f927(x104742,a915)),f927(x104742,f927(x104742,f927(a915,a915))),x104742),f857(f10(f927(x104742,a915),f927(x104742,f927(a915,a915)),x104742),f857(f10(a915,f927(a915,a915),x104742),a325))),f857(f857(f9(x104742,f927(x104742,f927(x104742,x104742)),f927(x104742,f927(x104742,a915))),f857(f857(f10(f927(f927(x104742,x104742),f927(x104742,a915)),f927(f927(x104742,f927(x104742,x104742)),f927(x104742,f927(x104742,a915))),x104742),f10(f927(x104742,x104742),f927(x104742,a915),x104742)),f857(f857(f10(f927(x104742,a915),f927(f927(x104742,x104742),f927(x104742,a915)),x104742),f10(x104742,a915,x104742)),a324))),f101(x104742)))))),f857(f857(f9(x104742,f927(x104742,a915),f927(x104742,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x104742,a915),f927(x104742,a915)),x104742),f10(a915,a915,x104742)),f857(f857(f10(a915,f927(a915,a915),x104742),a325),f857(f857(f9(x104742,f927(x104742,a915),a915),f328(x104742)),x104743)))),f857(f857(f9(x104742,f927(x104742,a915),a915),f328(x104742)),x104741))))))),f857(f857(f101(x104742),f12(x104742,x104743)),f12(x104742,x104741)))
% 15.02/14.81 [10475]~P109(x104752)+E(x104751,f189(f927(x104752,a915)))+E(x104753,f189(f927(x104752,a915)))+~P106(f857(f60(x104752),x104751))+~P106(f857(f60(x104752),x104753))+E(f15(x104752,f233(x104752),f857(f261(x104752),f857(f857(f10(f927(x104752,a915),a915,x104752),f86(x104752)),f857(f857(f10(f927(x104752,f927(x104752,a915)),f927(x104752,a915),x104752),f857(f10(f927(x104752,a915),a915,x104752),f86(x104752))),f857(f857(f9(x104752,f927(x104752,f927(x104752,a915)),f927(x104752,f927(x104752,a915))),f857(f857(f10(f927(x104752,f927(f927(x104752,a915),f927(x104752,a915))),f927(f927(x104752,f927(x104752,a915)),f927(x104752,f927(x104752,a915))),x104752),f20(x104752,f927(x104752,a915),f927(x104752,a915))),f857(f857(f10(f927(x104752,f927(x104752,f927(a915,a915))),f927(x104752,f927(f927(x104752,a915),f927(x104752,a915))),x104752),f857(f10(f927(x104752,f927(a915,a915)),f927(f927(x104752,a915),f927(x104752,a915)),x104752),f20(x104752,a915,a915))),f857(f857(f10(f927(x104752,f927(x104752,a915)),f927(x104752,f927(x104752,f927(a915,a915))),x104752),f857(f10(f927(x104752,a915),f927(x104752,f927(a915,a915)),x104752),f857(f10(a915,f927(a915,a915),x104752),a325))),f857(f857(f9(x104752,f927(x104752,f927(x104752,x104752)),f927(x104752,f927(x104752,a915))),f857(f857(f10(f927(f927(x104752,x104752),f927(x104752,a915)),f927(f927(x104752,f927(x104752,x104752)),f927(x104752,f927(x104752,a915))),x104752),f10(f927(x104752,x104752),f927(x104752,a915),x104752)),f857(f857(f10(f927(x104752,a915),f927(f927(x104752,x104752),f927(x104752,a915)),x104752),f10(x104752,a915,x104752)),a324))),f188(x104752)))))),f857(f857(f9(x104752,f927(x104752,a915),f927(x104752,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x104752,a915),f927(x104752,a915)),x104752),f10(a915,a915,x104752)),f857(f857(f10(a915,f927(a915,a915),x104752),a325),f857(f857(f9(x104752,f927(x104752,a915),a915),f328(x104752)),x104753)))),f857(f857(f9(x104752,f927(x104752,a915),a915),f328(x104752)),x104751))))))),f857(f857(f188(x104752),f15(x104752,f233(x104752),x104753)),f15(x104752,f233(x104752),x104751)))
% 15.02/14.81 [10476]~P109(x104762)+E(x104761,f189(f927(x104762,a915)))+E(x104763,f189(f927(x104762,a915)))+~P106(f857(f60(x104762),x104761))+~P106(f857(f60(x104762),x104763))+E(f14(x104762,f188(x104762),f857(f261(x104762),f857(f857(f10(f927(x104762,a915),a915,x104762),f86(x104762)),f857(f857(f10(f927(x104762,f927(x104762,a915)),f927(x104762,a915),x104762),f857(f10(f927(x104762,a915),a915,x104762),f86(x104762))),f857(f857(f9(x104762,f927(x104762,f927(x104762,a915)),f927(x104762,f927(x104762,a915))),f857(f857(f10(f927(x104762,f927(f927(x104762,a915),f927(x104762,a915))),f927(f927(x104762,f927(x104762,a915)),f927(x104762,f927(x104762,a915))),x104762),f20(x104762,f927(x104762,a915),f927(x104762,a915))),f857(f857(f10(f927(x104762,f927(x104762,f927(a915,a915))),f927(x104762,f927(f927(x104762,a915),f927(x104762,a915))),x104762),f857(f10(f927(x104762,f927(a915,a915)),f927(f927(x104762,a915),f927(x104762,a915)),x104762),f20(x104762,a915,a915))),f857(f857(f10(f927(x104762,f927(x104762,a915)),f927(x104762,f927(x104762,f927(a915,a915))),x104762),f857(f10(f927(x104762,a915),f927(x104762,f927(a915,a915)),x104762),f857(f10(a915,f927(a915,a915),x104762),a325))),f857(f857(f9(x104762,f927(x104762,f927(x104762,x104762)),f927(x104762,f927(x104762,a915))),f857(f857(f10(f927(f927(x104762,x104762),f927(x104762,a915)),f927(f927(x104762,f927(x104762,x104762)),f927(x104762,f927(x104762,a915))),x104762),f10(f927(x104762,x104762),f927(x104762,a915),x104762)),f857(f857(f10(f927(x104762,a915),f927(f927(x104762,x104762),f927(x104762,a915)),x104762),f10(x104762,a915,x104762)),a324))),f233(x104762)))))),f857(f857(f9(x104762,f927(x104762,a915),f927(x104762,a915)),f857(f857(f10(f927(a915,a915),f927(f927(x104762,a915),f927(x104762,a915)),x104762),f10(a915,a915,x104762)),f857(f857(f10(a915,f927(a915,a915),x104762),a325),f857(f857(f9(x104762,f927(x104762,a915),a915),f328(x104762)),x104763)))),f857(f857(f9(x104762,f927(x104762,a915),a915),f328(x104762)),x104761))))))),f857(f857(f233(x104762),f14(x104762,f188(x104762),x104763)),f14(x104762,f188(x104762),x104761)))
% 15.02/14.81 [7419]~P127(x74193)+E(x74191,x74192)+~E(f857(f857(f243(x74193),x74191),x74194),f857(f857(f243(x74193),x74192),x74194))+~P106(f857(f857(f234(x74193),f2(x74193)),x74192))+~P106(f857(f857(f234(x74193),f2(x74193)),x74191))+~P106(f857(f857(f235(a919),f2(a919)),x74194))
% 15.02/14.81 [7690]~P109(x76902)+E(x76901,f189(f927(x76902,a915)))+~P106(f857(f60(x76902),x76901))+~P106(f857(f857(f328(x76902),x76904),x76901))+P106(f857(f857(f234(x76902),x76903),x76904))+~P106(f857(f857(f234(x76902),x76903),f857(f62(x76902,f188(x76902)),x76901)))
% 15.02/14.81 [7691]~P102(x76912)+E(x76911,f189(f927(x76912,a915)))+~P106(f857(f60(x76912),x76911))+~P106(f857(f857(f328(x76912),x76914),x76911))+P106(f857(f857(f234(x76912),x76913),x76914))+~P106(f857(f857(f234(x76912),x76913),f857(f62(x76912,f101(x76912)),x76911)))
% 15.02/14.81 [7692]~P109(x76922)+E(x76921,f189(f927(x76922,a915)))+~P106(f857(f60(x76922),x76921))+~P106(f857(f857(f328(x76922),x76924),x76921))+P106(f857(f857(f235(x76922),x76923),x76924))+~P106(f857(f857(f235(x76922),x76923),f857(f62(x76922,f188(x76922)),x76921)))
% 15.02/14.81 [7596]E(x75961,f2(a1))+E(f857(f857(f35(a1),x75962),x75961),x75963)+~P106(f857(f857(f234(a1),x75964),f2(a1)))+~E(x75962,f857(f857(f79(a1),f857(f857(f80(a1),x75961),x75963)),x75964))+P106(f857(f857(f235(a1),f2(a1)),x75961))+~P106(f857(f857(f235(a1),x75961),x75964))
% 15.02/14.81 [7612]E(f44(a1,x76122,x76121),x76123)+E(x76121,f2(a1))+~P106(f857(f857(f234(a1),x76123),f2(a1)))+~E(x76122,f857(f857(f79(a1),f857(f857(f80(a1),x76121),x76124)),x76123))+P106(f857(f857(f235(a1),f2(a1)),x76121))+~P106(f857(f857(f235(a1),x76121),x76123))
% 15.02/14.81 [7728]E(x77281,f2(a1))+E(f857(f857(f35(a1),x77282),x77281),x77283)+~E(x77282,f857(f857(f79(a1),f857(f857(f80(a1),x77281),x77283)),x77284))+~P106(f857(f857(f234(a1),f2(a1)),x77284))+~P106(f857(f857(f235(a1),f2(a1)),x77281))+~P106(f857(f857(f235(a1),x77284),x77281))
% 15.02/14.81 [7750]E(f44(a1,x77502,x77501),x77503)+E(x77501,f2(a1))+~E(x77502,f857(f857(f79(a1),f857(f857(f80(a1),x77501),x77504)),x77503))+~P106(f857(f857(f234(a1),f2(a1)),x77503))+~P106(f857(f857(f235(a1),f2(a1)),x77501))+~P106(f857(f857(f235(a1),x77503),x77501))
% 15.02/14.81 [7894]~P109(x78942)+E(x78941,f189(f927(x78942,a915)))+~P106(f857(f60(x78942),x78941))+~P106(f857(f857(f328(x78942),x78944),x78941))+~P106(f857(f857(f234(x78942),x78944),x78943))+P106(f857(f857(f234(x78942),f857(f62(x78942,f188(x78942)),x78941)),x78943))
% 15.02/14.81 [7895]~P109(x78952)+E(x78951,f189(f927(x78952,a915)))+~P106(f857(f60(x78952),x78951))+~P106(f857(f857(f235(x78952),x78954),x78953))+~P106(f857(f857(f328(x78952),x78954),x78951))+P106(f857(f857(f235(x78952),f857(f62(x78952,f188(x78952)),x78951)),x78953))
% 15.02/14.81 [8456]~P106(f857(f857(f234(a1),x84564),f2(a1)))+~E(x84561,f857(f857(f79(a1),f857(f857(f80(a1),x84562),x84563)),x84564))+~P106(f857(f857(f234(a1),f2(a1)),x84564))+~P106(f857(f857(f235(a1),x84564),x84562))+~P106(f857(f857(f235(a1),x84562),x84564))+P106(f857(f48(x84561,x84562),f857(f857(f251(a1,a1),x84563),x84564)))
% 15.02/14.81 [8622]~P110(x86221)+P106(f857(f857(f235(f927(x86221,a915)),f302(x86221,x86222,x86223)),f302(x86221,x86224,x86225)))+~P106(f857(f857(f234(x86221),x86224),x86222))+~P106(f857(f857(f234(x86221),x86224),x86225))+~P106(f857(f857(f234(x86221),x86223),x86225))+~P106(f857(f857(f235(x86221),x86223),x86225))
% 15.02/14.81 [8623]~P110(x86231)+P106(f857(f857(f235(f927(x86231,a915)),f302(x86231,x86232,x86233)),f302(x86231,x86234,x86235)))+~P106(f857(f857(f234(x86231),x86233),x86235))+~P106(f857(f857(f234(x86231),x86234),x86235))+~P106(f857(f857(f234(x86231),x86234),x86232))+~P106(f857(f857(f235(x86231),x86234),x86232))
% 15.02/14.81 [9481]P60(x94812,x94813,x94814,x94811)+E(x94811,f189(f927(x94812,a915)))+~P106(f857(f60(x94812),x94814))+~P106(f857(f60(x94812),x94811))+~P106(f857(f857(x94813,f520(x94811,x94814,x94813,x94812)),x94815))+~P106(f857(f857(f328(x94812),x94815),x94811))
% 15.02/14.81 [9482]P60(x94822,x94823,x94824,x94821)+E(x94821,f189(f927(x94822,a915)))+~P106(f857(f60(x94822),x94824))+~P106(f857(f60(x94822),x94821))+~P106(f857(f857(x94823,f798(x94823,x94821,x94824,x94822)),x94825))+~P106(f857(f857(f328(x94822),x94825),x94821))
% 15.02/14.81 [9483]P60(x94832,x94833,x94834,x94831)+E(x94831,f189(f927(x94832,a915)))+~P106(f857(f60(x94832),x94834))+~P106(f857(f60(x94832),x94831))+~P106(f857(f857(x94833,f799(x94831,x94834,x94833,x94832)),x94835))+~P106(f857(f857(f328(x94832),x94835),x94831))
% 15.02/14.81 [9631]~E(x96313,x96315)+~P72(x96311)+~P77(x96311)+~P42(x96313)+E(f857(f857(f8(a1,x96311),x96312),x96313),f857(f857(f8(a1,x96311),x96314),x96315))+P106(f857(f857(f234(a1),f2(a1)),f527(x96312,x96314,x96313,x96315,x96311)))
% 15.02/14.81 [9632]~E(x96323,x96325)+~P72(x96321)+~P77(x96321)+~P42(x96323)+E(f857(f857(f11(a1,x96321),x96322),x96323),f857(f857(f11(a1,x96321),x96324),x96325))+P106(f857(f857(f234(a1),f2(a1)),f528(x96322,x96324,x96323,x96325,x96321)))
% 15.02/14.81 [9812]~E(x98125,x98123)+~P72(x98121)+~P77(x98121)+~P42(x98125)+~E(f857(x98122,f527(x98124,x98122,x98125,x98123,x98121)),f857(x98124,f527(x98124,x98122,x98125,x98123,x98121)))+E(f857(f857(f8(a1,x98121),x98122),x98123),f857(f857(f8(a1,x98121),x98124),x98125))
% 15.02/14.81 [9813]~E(x98135,x98133)+~P72(x98131)+~P77(x98131)+~P42(x98135)+~E(f857(x98132,f528(x98134,x98132,x98135,x98133,x98131)),f857(x98134,f528(x98134,x98132,x98135,x98133,x98131)))+E(f857(f857(f11(a1,x98131),x98132),x98133),f857(f857(f11(a1,x98131),x98134),x98135))
% 15.02/14.81 [9900]~P80(x99003)+E(f857(x99001,x99002),f2(x99003))+~E(f857(f857(f8(x99004,x99003),x99001),x99005),f2(x99003))+~P106(f857(f60(x99004),x99005))+P106(f857(f857(f328(x99004),f418(x99002,x99001,x99005,x99004,x99003)),x99005))+~P106(f857(f857(f328(x99004),x99002),x99005))
% 15.02/14.81 [10028]~P80(x100283)+E(f857(x100281,x100282),f2(x100283))+~E(f857(f857(f8(x100284,x100283),x100281),x100285),f2(x100283))+~P106(f857(f60(x100284),x100285))+~P106(f857(f857(f328(x100284),x100282),x100285))+~P106(f857(f857(f234(x100283),f2(x100283)),f857(x100281,f418(x100282,x100281,x100285,x100284,x100283))))
% 15.02/14.81 [8541]~P138(x85411)+~P106(f857(f857(f234(x85411),x85413),x85415))+~P106(f857(f857(f234(x85411),x85412),x85414))+~P106(f857(f857(f234(x85411),f2(x85411)),x85413))+~P106(f857(f857(f234(x85411),f2(x85411)),x85414))+P106(f857(f857(f234(x85411),f857(f857(f80(x85411),x85412),x85413)),f857(f857(f80(x85411),x85414),x85415)))
% 15.02/14.81 [8542]~P138(x85421)+~P106(f857(f857(f234(x85421),x85423),x85425))+~P106(f857(f857(f234(x85421),x85422),x85424))+~P106(f857(f857(f234(x85421),f2(x85421)),x85423))+~P106(f857(f857(f234(x85421),f2(x85421)),x85422))+P106(f857(f857(f234(x85421),f857(f857(f80(x85421),x85422),x85423)),f857(f857(f80(x85421),x85424),x85425)))
% 15.02/14.81 [8543]~P68(x85431)+~P106(f857(f857(f235(x85431),f2(x85431)),x85435))+~P106(f857(f857(f234(x85431),x85435),x85433))+~P106(f857(f857(f234(x85431),x85432),x85434))+~P106(f857(f857(f234(x85431),f2(x85431)),x85432))+P106(f857(f857(f234(x85431),f857(f857(f290(x85431),x85432),x85433)),f857(f857(f290(x85431),x85434),x85435)))
% 15.02/14.81 [8544]~P135(x85441)+~P106(f857(f857(f234(x85441),x85443),x85445))+~P106(f857(f857(f234(x85441),f2(x85441)),x85442))+~P106(f857(f857(f235(x85441),x85442),x85444))+~P106(f857(f857(f235(x85441),f2(x85441)),x85443))+P106(f857(f857(f235(x85441),f857(f857(f80(x85441),x85442),x85443)),f857(f857(f80(x85441),x85444),x85445)))
% 15.02/14.81 [8545]~P135(x85451)+~P106(f857(f857(f234(x85451),x85452),x85454))+~P106(f857(f857(f234(x85451),f2(x85451)),x85453))+~P106(f857(f857(f235(x85451),x85453),x85455))+~P106(f857(f857(f235(x85451),f2(x85451)),x85452))+P106(f857(f857(f235(x85451),f857(f857(f80(x85451),x85452),x85453)),f857(f857(f80(x85451),x85454),x85455)))
% 15.02/14.81 [8546]~P135(x85461)+~P106(f857(f857(f234(x85461),f2(x85461)),x85463))+~P106(f857(f857(f234(x85461),f2(x85461)),x85462))+~P106(f857(f857(f235(x85461),x85463),x85465))+~P106(f857(f857(f235(x85461),x85462),x85464))+P106(f857(f857(f235(x85461),f857(f857(f80(x85461),x85462),x85463)),f857(f857(f80(x85461),x85464),x85465)))
% 15.02/14.81 [8547]~P135(x85471)+~P106(f857(f857(f234(x85471),f2(x85471)),x85473))+~P106(f857(f857(f235(x85471),x85473),x85475))+~P106(f857(f857(f235(x85471),x85472),x85474))+~P106(f857(f857(f235(x85471),f2(x85471)),x85474))+P106(f857(f857(f235(x85471),f857(f857(f80(x85471),x85472),x85473)),f857(f857(f80(x85471),x85474),x85475)))
% 15.02/14.81 [8548]~P68(x85481)+~P106(f857(f857(f234(x85481),x85485),x85483))+~P106(f857(f857(f234(x85481),f2(x85481)),x85482))+~P106(f857(f857(f235(x85481),x85482),x85484))+~P106(f857(f857(f235(x85481),f2(x85481)),x85485))+P106(f857(f857(f235(x85481),f857(f857(f290(x85481),x85482),x85483)),f857(f857(f290(x85481),x85484),x85485)))
% 15.02/14.81 [8549]~P68(x85491)+~P106(f857(f857(f234(x85491),x85492),x85494))+~P106(f857(f857(f235(x85491),x85495),x85493))+~P106(f857(f857(f235(x85491),f2(x85491)),x85495))+~P106(f857(f857(f235(x85491),f2(x85491)),x85492))+P106(f857(f857(f235(x85491),f857(f857(f290(x85491),x85492),x85493)),f857(f857(f290(x85491),x85494),x85495)))
% 15.02/14.81 [9943]~P72(x99435)+~P84(x99435)+E(x99431,f189(f927(x99432,a915)))+~P106(f857(f60(x99432),x99431))+P106(f857(f857(f328(x99432),f623(x99433,x99434,x99431,x99432,x99435)),x99431))+P106(f857(f857(f235(x99435),f857(f857(f8(x99432,x99435),x99434),x99431)),f857(f857(f8(x99432,x99435),x99433),x99431)))
% 15.02/14.81 [10053]~P72(x100531)+~P86(x100531)+~P106(f857(f60(x100532),x100535))+~P106(f857(f857(f234(x100531),f2(x100531)),f857(x100533,f903(x100533,x100534,x100535,x100532,x100531))))+P106(f857(f857(f234(x100531),f857(f857(f8(x100532,x100531),x100533),x100534)),f857(f857(f8(x100532,x100531),x100533),x100535)))+~P106(f857(f857(f234(f927(x100532,a915)),x100534),x100535))
% 15.02/14.81 [10224]~P72(x102243)+~P84(x102243)+E(x102241,f189(f927(x102242,a915)))+~P106(f857(f60(x102242),x102241))+~P106(f857(f857(f235(x102243),f857(x102244,f623(x102245,x102244,x102241,x102242,x102243))),f857(x102245,f623(x102245,x102244,x102241,x102242,x102243))))+P106(f857(f857(f235(x102243),f857(f857(f8(x102242,x102243),x102244),x102241)),f857(f857(f8(x102242,x102243),x102245),x102241)))
% 15.02/14.81 [7273]~P18(x72732,x72735,x72734)+E(x72731,f189(f927(x72732,a915)))+E(x72733,f189(f927(x72732,a915)))+~P106(f857(f60(x72732),x72731))+~P106(f857(f60(x72732),x72733))+E(f857(x72734,f857(f857(f110(f927(x72732,a915)),x72733),x72731)),f857(f857(x72735,f857(x72734,x72733)),f857(x72734,x72731)))
% 15.02/14.81 [7860]~P149(x78601,x78604,x78603)+P106(f857(x78601,x78602))+~P106(f857(f857(f235(a1),x78604),f2(a1)))+~P106(f857(f857(f234(a1),x78605),f2(a1)))+~E(x78603,f857(f857(f79(a1),f857(f857(f80(a1),x78604),x78602)),x78605))+~P106(f857(f857(f235(a1),x78604),x78605))
% 15.02/14.81 [7861]~P148(x78611,x78614,x78613)+P106(f857(x78611,x78612))+~P106(f857(f857(f235(a1),x78614),f2(a1)))+~P106(f857(f857(f234(a1),x78612),f2(a1)))+~E(x78613,f857(f857(f79(a1),f857(f857(f80(a1),x78614),x78615)),x78612))+~P106(f857(f857(f235(a1),x78614),x78612))
% 15.02/14.81 [7903]~P149(x79031,x79034,x79033)+P106(f857(x79031,x79032))+~E(x79033,f857(f857(f79(a1),f857(f857(f80(a1),x79034),x79032)),x79035))+~P106(f857(f857(f234(a1),f2(a1)),x79035))+~P106(f857(f857(f235(a1),f2(a1)),x79034))+~P106(f857(f857(f235(a1),x79035),x79034))
% 15.02/14.81 [7904]~P148(x79041,x79044,x79043)+P106(f857(x79041,x79042))+~E(x79043,f857(f857(f79(a1),f857(f857(f80(a1),x79044),x79045)),x79042))+~P106(f857(f857(f234(a1),f2(a1)),x79042))+~P106(f857(f857(f235(a1),f2(a1)),x79044))+~P106(f857(f857(f235(a1),x79042),x79044))
% 15.02/14.81 [8831]P106(f857(f857(x88311,x88312),x88313))+~P106(f857(f857(x88311,f857(f857(f35(a1),x88314),x88315)),f44(a1,x88314,x88315)))+~P106(f857(f857(f235(a1),x88315),f2(a1)))+~P106(f857(f857(f234(a1),x88313),f2(a1)))+~E(x88314,f857(f857(f79(a1),f857(f857(f80(a1),x88315),x88312)),x88313))+~P106(f857(f857(f235(a1),x88315),x88313))
% 15.02/14.81 [8840]P106(f857(f857(x88401,x88402),x88403))+~P106(f857(f857(x88401,f857(f857(f35(a1),x88404),x88405)),f44(a1,x88404,x88405)))+~E(x88404,f857(f857(f79(a1),f857(f857(f80(a1),x88405),x88402)),x88403))+~P106(f857(f857(f234(a1),f2(a1)),x88403))+~P106(f857(f857(f235(a1),f2(a1)),x88405))+~P106(f857(f857(f235(a1),x88403),x88405))
% 15.02/14.81 [9101]E(x91011,x91012)+~P57(x91013,x91015,x91014)+~P106(f857(f857(f328(x91013),x91012),x91015))+~P106(f857(f857(f328(x91013),x91011),x91015))+P106(f857(f857(f328(f926(x91013,x91013)),f857(f857(f251(x91013,x91013),x91011),x91012)),x91014))+P106(f857(f857(f328(f926(x91013,x91013)),f857(f857(f251(x91013,x91013),x91012),x91011)),x91014))
% 15.02/14.81 [9970]~P72(x99705)+~P86(x99705)+~P106(f857(f60(x99701),x99704))+P106(f857(f857(f234(x99705),f857(f857(f8(x99701,x99705),x99702),x99703)),f857(f857(f8(x99701,x99705),x99702),x99704)))+~P106(f857(f857(f234(f927(x99701,a915)),x99703),x99704))+P106(f857(f857(f328(x99701),f903(x99702,x99703,x99704,x99701,x99705)),f857(f857(f3(f927(x99701,a915)),x99704),x99703)))
% 15.02/14.81 [10061]E(x100611,f189(f927(x100612,a915)))+~P106(f857(f60(x100612),x100613))+~P106(f857(f60(x100612),x100611))+P106(f857(f857(f328(f926(f927(x100612,a915),f927(x100612,a915))),f857(f857(f251(f927(x100612,a915),f927(x100612,a915)),x100613),x100611)),f317(x100612,x100614)))+~P106(f857(f857(f328(x100612),x100615),x100611))+~P106(f857(f857(f328(f926(x100612,x100612)),f857(f857(f251(x100612,x100612),f400(x100614,x100611,x100613,x100612)),x100615)),x100614))
% 15.02/14.81 [10062]E(x100621,f189(f927(x100622,a915)))+~P106(f857(f60(x100622),x100623))+~P106(f857(f60(x100622),x100621))+P106(f857(f857(f328(f926(f927(x100622,a915),f927(x100622,a915))),f857(f857(f251(f927(x100622,a915),f927(x100622,a915)),x100623),x100621)),f317(x100622,x100624)))+~P106(f857(f857(f328(x100622),x100625),x100621))+~P106(f857(f857(f328(f926(x100622,x100622)),f857(f857(f251(x100622,x100622),f606(x100624,x100621,x100623,x100622)),x100625)),x100624))
% 15.02/14.81 [10228]~P80(x102281)+~E(f857(f857(f8(x102285,x102281),x102282),x102286),x102284)+~P106(f857(f60(x102285),x102286))+P106(f857(f857(f328(x102285),f419(x102283,x102284,x102282,x102286,x102285,x102281)),x102286))+P106(f857(f857(f234(x102281),f857(x102282,x102283)),x102284))+~P106(f857(f857(f328(x102285),x102283),x102286))
% 15.02/14.81 [10277]~P80(x102771)+~E(f857(f857(f8(x102775,x102771),x102772),x102776),x102774)+~P106(f857(f60(x102775),x102776))+~P106(f857(f857(f328(x102775),x102773),x102776))+~P106(f857(f857(f234(x102771),f2(x102771)),f857(x102772,f419(x102773,x102774,x102772,x102776,x102775,x102771))))+P106(f857(f857(f234(x102771),f857(x102772,x102773)),x102774))
% 15.02/14.81 [10419]~E(x104195,x104198)+~E(x104194,x104197)+~P108(x104191)+~P72(x104192)+E(f857(f857(f8(x104191,x104192),x104193),f857(f301(x104191,x104194),x104195)),f857(f857(f8(x104191,x104192),x104196),f857(f301(x104191,x104197),x104198)))+P106(f857(f857(f234(x104191),x104194),f611(x104193,x104196,x104195,x104198,x104194,x104197,x104191,x104192)))
% 15.02/14.81 [10436]~E(x104367,x104364)+~E(x104368,x104365)+~P108(x104361)+~P72(x104362)+~E(f857(x104363,f611(x104366,x104363,x104368,x104365,x104367,x104364,x104361,x104362)),f857(x104366,f611(x104366,x104363,x104368,x104365,x104367,x104364,x104361,x104362)))+E(f857(f857(f8(x104361,x104362),x104363),f857(f301(x104361,x104364),x104365)),f857(f857(f8(x104361,x104362),x104366),f857(f301(x104361,x104367),x104368)))
% 15.02/14.81 [10439]~E(x104394,x104397)+~E(x104395,x104398)+~P108(x104391)+~P72(x104392)+E(f857(f857(f8(x104391,x104392),x104393),f857(f301(x104391,x104394),x104395)),f857(f857(f8(x104391,x104392),x104396),f857(f301(x104391,x104397),x104398)))+P106(f857(f857(f235(x104391),f611(x104393,x104396,x104395,x104398,x104394,x104397,x104391,x104392)),x104395))
% 15.02/14.81 [10068]~P9(x100685,x100689,x100686)+~P9(x100681,x1006810,x100683)+~P13(x100681,x100685,f927(x100682,a915),x100683,x100686,x100688)+~P106(f857(f857(f328(x100685),x100687),x100689))+~P106(f857(f857(f328(x100681),x100684),x1006810))+E(f857(f857(f39(x100681,f927(x100682,a915)),f857(f284(x100681,x100681,x100683),f857(f857(f308(x100681),x100684),f189(f927(x100681,a915))))),f857(f857(f10(f927(x100685,f927(x100682,a915)),f927(x100682,a915),x100681),f857(f39(x100685,f927(x100682,a915)),f857(f284(x100685,x100685,x100686),f857(f857(f308(x100685),x100687),f189(f927(x100685,a915)))))),x100688)),f857(f857(x100688,x100684),x100687))
% 15.02/14.81 [5792]~P109(x57923)+~P14(x57923,x57922)+~P14(x57923,x57921)+E(x57921,x57922)+~E(f857(f172(x57923),x57921),f857(f172(x57923),x57922))+~P106(f857(f137(x57923),x57922))+~P106(f857(f137(x57923),x57921))
% 15.02/14.81 [5119]~P133(x51192)+~P134(x51192)+~P145(x51192)+~P116(x51192)+~E(x51193,f2(x51192))+E(x51191,f2(a919))+E(f857(f857(f243(x51192),x51193),x51191),f2(x51192))
% 15.02/14.81 [9356]E(x93561,f2(a919))+~E(x93562,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x93563)),x93561)),f857(f255(a919,a919),x93563)))+P106(f857(f47(x93562,x93561),x93563))+~P106(f857(f857(f234(a919),f857(f255(a919,a919),x93563)),f2(a919)))+~P106(f857(f857(f234(a919),f2(a919)),f857(f255(a919,a919),x93563)))+~P106(f857(f857(f235(a919),x93561),f857(f255(a919,a919),x93563)))+~P106(f857(f857(f235(a919),f857(f255(a919,a919),x93563)),x93561))
% 15.02/14.81 [9364]~E(f857(f250(a919,a919),x93643),f2(a919))+~E(x93641,f857(f857(f79(a919),f857(f857(f80(a919),f857(f250(a919,a919),x93643)),x93642)),f857(f255(a919,a919),x93643)))+P106(f857(f47(x93641,x93642),x93643))+~P106(f857(f857(f234(a919),f857(f255(a919,a919),x93643)),f2(a919)))+~P106(f857(f857(f234(a919),f2(a919)),f857(f255(a919,a919),x93643)))+~P106(f857(f857(f235(a919),x93642),f857(f255(a919,a919),x93643)))+~P106(f857(f857(f235(a919),f857(f255(a919,a919),x93643)),x93642))
% 15.02/14.81 [8212]~P70(x82122)+E(x82121,f189(f927(x82122,a915)))+E(x82123,f189(f927(x82122,a915)))+~P106(f857(f60(x82122),x82121))+~P106(f857(f60(x82122),x82123))+~E(f857(f857(f101(f927(x82122,a915)),x82123),x82121),f189(f927(x82122,a915)))+E(f857(f857(f80(x82122),f857(f62(x82122,f80(x82122)),x82123)),f857(f62(x82122,f80(x82122)),x82121)),f857(f62(x82122,f80(x82122)),f857(f857(f110(f927(x82122,a915)),x82123),x82121)))
% 15.02/14.81 [7997]E(x79971,f2(a1))+E(f857(f857(f35(a1),x79972),x79971),x79973)+~P106(f857(f857(f234(a1),x79974),f2(a1)))+~E(x79972,f857(f857(f79(a1),f857(f857(f80(a1),x79971),x79973)),x79974))+~P106(f857(f857(f234(a1),f2(a1)),x79974))+~P106(f857(f857(f235(a1),x79974),x79971))+~P106(f857(f857(f235(a1),x79971),x79974))
% 15.02/14.81 [8005]E(f44(a1,x80052,x80051),x80053)+E(x80051,f2(a1))+~P106(f857(f857(f234(a1),x80053),f2(a1)))+~E(x80052,f857(f857(f79(a1),f857(f857(f80(a1),x80051),x80054)),x80053))+~P106(f857(f857(f234(a1),f2(a1)),x80053))+~P106(f857(f857(f235(a1),x80053),x80051))+~P106(f857(f857(f235(a1),x80051),x80053))
% 15.02/14.81 [7055]~P62(x70552)+E(x70551,f2(x70552))+E(x70553,f2(x70552))+~E(f857(f857(f35(x70552),x70554),x70553),f857(f857(f35(x70552),x70555),x70551))+E(f857(f857(f80(x70552),x70554),x70551),f857(f857(f80(x70552),x70553),x70555))+~P106(f857(f857(f286(x70552),x70551),x70555))+~P106(f857(f857(f286(x70552),x70553),x70554))
% 15.02/14.81 [7056]~P62(x70562)+E(x70561,f2(x70562))+E(x70563,f2(x70562))+~E(f857(f857(f80(x70562),x70564),x70563),f857(f857(f80(x70562),x70561),x70565))+E(f857(f857(f35(x70562),x70564),x70561),f857(f857(f35(x70562),x70565),x70563))+~P106(f857(f857(f286(x70562),x70561),x70564))+~P106(f857(f857(f286(x70562),x70563),x70565))
% 15.02/14.81 [7912]~P19(x79122,x79125,x79124)+E(x79121,f189(f927(x79122,a915)))+E(x79123,f189(f927(x79122,a915)))+~P106(f857(f60(x79122),x79121))+~P106(f857(f60(x79122),x79123))+~E(f857(f857(f101(f927(x79122,a915)),x79123),x79121),f189(f927(x79122,a915)))+E(f857(x79124,f857(f857(f110(f927(x79122,a915)),x79123),x79121)),f857(f857(x79125,f857(x79124,x79123)),f857(x79124,x79121)))
% 15.02/14.81 [9604]~P26(x96043,x96041,x96045,x96044)+~P26(x96041,x96043,x96046,x96042)+E(f857(f34(x96041),x96042),f857(f34(x96043),x96044))+~P106(f857(f60(x96043),x96044))+~P106(f857(f60(x96041),x96042))+~P106(f857(f857(f234(f927(x96043,a915)),f857(f309(x96041,x96043,x96046),x96042)),x96044))+~P106(f857(f857(f234(f927(x96041,a915)),f857(f309(x96043,x96041,x96045),x96044)),x96042))
% 15.02/14.81 [9546]~P106(f857(f857(f235(a1),f857(f857(f79(a1),f857(f857(f80(a1),x95465),x95461)),x95466)),f2(a1)))+~E(f857(f857(f79(a1),f857(f857(f80(a1),x95463),x95462)),x95464),f857(f857(f79(a1),f857(f857(f80(a1),x95465),x95461)),x95466))+~P106(f857(f857(f234(a1),f2(a1)),x95466))+~P106(f857(f857(f235(a1),f2(a1)),x95465))+~P106(f857(f857(f234(a1),x95465),x95463))+~P106(f857(f857(f235(a1),x95464),x95463))+P106(f857(f857(f234(a1),x95461),x95462))
% 15.02/14.81 [9307]~E(f857(f857(f79(a1),f857(f857(f80(a1),x93073),x93071)),x93074),f857(f857(f79(a1),f857(f857(f80(a1),x93075),x93072)),x93076))+~P106(f857(f857(f234(a1),f2(a1)),x93074))+~P106(f857(f857(f235(a1),f2(a1)),x93075))+~P106(f857(f857(f234(a1),x93075),x93073))+~P106(f857(f857(f235(a1),x93076),x93075))+P106(f857(f857(f234(a1),x93071),x93072))+~P106(f857(f857(f234(a1),f2(a1)),f857(f857(f79(a1),f857(f857(f80(a1),x93075),x93072)),x93076)))
% 15.02/14.81 [9486]~P132(x94861)+~E(f857(f857(f79(x94861),x94862),x94864),f77(x94861))+~P106(f857(f857(f234(x94861),x94865),x94866))+~P106(f857(f857(f234(x94861),x94863),x94866))+~P106(f857(f857(f234(x94861),f2(x94861)),x94864))+~P106(f857(f857(f234(x94861),f2(x94861)),x94862))+P106(f857(f857(f234(x94861),f857(f857(f79(x94861),f857(f857(f80(x94861),x94862),x94863)),f857(f857(f80(x94861),x94864),x94865))),x94866))
% 15.02/14.81 [9487]~P130(x94871)+~E(f857(f857(f79(x94871),x94872),x94874),f77(x94871))+~P106(f857(f857(f234(x94871),f2(x94871)),x94874))+~P106(f857(f857(f234(x94871),f2(x94871)),x94872))+~P106(f857(f857(f235(x94871),x94875),x94876))+~P106(f857(f857(f235(x94871),x94873),x94876))+P106(f857(f857(f235(x94871),f857(f857(f79(x94871),f857(f857(f80(x94871),x94872),x94873)),f857(f857(f80(x94871),x94874),x94875))),x94876))
% 15.02/14.81 [10327]~P9(x103277,x103276,x103275)+E(x103271,x103272)+~P12(x103277,f927(x103274,a915),x103275,x103273)+E(f857(x103273,f485(x103271,x103272,x103273,x103274,x103275,x103276,x103277)),f857(x103273,f486(x103271,x103272,x103273,x103274,x103275,x103276,x103277)))+~E(f857(f857(f39(x103277,f927(x103274,a915)),x103271),x103273),f857(f857(f39(x103277,f927(x103274,a915)),x103272),x103273))+~P106(f857(f857(f328(f927(x103277,a915)),x103272),f857(f857(f59(x103277),x103276),x103275)))+~P106(f857(f857(f328(f927(x103277,a915)),x103271),f857(f857(f59(x103277),x103276),x103275)))
% 15.02/14.81 [10372]~P9(x103723,x103727,x103726)+E(x103721,x103722)+~P12(x103723,f927(x103725,a915),x103726,x103724)+~E(f857(f857(f39(x103723,f927(x103725,a915)),x103721),x103724),f857(f857(f39(x103723,f927(x103725,a915)),x103722),x103724))+P106(f857(f857(f328(x103723),f486(x103721,x103722,x103724,x103725,x103726,x103727,x103723)),x103727))+~P106(f857(f857(f328(f927(x103723,a915)),x103722),f857(f857(f59(x103723),x103727),x103726)))+~P106(f857(f857(f328(f927(x103723,a915)),x103721),f857(f857(f59(x103723),x103727),x103726)))
% 15.02/14.81 [10373]~P9(x103733,x103737,x103736)+E(x103731,x103732)+~P12(x103733,f927(x103735,a915),x103736,x103734)+~E(f857(f857(f39(x103733,f927(x103735,a915)),x103731),x103734),f857(f857(f39(x103733,f927(x103735,a915)),x103732),x103734))+P106(f857(f857(f328(x103733),f485(x103731,x103732,x103734,x103735,x103736,x103737,x103733)),x103737))+~P106(f857(f857(f328(f927(x103733,a915)),x103732),f857(f857(f59(x103733),x103737),x103736)))+~P106(f857(f857(f328(f927(x103733,a915)),x103731),f857(f857(f59(x103733),x103737),x103736)))
% 15.02/14.81 [10455]E(x104551,x104552)+~P9(x104553,x104556,x104557)+~P12(x104553,f927(x104554,a915),x104557,x104555)+~E(f857(f857(f39(x104553,f927(x104554,a915)),x104551),x104555),f857(f857(f39(x104553,f927(x104554,a915)),x104552),x104555))+~P106(f857(f857(f328(f926(x104553,x104553)),f857(f857(f251(x104553,x104553),f486(x104551,x104552,x104555,x104554,x104557,x104556,x104553)),f485(x104551,x104552,x104555,x104554,x104557,x104556,x104553))),x104557))+~P106(f857(f857(f328(f927(x104553,a915)),x104552),f857(f857(f59(x104553),x104556),x104557)))+~P106(f857(f857(f328(f927(x104553,a915)),x104551),f857(f857(f59(x104553),x104556),x104557)))
% 15.02/14.81 [9306]~P9(x93061,x93067,x93064)+~E(x93065,x93066)+~P106(f857(f857(f328(x93061),x93063),x93066))+~P106(f857(f857(f328(x93061),x93062),x93065))+~P106(f857(f857(f328(f927(x93061,a915)),x93066),f857(f857(f59(x93061),x93067),x93064)))+~P106(f857(f857(f328(f927(x93061,a915)),x93065),f857(f857(f59(x93061),x93067),x93064)))+P106(f857(f857(f328(f926(x93061,x93061)),f857(f857(f251(x93061,x93061),x93062),x93063)),x93064))
% 15.02/14.81 [9443]E(x94431,x94432)+~P9(x94433,x94434,x94435)+~P106(f857(f857(f328(x94433),x94436),x94432))+~P106(f857(f857(f328(x94433),x94437),x94431))+~P106(f857(f857(f328(f927(x94433,a915)),x94432),f857(f857(f59(x94433),x94434),x94435)))+~P106(f857(f857(f328(f927(x94433,a915)),x94431),f857(f857(f59(x94433),x94434),x94435)))+~P106(f857(f857(f328(f926(x94433,x94433)),f857(f857(f251(x94433,x94433),x94437),x94436)),x94435))
% 15.02/14.81 [10482]~P9(x104829,x104828,x104827)+~P9(x104821,x1048211,x1048210)+~P13(x104821,x104829,f927(x104826,a915),x1048210,x104827,x104825)+P106(f857(f857(f328(x104821),f487(x104822,x104823,x104824,x104825,x104826,x104827,x104828,x104829,x1048210,x1048211,x104821)),x1048211))+~P106(f857(f857(f328(f927(x104829,a915)),x104823),f857(f857(f59(x104829),x104828),x104827)))+~P106(f857(f857(f328(f927(x104821,a915)),x104824),f857(f857(f59(x104821),x1048211),x1048210)))+P106(f857(f857(f328(f927(x104826,a915)),f857(f857(f39(x104821,f927(x104826,a915)),x104824),f857(f857(f10(f927(x104829,f927(x104826,a915)),f927(x104826,a915),x104821),f857(f39(x104829,f927(x104826,a915)),x104823)),x104825))),x104822))
% 15.02/14.81 [10483]~P9(x1048311,x1048310,x104839)+~P9(x104831,x104838,x104837)+~P13(x1048311,x104831,f927(x104836,a915),x104839,x104837,x104835)+P106(f857(f857(f328(x104831),f489(x104832,x104833,x104834,x104835,x104836,x104837,x104838,x104831,x104839,x1048310,x1048311)),x104838))+~P106(f857(f857(f328(f927(x1048311,a915)),x104834),f857(f857(f59(x1048311),x1048310),x104839)))+~P106(f857(f857(f328(f927(x104831,a915)),x104833),f857(f857(f59(x104831),x104838),x104837)))+P106(f857(f857(f328(f927(x104836,a915)),f857(f857(f39(x1048311,f927(x104836,a915)),x104834),f857(f857(f10(f927(x104831,f927(x104836,a915)),f927(x104836,a915),x1048311),f857(f39(x104831,f927(x104836,a915)),x104833)),x104835))),x104832))
% 15.02/14.81 [10486]~P9(x104862,x104868,x104869)+~P9(x104864,x1048610,x1048611)+~P13(x104862,x104864,f927(x104861,a915),x104869,x1048611,x104866)+~P106(f857(f857(f328(f927(x104862,a915)),x104863),f857(f857(f59(x104862),x104868),x104869)))+~P106(f857(f857(f328(f927(x104864,a915)),x104865),f857(f857(f59(x104864),x1048610),x1048611)))+~P106(f857(f857(f328(f927(x104861,a915)),f857(f857(x104866,f487(x104867,x104865,x104863,x104866,x104861,x1048611,x1048610,x104864,x104869,x104868,x104862)),f489(x104867,x104865,x104863,x104866,x104861,x1048611,x1048610,x104864,x104869,x104868,x104862))),x104867))+P106(f857(f857(f328(f927(x104861,a915)),f857(f857(f39(x104862,f927(x104861,a915)),x104863),f857(f857(f10(f927(x104864,f927(x104861,a915)),f927(x104861,a915),x104862),f857(f39(x104864,f927(x104861,a915)),x104865)),x104866))),x104867))
% 15.02/14.81 [9342]E(x93421,x93422)+~P109(x93424)+~P26(x93423,x93424,x93425,f857(f857(f110(f927(x93423,a915)),f857(f172(x93423),x93421)),f857(f172(x93423),x93422)))+~E(f857(f172(x93423),x93421),f857(f172(x93423),x93422))+~P14(x93424,f857(f857(f154(x93423,x93424),x93425),x93422))+~P14(x93424,f857(f857(f154(x93423,x93424),x93425),x93421))+~P106(f857(f137(x93424),f857(f857(f154(x93423,x93424),x93425),x93422)))+~P106(f857(f137(x93424),f857(f857(f154(x93423,x93424),x93425),x93421)))
% 15.02/14.81 %EqnAxiom
% 15.02/14.81 [1]E(x11,x11)
% 15.02/14.81 [2]E(x22,x21)+~E(x21,x22)
% 15.02/14.81 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 15.02/14.81 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 15.02/14.81 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 15.02/14.81 [6]~E(x61,x62)+E(f100(x61),f100(x62))
% 15.02/14.81 [7]~E(x71,x72)+E(f101(x71),f101(x72))
% 15.02/14.81 [8]~E(x81,x82)+E(f188(x81),f188(x82))
% 15.02/14.81 [9]~E(x91,x92)+E(f189(x91),f189(x92))
% 15.02/14.81 [10]~E(x101,x102)+E(f857(x101,x103),f857(x102,x103))
% 15.02/14.81 [11]~E(x111,x112)+E(f857(x113,x111),f857(x113,x112))
% 15.02/14.81 [12]~E(x121,x122)+E(f28(x121),f28(x122))
% 15.02/14.81 [13]~E(x131,x132)+E(f927(x131,x133),f927(x132,x133))
% 15.02/14.81 [14]~E(x141,x142)+E(f927(x143,x141),f927(x143,x142))
% 15.02/14.81 [15]~E(x151,x152)+E(f110(x151),f110(x152))
% 15.02/14.81 [16]~E(x161,x162)+E(f233(x161),f233(x162))
% 15.02/14.81 [17]~E(x171,x172)+E(f102(x171),f102(x172))
% 15.02/14.81 [18]~E(x181,x182)+E(f31(x181),f31(x182))
% 15.02/14.81 [19]~E(x191,x192)+E(f83(x191),f83(x192))
% 15.02/14.81 [20]~E(x201,x202)+E(f103(x201),f103(x202))
% 15.02/14.81 [21]~E(x211,x212)+E(f234(x211),f234(x212))
% 15.02/14.81 [22]~E(x221,x222)+E(f489(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f489(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 15.02/14.81 [23]~E(x231,x232)+E(f489(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f489(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 15.02/14.81 [24]~E(x241,x242)+E(f489(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f489(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 15.02/14.81 [25]~E(x251,x252)+E(f489(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f489(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512))
% 15.02/14.81 [26]~E(x261,x262)+E(f489(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f489(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612))
% 15.02/14.81 [27]~E(x271,x272)+E(f489(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f489(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712))
% 15.02/14.81 [28]~E(x281,x282)+E(f489(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f489(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812))
% 15.02/14.81 [29]~E(x291,x292)+E(f489(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f489(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912))
% 15.02/14.81 [30]~E(x301,x302)+E(f489(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f489(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012))
% 15.02/14.81 [31]~E(x311,x312)+E(f489(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f489(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112))
% 15.02/14.81 [32]~E(x321,x322)+E(f489(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f489(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322))
% 15.02/14.81 [33]~E(x331,x332)+E(f77(x331),f77(x332))
% 15.02/14.81 [34]~E(x341,x342)+E(f79(x341),f79(x342))
% 15.02/14.81 [35]~E(x351,x352)+E(f487(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f487(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 15.02/14.81 [36]~E(x361,x362)+E(f487(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f487(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 15.02/14.81 [37]~E(x371,x372)+E(f487(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f487(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 15.02/14.81 [38]~E(x381,x382)+E(f487(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f487(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812))
% 15.02/14.81 [39]~E(x391,x392)+E(f487(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f487(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912))
% 15.02/14.81 [40]~E(x401,x402)+E(f487(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f487(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012))
% 15.02/14.81 [41]~E(x411,x412)+E(f487(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f487(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112))
% 15.02/14.81 [42]~E(x421,x422)+E(f487(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f487(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212))
% 15.02/14.81 [43]~E(x431,x432)+E(f487(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f487(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312))
% 15.02/14.81 [44]~E(x441,x442)+E(f487(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f487(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412))
% 15.02/14.81 [45]~E(x451,x452)+E(f487(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f487(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452))
% 15.02/14.81 [46]~E(x461,x462)+E(f6(x461),f6(x462))
% 15.02/14.81 [47]~E(x471,x472)+E(f328(x471),f328(x472))
% 15.02/14.81 [48]~E(x481,x482)+E(f301(x481,x483),f301(x482,x483))
% 15.02/14.81 [49]~E(x491,x492)+E(f301(x493,x491),f301(x493,x492))
% 15.02/14.81 [50]~E(x501,x502)+E(f111(x501),f111(x502))
% 15.02/14.81 [51]~E(x511,x512)+E(f9(x511,x513,x514),f9(x512,x513,x514))
% 15.02/14.81 [52]~E(x521,x522)+E(f9(x523,x521,x524),f9(x523,x522,x524))
% 15.02/14.81 [53]~E(x531,x532)+E(f9(x533,x534,x531),f9(x533,x534,x532))
% 15.02/14.81 [54]~E(x541,x542)+E(f918(x541),f918(x542))
% 15.02/14.81 [55]~E(x551,x552)+E(f923(x551),f923(x552))
% 15.02/14.81 [56]~E(x561,x562)+E(f920(x561),f920(x562))
% 15.02/14.81 [57]~E(x571,x572)+E(f921(x571),f921(x572))
% 15.02/14.81 [58]~E(x581,x582)+E(f78(x581),f78(x582))
% 15.02/14.81 [59]~E(x591,x592)+E(f383(x591,x593,x594),f383(x592,x593,x594))
% 15.02/14.81 [60]~E(x601,x602)+E(f383(x603,x601,x604),f383(x603,x602,x604))
% 15.02/14.81 [61]~E(x611,x612)+E(f383(x613,x614,x611),f383(x613,x614,x612))
% 15.02/14.81 [62]~E(x621,x622)+E(f190(x621),f190(x622))
% 15.02/14.81 [63]~E(x631,x632)+E(f80(x631),f80(x632))
% 15.02/14.81 [64]~E(x641,x642)+E(f314(x641,x643),f314(x642,x643))
% 15.02/14.81 [65]~E(x651,x652)+E(f314(x653,x651),f314(x653,x652))
% 15.02/14.81 [66]~E(x661,x662)+E(f20(x661,x663,x664),f20(x662,x663,x664))
% 15.02/14.81 [67]~E(x671,x672)+E(f20(x673,x671,x674),f20(x673,x672,x674))
% 15.02/14.81 [68]~E(x681,x682)+E(f20(x683,x684,x681),f20(x683,x684,x682))
% 15.02/14.81 [69]~E(x691,x692)+E(f235(x691),f235(x692))
% 15.02/14.81 [70]~E(x701,x702)+E(f64(x701,x703,x704),f64(x702,x703,x704))
% 15.02/14.81 [71]~E(x711,x712)+E(f64(x713,x711,x714),f64(x713,x712,x714))
% 15.02/14.81 [72]~E(x721,x722)+E(f64(x723,x724,x721),f64(x723,x724,x722))
% 15.02/14.81 [73]~E(x731,x732)+E(f60(x731),f60(x732))
% 15.02/14.81 [74]~E(x741,x742)+E(f134(x741),f134(x742))
% 15.02/14.81 [75]~E(x751,x752)+E(f159(x751,x753),f159(x752,x753))
% 15.02/14.81 [76]~E(x761,x762)+E(f159(x763,x761),f159(x763,x762))
% 15.02/14.81 [77]~E(x771,x772)+E(f144(x771,x773),f144(x772,x773))
% 15.02/14.81 [78]~E(x781,x782)+E(f144(x783,x781),f144(x783,x782))
% 15.02/14.81 [79]~E(x791,x792)+E(f72(x791,x793,x794,x795),f72(x792,x793,x794,x795))
% 15.02/14.81 [80]~E(x801,x802)+E(f72(x803,x801,x804,x805),f72(x803,x802,x804,x805))
% 15.02/14.81 [81]~E(x811,x812)+E(f72(x813,x814,x811,x815),f72(x813,x814,x812,x815))
% 15.02/14.81 [82]~E(x821,x822)+E(f72(x823,x824,x825,x821),f72(x823,x824,x825,x822))
% 15.02/14.81 [83]~E(x831,x832)+E(f837(x831,x833,x834,x835,x836,x837),f837(x832,x833,x834,x835,x836,x837))
% 15.02/14.81 [84]~E(x841,x842)+E(f837(x843,x841,x844,x845,x846,x847),f837(x843,x842,x844,x845,x846,x847))
% 15.02/14.81 [85]~E(x851,x852)+E(f837(x853,x854,x851,x855,x856,x857),f837(x853,x854,x852,x855,x856,x857))
% 15.02/14.81 [86]~E(x861,x862)+E(f837(x863,x864,x865,x861,x866,x867),f837(x863,x864,x865,x862,x866,x867))
% 15.02/14.81 [87]~E(x871,x872)+E(f837(x873,x874,x875,x876,x871,x877),f837(x873,x874,x875,x876,x872,x877))
% 15.02/14.81 [88]~E(x881,x882)+E(f837(x883,x884,x885,x886,x887,x881),f837(x883,x884,x885,x886,x887,x882))
% 15.02/14.81 [89]~E(x891,x892)+E(f253(x891,x893),f253(x892,x893))
% 15.02/14.81 [90]~E(x901,x902)+E(f253(x903,x901),f253(x903,x902))
% 15.02/14.81 [91]~E(x911,x912)+E(f256(x911,x913,x914),f256(x912,x913,x914))
% 15.02/14.81 [92]~E(x921,x922)+E(f256(x923,x921,x924),f256(x923,x922,x924))
% 15.02/14.81 [93]~E(x931,x932)+E(f256(x933,x934,x931),f256(x933,x934,x932))
% 15.02/14.81 [94]~E(x941,x942)+E(f285(x941,x943),f285(x942,x943))
% 15.02/14.81 [95]~E(x951,x952)+E(f285(x953,x951),f285(x953,x952))
% 15.02/14.81 [96]~E(x961,x962)+E(f59(x961),f59(x962))
% 15.02/14.81 [97]~E(x971,x972)+E(f35(x971),f35(x972))
% 15.02/14.81 [98]~E(x981,x982)+E(f380(x981,x983,x984),f380(x982,x983,x984))
% 15.02/14.81 [99]~E(x991,x992)+E(f380(x993,x991,x994),f380(x993,x992,x994))
% 15.02/14.81 [100]~E(x1001,x1002)+E(f380(x1003,x1004,x1001),f380(x1003,x1004,x1002))
% 15.02/14.81 [101]~E(x1011,x1012)+E(f425(x1011,x1013,x1014,x1015),f425(x1012,x1013,x1014,x1015))
% 15.02/14.81 [102]~E(x1021,x1022)+E(f425(x1023,x1021,x1024,x1025),f425(x1023,x1022,x1024,x1025))
% 15.02/14.81 [103]~E(x1031,x1032)+E(f425(x1033,x1034,x1031,x1035),f425(x1033,x1034,x1032,x1035))
% 15.02/14.81 [104]~E(x1041,x1042)+E(f425(x1043,x1044,x1045,x1041),f425(x1043,x1044,x1045,x1042))
% 15.02/14.81 [105]~E(x1051,x1052)+E(f10(x1051,x1053,x1054),f10(x1052,x1053,x1054))
% 15.02/14.81 [106]~E(x1061,x1062)+E(f10(x1063,x1061,x1064),f10(x1063,x1062,x1064))
% 15.02/14.81 [107]~E(x1071,x1072)+E(f10(x1073,x1074,x1071),f10(x1073,x1074,x1072))
% 15.02/14.81 [108]~E(x1081,x1082)+E(f141(x1081),f141(x1082))
% 15.02/14.81 [109]~E(x1091,x1092)+E(f37(x1091,x1093),f37(x1092,x1093))
% 15.02/14.81 [110]~E(x1101,x1102)+E(f37(x1103,x1101),f37(x1103,x1102))
% 15.02/14.81 [111]~E(x1111,x1112)+E(f308(x1111),f308(x1112))
% 15.02/14.81 [112]~E(x1121,x1122)+E(f38(x1121,x1123),f38(x1122,x1123))
% 15.02/14.81 [113]~E(x1131,x1132)+E(f38(x1133,x1131),f38(x1133,x1132))
% 15.02/14.81 [114]~E(x1141,x1142)+E(f650(x1141,x1143),f650(x1142,x1143))
% 15.02/14.81 [115]~E(x1151,x1152)+E(f650(x1153,x1151),f650(x1153,x1152))
% 15.02/14.81 [116]~E(x1161,x1162)+E(f75(x1161),f75(x1162))
% 15.02/14.81 [117]~E(x1171,x1172)+E(f61(x1171,x1173,x1174),f61(x1172,x1173,x1174))
% 15.02/14.81 [118]~E(x1181,x1182)+E(f61(x1183,x1181,x1184),f61(x1183,x1182,x1184))
% 15.02/14.81 [119]~E(x1191,x1192)+E(f61(x1193,x1194,x1191),f61(x1193,x1194,x1192))
% 15.02/14.81 [120]~E(x1201,x1202)+E(f151(x1201),f151(x1202))
% 15.02/14.81 [121]~E(x1211,x1212)+E(f864(x1211,x1213,x1214),f864(x1212,x1213,x1214))
% 15.02/14.81 [122]~E(x1221,x1222)+E(f864(x1223,x1221,x1224),f864(x1223,x1222,x1224))
% 15.02/14.81 [123]~E(x1231,x1232)+E(f864(x1233,x1234,x1231),f864(x1233,x1234,x1232))
% 15.02/14.81 [124]~E(x1241,x1242)+E(f39(x1241,x1243),f39(x1242,x1243))
% 15.02/14.81 [125]~E(x1251,x1252)+E(f39(x1253,x1251),f39(x1253,x1252))
% 15.02/14.81 [126]~E(x1261,x1262)+E(f157(x1261,x1263),f157(x1262,x1263))
% 15.02/14.81 [127]~E(x1271,x1272)+E(f157(x1273,x1271),f157(x1273,x1272))
% 15.02/14.81 [128]~E(x1281,x1282)+E(f372(x1281,x1283,x1284),f372(x1282,x1283,x1284))
% 15.02/14.81 [129]~E(x1291,x1292)+E(f372(x1293,x1291,x1294),f372(x1293,x1292,x1294))
% 15.02/14.81 [130]~E(x1301,x1302)+E(f372(x1303,x1304,x1301),f372(x1303,x1304,x1302))
% 15.02/14.81 [131]~E(x1311,x1312)+E(f603(x1311,x1313,x1314,x1315,x1316,x1317),f603(x1312,x1313,x1314,x1315,x1316,x1317))
% 15.02/14.81 [132]~E(x1321,x1322)+E(f603(x1323,x1321,x1324,x1325,x1326,x1327),f603(x1323,x1322,x1324,x1325,x1326,x1327))
% 15.02/14.81 [133]~E(x1331,x1332)+E(f603(x1333,x1334,x1331,x1335,x1336,x1337),f603(x1333,x1334,x1332,x1335,x1336,x1337))
% 15.02/14.81 [134]~E(x1341,x1342)+E(f603(x1343,x1344,x1345,x1341,x1346,x1347),f603(x1343,x1344,x1345,x1342,x1346,x1347))
% 15.02/14.81 [135]~E(x1351,x1352)+E(f603(x1353,x1354,x1355,x1356,x1351,x1357),f603(x1353,x1354,x1355,x1356,x1352,x1357))
% 15.02/14.81 [136]~E(x1361,x1362)+E(f603(x1363,x1364,x1365,x1366,x1367,x1361),f603(x1363,x1364,x1365,x1366,x1367,x1362))
% 15.02/14.81 [137]~E(x1371,x1372)+E(f177(x1371,x1373,x1374),f177(x1372,x1373,x1374))
% 15.02/14.81 [138]~E(x1381,x1382)+E(f177(x1383,x1381,x1384),f177(x1383,x1382,x1384))
% 15.02/14.81 [139]~E(x1391,x1392)+E(f177(x1393,x1394,x1391),f177(x1393,x1394,x1392))
% 15.02/14.81 [140]~E(x1401,x1402)+E(f309(x1401,x1403,x1404),f309(x1402,x1403,x1404))
% 15.02/14.81 [141]~E(x1411,x1412)+E(f309(x1413,x1411,x1414),f309(x1413,x1412,x1414))
% 15.02/14.81 [142]~E(x1421,x1422)+E(f309(x1423,x1424,x1421),f309(x1423,x1424,x1422))
% 15.02/14.81 [143]~E(x1431,x1432)+E(f115(x1431),f115(x1432))
% 15.02/14.81 [144]~E(x1441,x1442)+E(f164(x1441),f164(x1442))
% 15.02/14.81 [145]~E(x1451,x1452)+E(f251(x1451,x1453),f251(x1452,x1453))
% 15.02/14.81 [146]~E(x1461,x1462)+E(f251(x1463,x1461),f251(x1463,x1462))
% 15.02/14.81 [147]~E(x1471,x1472)+E(f290(x1471),f290(x1472))
% 15.02/14.81 [148]~E(x1481,x1482)+E(f81(x1481,x1483),f81(x1482,x1483))
% 15.02/14.81 [149]~E(x1491,x1492)+E(f81(x1493,x1491),f81(x1493,x1492))
% 15.02/14.81 [150]~E(x1501,x1502)+E(f926(x1501,x1503),f926(x1502,x1503))
% 15.02/14.81 [151]~E(x1511,x1512)+E(f926(x1513,x1511),f926(x1513,x1512))
% 15.02/14.81 [152]~E(x1521,x1522)+E(f863(x1521,x1523,x1524),f863(x1522,x1523,x1524))
% 15.02/14.81 [153]~E(x1531,x1532)+E(f863(x1533,x1531,x1534),f863(x1533,x1532,x1534))
% 15.02/14.81 [154]~E(x1541,x1542)+E(f863(x1543,x1544,x1541),f863(x1543,x1544,x1542))
% 15.02/14.81 [155]~E(x1551,x1552)+E(f862(x1551,x1553,x1554),f862(x1552,x1553,x1554))
% 15.02/14.81 [156]~E(x1561,x1562)+E(f862(x1563,x1561,x1564),f862(x1563,x1562,x1564))
% 15.02/14.81 [157]~E(x1571,x1572)+E(f862(x1573,x1574,x1571),f862(x1573,x1574,x1572))
% 15.02/14.81 [158]~E(x1581,x1582)+E(f105(x1581),f105(x1582))
% 15.02/14.81 [159]~E(x1591,x1592)+E(f107(x1591),f107(x1592))
% 15.02/14.81 [160]~E(x1601,x1602)+E(f327(x1601),f327(x1602))
% 15.02/14.81 [161]~E(x1611,x1612)+E(f397(x1611,x1613,x1614),f397(x1612,x1613,x1614))
% 15.02/14.81 [162]~E(x1621,x1622)+E(f397(x1623,x1621,x1624),f397(x1623,x1622,x1624))
% 15.02/14.81 [163]~E(x1631,x1632)+E(f397(x1633,x1634,x1631),f397(x1633,x1634,x1632))
% 15.02/14.81 [164]~E(x1641,x1642)+E(f579(x1641),f579(x1642))
% 15.02/14.81 [165]~E(x1651,x1652)+E(f307(x1651),f307(x1652))
% 15.02/14.81 [166]~E(x1661,x1662)+E(f136(x1661,x1663),f136(x1662,x1663))
% 15.02/14.81 [167]~E(x1671,x1672)+E(f136(x1673,x1671),f136(x1673,x1672))
% 15.02/14.81 [168]~E(x1681,x1682)+E(f240(x1681,x1683),f240(x1682,x1683))
% 15.02/14.81 [169]~E(x1691,x1692)+E(f240(x1693,x1691),f240(x1693,x1692))
% 15.02/14.81 [170]~E(x1701,x1702)+E(f154(x1701,x1703),f154(x1702,x1703))
% 15.02/14.81 [171]~E(x1711,x1712)+E(f154(x1713,x1711),f154(x1713,x1712))
% 15.02/14.81 [172]~E(x1721,x1722)+E(f289(x1721,x1723,x1724,x1725),f289(x1722,x1723,x1724,x1725))
% 15.02/14.81 [173]~E(x1731,x1732)+E(f289(x1733,x1731,x1734,x1735),f289(x1733,x1732,x1734,x1735))
% 15.02/14.81 [174]~E(x1741,x1742)+E(f289(x1743,x1744,x1741,x1745),f289(x1743,x1744,x1742,x1745))
% 15.02/14.81 [175]~E(x1751,x1752)+E(f289(x1753,x1754,x1755,x1751),f289(x1753,x1754,x1755,x1752))
% 15.02/14.81 [176]~E(x1761,x1762)+E(f44(x1761,x1763,x1764),f44(x1762,x1763,x1764))
% 15.02/14.81 [177]~E(x1771,x1772)+E(f44(x1773,x1771,x1774),f44(x1773,x1772,x1774))
% 15.02/14.81 [178]~E(x1781,x1782)+E(f44(x1783,x1784,x1781),f44(x1783,x1784,x1782))
% 15.02/14.81 [179]~E(x1791,x1792)+E(f287(x1791,x1793),f287(x1792,x1793))
% 15.02/14.81 [180]~E(x1801,x1802)+E(f287(x1803,x1801),f287(x1803,x1802))
% 15.02/14.81 [181]~E(x1811,x1812)+E(f7(x1811),f7(x1812))
% 15.02/14.81 [182]~E(x1821,x1822)+E(f697(x1821,x1823,x1824),f697(x1822,x1823,x1824))
% 15.02/14.81 [183]~E(x1831,x1832)+E(f697(x1833,x1831,x1834),f697(x1833,x1832,x1834))
% 15.02/14.81 [184]~E(x1841,x1842)+E(f697(x1843,x1844,x1841),f697(x1843,x1844,x1842))
% 15.02/14.81 [185]~E(x1851,x1852)+E(f261(x1851),f261(x1852))
% 15.02/14.81 [186]~E(x1861,x1862)+E(f592(x1861,x1863,x1864,x1865,x1866,x1867),f592(x1862,x1863,x1864,x1865,x1866,x1867))
% 15.02/14.81 [187]~E(x1871,x1872)+E(f592(x1873,x1871,x1874,x1875,x1876,x1877),f592(x1873,x1872,x1874,x1875,x1876,x1877))
% 15.02/14.81 [188]~E(x1881,x1882)+E(f592(x1883,x1884,x1881,x1885,x1886,x1887),f592(x1883,x1884,x1882,x1885,x1886,x1887))
% 15.02/14.81 [189]~E(x1891,x1892)+E(f592(x1893,x1894,x1895,x1891,x1896,x1897),f592(x1893,x1894,x1895,x1892,x1896,x1897))
% 15.02/14.81 [190]~E(x1901,x1902)+E(f592(x1903,x1904,x1905,x1906,x1901,x1907),f592(x1903,x1904,x1905,x1906,x1902,x1907))
% 15.02/14.81 [191]~E(x1911,x1912)+E(f592(x1913,x1914,x1915,x1916,x1917,x1911),f592(x1913,x1914,x1915,x1916,x1917,x1912))
% 15.02/14.81 [192]~E(x1921,x1922)+E(f663(x1921,x1923),f663(x1922,x1923))
% 15.02/14.81 [193]~E(x1931,x1932)+E(f663(x1933,x1931),f663(x1933,x1932))
% 15.02/14.81 [194]~E(x1941,x1942)+E(f591(x1941,x1943,x1944,x1945,x1946,x1947),f591(x1942,x1943,x1944,x1945,x1946,x1947))
% 15.02/14.81 [195]~E(x1951,x1952)+E(f591(x1953,x1951,x1954,x1955,x1956,x1957),f591(x1953,x1952,x1954,x1955,x1956,x1957))
% 15.02/14.81 [196]~E(x1961,x1962)+E(f591(x1963,x1964,x1961,x1965,x1966,x1967),f591(x1963,x1964,x1962,x1965,x1966,x1967))
% 15.02/14.81 [197]~E(x1971,x1972)+E(f591(x1973,x1974,x1975,x1971,x1976,x1977),f591(x1973,x1974,x1975,x1972,x1976,x1977))
% 15.02/14.81 [198]~E(x1981,x1982)+E(f591(x1983,x1984,x1985,x1986,x1981,x1987),f591(x1983,x1984,x1985,x1986,x1982,x1987))
% 15.02/14.81 [199]~E(x1991,x1992)+E(f591(x1993,x1994,x1995,x1996,x1997,x1991),f591(x1993,x1994,x1995,x1996,x1997,x1992))
% 15.02/14.81 [200]~E(x2001,x2002)+E(f8(x2001,x2003),f8(x2002,x2003))
% 15.02/14.81 [201]~E(x2011,x2012)+E(f8(x2013,x2011),f8(x2013,x2012))
% 15.02/14.81 [202]~E(x2021,x2022)+E(f247(x2021,x2023),f247(x2022,x2023))
% 15.02/14.81 [203]~E(x2031,x2032)+E(f247(x2033,x2031),f247(x2033,x2032))
% 15.02/14.81 [204]~E(x2041,x2042)+E(f36(x2041,x2043),f36(x2042,x2043))
% 15.02/14.81 [205]~E(x2051,x2052)+E(f36(x2053,x2051),f36(x2053,x2052))
% 15.02/14.81 [206]~E(x2061,x2062)+E(f138(x2061),f138(x2062))
% 15.02/14.81 [207]~E(x2071,x2072)+E(f869(x2071,x2073,x2074),f869(x2072,x2073,x2074))
% 15.02/14.81 [208]~E(x2081,x2082)+E(f869(x2083,x2081,x2084),f869(x2083,x2082,x2084))
% 15.02/14.81 [209]~E(x2091,x2092)+E(f869(x2093,x2094,x2091),f869(x2093,x2094,x2092))
% 15.02/14.81 [210]~E(x2101,x2102)+E(f18(x2101,x2103),f18(x2102,x2103))
% 15.02/14.81 [211]~E(x2111,x2112)+E(f18(x2113,x2111),f18(x2113,x2112))
% 15.02/14.81 [212]~E(x2121,x2122)+E(f611(x2121,x2123,x2124,x2125,x2126,x2127,x2128,x2129),f611(x2122,x2123,x2124,x2125,x2126,x2127,x2128,x2129))
% 15.02/14.81 [213]~E(x2131,x2132)+E(f611(x2133,x2131,x2134,x2135,x2136,x2137,x2138,x2139),f611(x2133,x2132,x2134,x2135,x2136,x2137,x2138,x2139))
% 15.02/14.81 [214]~E(x2141,x2142)+E(f611(x2143,x2144,x2141,x2145,x2146,x2147,x2148,x2149),f611(x2143,x2144,x2142,x2145,x2146,x2147,x2148,x2149))
% 15.02/14.81 [215]~E(x2151,x2152)+E(f611(x2153,x2154,x2155,x2151,x2156,x2157,x2158,x2159),f611(x2153,x2154,x2155,x2152,x2156,x2157,x2158,x2159))
% 15.02/14.81 [216]~E(x2161,x2162)+E(f611(x2163,x2164,x2165,x2166,x2161,x2167,x2168,x2169),f611(x2163,x2164,x2165,x2166,x2162,x2167,x2168,x2169))
% 15.02/14.81 [217]~E(x2171,x2172)+E(f611(x2173,x2174,x2175,x2176,x2177,x2171,x2178,x2179),f611(x2173,x2174,x2175,x2176,x2177,x2172,x2178,x2179))
% 15.02/14.81 [218]~E(x2181,x2182)+E(f611(x2183,x2184,x2185,x2186,x2187,x2188,x2181,x2189),f611(x2183,x2184,x2185,x2186,x2187,x2188,x2182,x2189))
% 15.02/14.81 [219]~E(x2191,x2192)+E(f611(x2193,x2194,x2195,x2196,x2197,x2198,x2199,x2191),f611(x2193,x2194,x2195,x2196,x2197,x2198,x2199,x2192))
% 15.02/14.81 [220]~E(x2201,x2202)+E(f564(x2201,x2203,x2204,x2205,x2206),f564(x2202,x2203,x2204,x2205,x2206))
% 15.02/14.81 [221]~E(x2211,x2212)+E(f564(x2213,x2211,x2214,x2215,x2216),f564(x2213,x2212,x2214,x2215,x2216))
% 15.02/14.81 [222]~E(x2221,x2222)+E(f564(x2223,x2224,x2221,x2225,x2226),f564(x2223,x2224,x2222,x2225,x2226))
% 15.02/14.81 [223]~E(x2231,x2232)+E(f564(x2233,x2234,x2235,x2231,x2236),f564(x2233,x2234,x2235,x2232,x2236))
% 15.02/14.81 [224]~E(x2241,x2242)+E(f564(x2243,x2244,x2245,x2246,x2241),f564(x2243,x2244,x2245,x2246,x2242))
% 15.02/14.81 [225]~E(x2251,x2252)+E(f113(x2251),f113(x2252))
% 15.02/14.81 [226]~E(x2261,x2262)+E(f870(x2261,x2263,x2264),f870(x2262,x2263,x2264))
% 15.02/14.81 [227]~E(x2271,x2272)+E(f870(x2273,x2271,x2274),f870(x2273,x2272,x2274))
% 15.02/14.81 [228]~E(x2281,x2282)+E(f870(x2283,x2284,x2281),f870(x2283,x2284,x2282))
% 15.02/14.81 [229]~E(x2291,x2292)+E(f241(x2291),f241(x2292))
% 15.02/14.81 [230]~E(x2301,x2302)+E(f925(x2301,x2303),f925(x2302,x2303))
% 15.02/14.81 [231]~E(x2311,x2312)+E(f925(x2313,x2311),f925(x2313,x2312))
% 15.02/14.81 [232]~E(x2321,x2322)+E(f250(x2321,x2323),f250(x2322,x2323))
% 15.02/14.81 [233]~E(x2331,x2332)+E(f250(x2333,x2331),f250(x2333,x2332))
% 15.02/14.81 [234]~E(x2341,x2342)+E(f339(x2341,x2343,x2344),f339(x2342,x2343,x2344))
% 15.02/14.81 [235]~E(x2351,x2352)+E(f339(x2353,x2351,x2354),f339(x2353,x2352,x2354))
% 15.02/14.81 [236]~E(x2361,x2362)+E(f339(x2363,x2364,x2361),f339(x2363,x2364,x2362))
% 15.02/14.81 [237]~E(x2371,x2372)+E(f243(x2371),f243(x2372))
% 15.02/14.81 [238]~E(x2381,x2382)+E(f655(x2381,x2383,x2384,x2385,x2386),f655(x2382,x2383,x2384,x2385,x2386))
% 15.02/14.81 [239]~E(x2391,x2392)+E(f655(x2393,x2391,x2394,x2395,x2396),f655(x2393,x2392,x2394,x2395,x2396))
% 15.02/14.81 [240]~E(x2401,x2402)+E(f655(x2403,x2404,x2401,x2405,x2406),f655(x2403,x2404,x2402,x2405,x2406))
% 15.02/14.81 [241]~E(x2411,x2412)+E(f655(x2413,x2414,x2415,x2411,x2416),f655(x2413,x2414,x2415,x2412,x2416))
% 15.02/14.81 [242]~E(x2421,x2422)+E(f655(x2423,x2424,x2425,x2426,x2421),f655(x2423,x2424,x2425,x2426,x2422))
% 15.02/14.81 [243]~E(x2431,x2432)+E(f609(x2431,x2433,x2434,x2435,x2436,x2437,x2438,x2439),f609(x2432,x2433,x2434,x2435,x2436,x2437,x2438,x2439))
% 15.02/14.81 [244]~E(x2441,x2442)+E(f609(x2443,x2441,x2444,x2445,x2446,x2447,x2448,x2449),f609(x2443,x2442,x2444,x2445,x2446,x2447,x2448,x2449))
% 15.02/14.81 [245]~E(x2451,x2452)+E(f609(x2453,x2454,x2451,x2455,x2456,x2457,x2458,x2459),f609(x2453,x2454,x2452,x2455,x2456,x2457,x2458,x2459))
% 15.02/14.81 [246]~E(x2461,x2462)+E(f609(x2463,x2464,x2465,x2461,x2466,x2467,x2468,x2469),f609(x2463,x2464,x2465,x2462,x2466,x2467,x2468,x2469))
% 15.02/14.81 [247]~E(x2471,x2472)+E(f609(x2473,x2474,x2475,x2476,x2471,x2477,x2478,x2479),f609(x2473,x2474,x2475,x2476,x2472,x2477,x2478,x2479))
% 15.02/14.81 [248]~E(x2481,x2482)+E(f609(x2483,x2484,x2485,x2486,x2487,x2481,x2488,x2489),f609(x2483,x2484,x2485,x2486,x2487,x2482,x2488,x2489))
% 15.02/14.81 [249]~E(x2491,x2492)+E(f609(x2493,x2494,x2495,x2496,x2497,x2498,x2491,x2499),f609(x2493,x2494,x2495,x2496,x2497,x2498,x2492,x2499))
% 15.02/14.81 [250]~E(x2501,x2502)+E(f609(x2503,x2504,x2505,x2506,x2507,x2508,x2509,x2501),f609(x2503,x2504,x2505,x2506,x2507,x2508,x2509,x2502))
% 15.02/14.81 [251]~E(x2511,x2512)+E(f270(x2511,x2513,x2514,x2515),f270(x2512,x2513,x2514,x2515))
% 15.02/14.81 [252]~E(x2521,x2522)+E(f270(x2523,x2521,x2524,x2525),f270(x2523,x2522,x2524,x2525))
% 15.02/14.81 [253]~E(x2531,x2532)+E(f270(x2533,x2534,x2531,x2535),f270(x2533,x2534,x2532,x2535))
% 15.02/14.81 [254]~E(x2541,x2542)+E(f270(x2543,x2544,x2545,x2541),f270(x2543,x2544,x2545,x2542))
% 15.02/14.81 [255]~E(x2551,x2552)+E(f172(x2551),f172(x2552))
% 15.02/14.81 [256]~E(x2561,x2562)+E(f283(x2561,x2563),f283(x2562,x2563))
% 15.02/14.81 [257]~E(x2571,x2572)+E(f283(x2573,x2571),f283(x2573,x2572))
% 15.02/14.81 [258]~E(x2581,x2582)+E(f902(x2581,x2583,x2584,x2585,x2586),f902(x2582,x2583,x2584,x2585,x2586))
% 15.02/14.81 [259]~E(x2591,x2592)+E(f902(x2593,x2591,x2594,x2595,x2596),f902(x2593,x2592,x2594,x2595,x2596))
% 15.02/14.81 [260]~E(x2601,x2602)+E(f902(x2603,x2604,x2601,x2605,x2606),f902(x2603,x2604,x2602,x2605,x2606))
% 15.02/14.81 [261]~E(x2611,x2612)+E(f902(x2613,x2614,x2615,x2611,x2616),f902(x2613,x2614,x2615,x2612,x2616))
% 15.02/14.81 [262]~E(x2621,x2622)+E(f902(x2623,x2624,x2625,x2626,x2621),f902(x2623,x2624,x2625,x2626,x2622))
% 15.02/14.81 [263]~E(x2631,x2632)+E(f186(x2631),f186(x2632))
% 15.02/14.81 [264]~E(x2641,x2642)+E(f181(x2641,x2643),f181(x2642,x2643))
% 15.02/14.81 [265]~E(x2651,x2652)+E(f181(x2653,x2651),f181(x2653,x2652))
% 15.02/14.81 [266]~E(x2661,x2662)+E(f838(x2661,x2663,x2664,x2665,x2666,x2667,x2668,x2669),f838(x2662,x2663,x2664,x2665,x2666,x2667,x2668,x2669))
% 15.02/14.81 [267]~E(x2671,x2672)+E(f838(x2673,x2671,x2674,x2675,x2676,x2677,x2678,x2679),f838(x2673,x2672,x2674,x2675,x2676,x2677,x2678,x2679))
% 15.02/14.81 [268]~E(x2681,x2682)+E(f838(x2683,x2684,x2681,x2685,x2686,x2687,x2688,x2689),f838(x2683,x2684,x2682,x2685,x2686,x2687,x2688,x2689))
% 15.02/14.81 [269]~E(x2691,x2692)+E(f838(x2693,x2694,x2695,x2691,x2696,x2697,x2698,x2699),f838(x2693,x2694,x2695,x2692,x2696,x2697,x2698,x2699))
% 15.02/14.81 [270]~E(x2701,x2702)+E(f838(x2703,x2704,x2705,x2706,x2701,x2707,x2708,x2709),f838(x2703,x2704,x2705,x2706,x2702,x2707,x2708,x2709))
% 15.02/14.81 [271]~E(x2711,x2712)+E(f838(x2713,x2714,x2715,x2716,x2717,x2711,x2718,x2719),f838(x2713,x2714,x2715,x2716,x2717,x2712,x2718,x2719))
% 15.02/14.81 [272]~E(x2721,x2722)+E(f838(x2723,x2724,x2725,x2726,x2727,x2728,x2721,x2729),f838(x2723,x2724,x2725,x2726,x2727,x2728,x2722,x2729))
% 15.02/14.81 [273]~E(x2731,x2732)+E(f838(x2733,x2734,x2735,x2736,x2737,x2738,x2739,x2731),f838(x2733,x2734,x2735,x2736,x2737,x2738,x2739,x2732))
% 15.02/14.81 [274]~E(x2741,x2742)+E(f255(x2741,x2743),f255(x2742,x2743))
% 15.02/14.81 [275]~E(x2751,x2752)+E(f255(x2753,x2751),f255(x2753,x2752))
% 15.02/14.81 [276]~E(x2761,x2762)+E(f310(x2761,x2763,x2764),f310(x2762,x2763,x2764))
% 15.02/14.81 [277]~E(x2771,x2772)+E(f310(x2773,x2771,x2774),f310(x2773,x2772,x2774))
% 15.02/14.81 [278]~E(x2781,x2782)+E(f310(x2783,x2784,x2781),f310(x2783,x2784,x2782))
% 15.02/14.81 [279]~E(x2791,x2792)+E(f286(x2791),f286(x2792))
% 15.02/14.81 [280]~E(x2801,x2802)+E(f178(x2801,x2803),f178(x2802,x2803))
% 15.02/14.81 [281]~E(x2811,x2812)+E(f178(x2813,x2811),f178(x2813,x2812))
% 15.02/14.81 [282]~E(x2821,x2822)+E(f302(x2821,x2823,x2824),f302(x2822,x2823,x2824))
% 15.02/14.81 [283]~E(x2831,x2832)+E(f302(x2833,x2831,x2834),f302(x2833,x2832,x2834))
% 15.02/14.81 [284]~E(x2841,x2842)+E(f302(x2843,x2844,x2841),f302(x2843,x2844,x2842))
% 15.02/14.81 [285]~E(x2851,x2852)+E(f242(x2851,x2853,x2854),f242(x2852,x2853,x2854))
% 15.02/14.81 [286]~E(x2861,x2862)+E(f242(x2863,x2861,x2864),f242(x2863,x2862,x2864))
% 15.02/14.81 [287]~E(x2871,x2872)+E(f242(x2873,x2874,x2871),f242(x2873,x2874,x2872))
% 15.02/14.81 [288]~E(x2881,x2882)+E(f176(x2881,x2883,x2884),f176(x2882,x2883,x2884))
% 15.02/14.81 [289]~E(x2891,x2892)+E(f176(x2893,x2891,x2894),f176(x2893,x2892,x2894))
% 15.02/14.81 [290]~E(x2901,x2902)+E(f176(x2903,x2904,x2901),f176(x2903,x2904,x2902))
% 15.02/14.81 [291]~E(x2911,x2912)+E(f114(x2911,x2913),f114(x2912,x2913))
% 15.02/14.81 [292]~E(x2921,x2922)+E(f114(x2923,x2921),f114(x2923,x2922))
% 15.02/14.81 [293]~E(x2931,x2932)+E(f805(x2931,x2933),f805(x2932,x2933))
% 15.02/14.81 [294]~E(x2941,x2942)+E(f805(x2943,x2941),f805(x2943,x2942))
% 15.02/14.81 [295]~E(x2951,x2952)+E(f288(x2951,x2953,x2954),f288(x2952,x2953,x2954))
% 15.02/14.81 [296]~E(x2961,x2962)+E(f288(x2963,x2961,x2964),f288(x2963,x2962,x2964))
% 15.02/14.81 [297]~E(x2971,x2972)+E(f288(x2973,x2974,x2971),f288(x2973,x2974,x2972))
% 15.02/14.81 [298]~E(x2981,x2982)+E(f152(x2981,x2983),f152(x2982,x2983))
% 15.02/14.81 [299]~E(x2991,x2992)+E(f152(x2993,x2991),f152(x2993,x2992))
% 15.02/14.81 [300]~E(x3001,x3002)+E(f384(x3001,x3003,x3004),f384(x3002,x3003,x3004))
% 15.02/14.81 [301]~E(x3011,x3012)+E(f384(x3013,x3011,x3014),f384(x3013,x3012,x3014))
% 15.02/14.81 [302]~E(x3021,x3022)+E(f384(x3023,x3024,x3021),f384(x3023,x3024,x3022))
% 15.02/14.81 [303]~E(x3031,x3032)+E(f192(x3031),f192(x3032))
% 15.02/14.81 [304]~E(x3041,x3042)+E(f16(x3041,x3043),f16(x3042,x3043))
% 15.02/14.81 [305]~E(x3051,x3052)+E(f16(x3053,x3051),f16(x3053,x3052))
% 15.02/14.81 [306]~E(x3061,x3062)+E(f15(x3061,x3063,x3064),f15(x3062,x3063,x3064))
% 15.02/14.81 [307]~E(x3071,x3072)+E(f15(x3073,x3071,x3074),f15(x3073,x3072,x3074))
% 15.02/14.81 [308]~E(x3081,x3082)+E(f15(x3083,x3084,x3081),f15(x3083,x3084,x3082))
% 15.02/14.81 [309]~E(x3091,x3092)+E(f699(x3091,x3093),f699(x3092,x3093))
% 15.02/14.81 [310]~E(x3101,x3102)+E(f699(x3103,x3101),f699(x3103,x3102))
% 15.02/14.81 [311]~E(x3111,x3112)+E(f63(x3111,x3113,x3114),f63(x3112,x3113,x3114))
% 15.02/14.81 [312]~E(x3121,x3122)+E(f63(x3123,x3121,x3124),f63(x3123,x3122,x3124))
% 15.02/14.81 [313]~E(x3131,x3132)+E(f63(x3133,x3134,x3131),f63(x3133,x3134,x3132))
% 15.02/14.81 [314]~E(x3141,x3142)+E(f924(x3141,x3143),f924(x3142,x3143))
% 15.02/14.81 [315]~E(x3151,x3152)+E(f924(x3153,x3151),f924(x3153,x3152))
% 15.02/14.81 [316]~E(x3161,x3162)+E(f167(x3161),f167(x3162))
% 15.02/14.81 [317]~E(x3171,x3172)+E(f34(x3171),f34(x3172))
% 15.02/14.81 [318]~E(x3181,x3182)+E(f109(x3181),f109(x3182))
% 15.02/14.81 [319]~E(x3191,x3192)+E(f305(x3191,x3193,x3194),f305(x3192,x3193,x3194))
% 15.02/14.81 [320]~E(x3201,x3202)+E(f305(x3203,x3201,x3204),f305(x3203,x3202,x3204))
% 15.02/14.81 [321]~E(x3211,x3212)+E(f305(x3213,x3214,x3211),f305(x3213,x3214,x3212))
% 15.02/14.81 [322]~E(x3221,x3222)+E(f171(x3221),f171(x3222))
% 15.02/14.81 [323]~E(x3231,x3232)+E(f74(x3231,x3233,x3234,x3235,x3236),f74(x3232,x3233,x3234,x3235,x3236))
% 15.02/14.81 [324]~E(x3241,x3242)+E(f74(x3243,x3241,x3244,x3245,x3246),f74(x3243,x3242,x3244,x3245,x3246))
% 15.02/14.81 [325]~E(x3251,x3252)+E(f74(x3253,x3254,x3251,x3255,x3256),f74(x3253,x3254,x3252,x3255,x3256))
% 15.02/14.81 [326]~E(x3261,x3262)+E(f74(x3263,x3264,x3265,x3261,x3266),f74(x3263,x3264,x3265,x3262,x3266))
% 15.02/14.81 [327]~E(x3271,x3272)+E(f74(x3273,x3274,x3275,x3276,x3271),f74(x3273,x3274,x3275,x3276,x3272))
% 15.02/14.81 [328]~E(x3281,x3282)+E(f613(x3281,x3283,x3284,x3285,x3286),f613(x3282,x3283,x3284,x3285,x3286))
% 15.02/14.81 [329]~E(x3291,x3292)+E(f613(x3293,x3291,x3294,x3295,x3296),f613(x3293,x3292,x3294,x3295,x3296))
% 15.02/14.81 [330]~E(x3301,x3302)+E(f613(x3303,x3304,x3301,x3305,x3306),f613(x3303,x3304,x3302,x3305,x3306))
% 15.02/14.81 [331]~E(x3311,x3312)+E(f613(x3313,x3314,x3315,x3311,x3316),f613(x3313,x3314,x3315,x3312,x3316))
% 15.02/14.81 [332]~E(x3321,x3322)+E(f613(x3323,x3324,x3325,x3326,x3321),f613(x3323,x3324,x3325,x3326,x3322))
% 15.02/14.81 [333]~E(x3331,x3332)+E(f142(x3331,x3333,x3334,x3335),f142(x3332,x3333,x3334,x3335))
% 15.02/14.81 [334]~E(x3341,x3342)+E(f142(x3343,x3341,x3344,x3345),f142(x3343,x3342,x3344,x3345))
% 15.02/14.81 [335]~E(x3351,x3352)+E(f142(x3353,x3354,x3351,x3355),f142(x3353,x3354,x3352,x3355))
% 15.02/14.81 [336]~E(x3361,x3362)+E(f142(x3363,x3364,x3365,x3361),f142(x3363,x3364,x3365,x3362))
% 15.02/14.81 [337]~E(x3371,x3372)+E(f168(x3371),f168(x3372))
% 15.02/14.81 [338]~E(x3381,x3382)+E(f46(x3381,x3383),f46(x3382,x3383))
% 15.02/14.81 [339]~E(x3391,x3392)+E(f46(x3393,x3391),f46(x3393,x3392))
% 15.02/14.81 [340]~E(x3401,x3402)+E(f13(x3401,x3403),f13(x3402,x3403))
% 15.02/14.81 [341]~E(x3411,x3412)+E(f13(x3413,x3411),f13(x3413,x3412))
% 15.02/14.81 [342]~E(x3421,x3422)+E(f759(x3421,x3423,x3424),f759(x3422,x3423,x3424))
% 15.02/14.81 [343]~E(x3431,x3432)+E(f759(x3433,x3431,x3434),f759(x3433,x3432,x3434))
% 15.02/14.81 [344]~E(x3441,x3442)+E(f759(x3443,x3444,x3441),f759(x3443,x3444,x3442))
% 15.02/14.81 [345]~E(x3451,x3452)+E(f777(x3451,x3453,x3454,x3455),f777(x3452,x3453,x3454,x3455))
% 15.02/14.81 [346]~E(x3461,x3462)+E(f777(x3463,x3461,x3464,x3465),f777(x3463,x3462,x3464,x3465))
% 15.02/14.81 [347]~E(x3471,x3472)+E(f777(x3473,x3474,x3471,x3475),f777(x3473,x3474,x3472,x3475))
% 15.02/14.81 [348]~E(x3481,x3482)+E(f777(x3483,x3484,x3485,x3481),f777(x3483,x3484,x3485,x3482))
% 15.02/14.81 [349]~E(x3491,x3492)+E(f306(x3491,x3493),f306(x3492,x3493))
% 15.02/14.81 [350]~E(x3501,x3502)+E(f306(x3503,x3501),f306(x3503,x3502))
% 15.02/14.81 [351]~E(x3511,x3512)+E(f195(x3511,x3513),f195(x3512,x3513))
% 15.02/14.81 [352]~E(x3521,x3522)+E(f195(x3523,x3521),f195(x3523,x3522))
% 15.02/14.81 [353]~E(x3531,x3532)+E(f96(x3531),f96(x3532))
% 15.02/14.81 [354]~E(x3541,x3542)+E(f317(x3541,x3543),f317(x3542,x3543))
% 15.02/14.81 [355]~E(x3551,x3552)+E(f317(x3553,x3551),f317(x3553,x3552))
% 15.02/14.81 [356]~E(x3561,x3562)+E(f169(x3561,x3563,x3564),f169(x3562,x3563,x3564))
% 15.02/14.81 [357]~E(x3571,x3572)+E(f169(x3573,x3571,x3574),f169(x3573,x3572,x3574))
% 15.02/14.81 [358]~E(x3581,x3582)+E(f169(x3583,x3584,x3581),f169(x3583,x3584,x3582))
% 15.02/14.81 [359]~E(x3591,x3592)+E(f26(x3591,x3593,x3594),f26(x3592,x3593,x3594))
% 15.02/14.81 [360]~E(x3601,x3602)+E(f26(x3603,x3601,x3604),f26(x3603,x3602,x3604))
% 15.02/14.81 [361]~E(x3611,x3612)+E(f26(x3613,x3614,x3611),f26(x3613,x3614,x3612))
% 15.02/14.81 [362]~E(x3621,x3622)+E(f319(x3621,x3623),f319(x3622,x3623))
% 15.02/14.81 [363]~E(x3631,x3632)+E(f319(x3633,x3631),f319(x3633,x3632))
% 15.02/14.81 [364]~E(x3641,x3642)+E(f284(x3641,x3643,x3644),f284(x3642,x3643,x3644))
% 15.02/14.81 [365]~E(x3651,x3652)+E(f284(x3653,x3651,x3654),f284(x3653,x3652,x3654))
% 15.02/14.81 [366]~E(x3661,x3662)+E(f284(x3663,x3664,x3661),f284(x3663,x3664,x3662))
% 15.02/14.81 [367]~E(x3671,x3672)+E(f865(x3671,x3673,x3674),f865(x3672,x3673,x3674))
% 15.02/14.81 [368]~E(x3681,x3682)+E(f865(x3683,x3681,x3684),f865(x3683,x3682,x3684))
% 15.02/14.81 [369]~E(x3691,x3692)+E(f865(x3693,x3694,x3691),f865(x3693,x3694,x3692))
% 15.02/14.81 [370]~E(x3701,x3702)+E(f730(x3701,x3703,x3704,x3705),f730(x3702,x3703,x3704,x3705))
% 15.02/14.81 [371]~E(x3711,x3712)+E(f730(x3713,x3711,x3714,x3715),f730(x3713,x3712,x3714,x3715))
% 15.02/14.81 [372]~E(x3721,x3722)+E(f730(x3723,x3724,x3721,x3725),f730(x3723,x3724,x3722,x3725))
% 15.02/14.81 [373]~E(x3731,x3732)+E(f730(x3733,x3734,x3735,x3731),f730(x3733,x3734,x3735,x3732))
% 15.02/14.81 [374]~E(x3741,x3742)+E(f735(x3741,x3743),f735(x3742,x3743))
% 15.02/14.81 [375]~E(x3751,x3752)+E(f735(x3753,x3751),f735(x3753,x3752))
% 15.02/14.81 [376]~E(x3761,x3762)+E(f12(x3761,x3763),f12(x3762,x3763))
% 15.02/14.81 [377]~E(x3771,x3772)+E(f12(x3773,x3771),f12(x3773,x3772))
% 15.02/14.81 [378]~E(x3781,x3782)+E(f312(x3781,x3783,x3784,x3785),f312(x3782,x3783,x3784,x3785))
% 15.02/14.81 [379]~E(x3791,x3792)+E(f312(x3793,x3791,x3794,x3795),f312(x3793,x3792,x3794,x3795))
% 15.02/14.81 [380]~E(x3801,x3802)+E(f312(x3803,x3804,x3801,x3805),f312(x3803,x3804,x3802,x3805))
% 15.02/14.81 [381]~E(x3811,x3812)+E(f312(x3813,x3814,x3815,x3811),f312(x3813,x3814,x3815,x3812))
% 15.02/14.81 [382]~E(x3821,x3822)+E(f498(x3821,x3823,x3824,x3825),f498(x3822,x3823,x3824,x3825))
% 15.02/14.81 [383]~E(x3831,x3832)+E(f498(x3833,x3831,x3834,x3835),f498(x3833,x3832,x3834,x3835))
% 15.02/14.81 [384]~E(x3841,x3842)+E(f498(x3843,x3844,x3841,x3845),f498(x3843,x3844,x3842,x3845))
% 15.02/14.81 [385]~E(x3851,x3852)+E(f498(x3853,x3854,x3855,x3851),f498(x3853,x3854,x3855,x3852))
% 15.02/14.81 [386]~E(x3861,x3862)+E(f304(x3861,x3863,x3864),f304(x3862,x3863,x3864))
% 15.02/14.81 [387]~E(x3871,x3872)+E(f304(x3873,x3871,x3874),f304(x3873,x3872,x3874))
% 15.02/14.81 [388]~E(x3881,x3882)+E(f304(x3883,x3884,x3881),f304(x3883,x3884,x3882))
% 15.02/14.81 [389]~E(x3891,x3892)+E(f158(x3891,x3893),f158(x3892,x3893))
% 15.02/14.81 [390]~E(x3901,x3902)+E(f158(x3903,x3901),f158(x3903,x3902))
% 15.02/14.81 [391]~E(x3911,x3912)+E(f907(x3911,x3913,x3914),f907(x3912,x3913,x3914))
% 15.02/14.81 [392]~E(x3921,x3922)+E(f907(x3923,x3921,x3924),f907(x3923,x3922,x3924))
% 15.02/14.81 [393]~E(x3931,x3932)+E(f907(x3933,x3934,x3931),f907(x3933,x3934,x3932))
% 15.02/14.81 [394]~E(x3941,x3942)+E(f62(x3941,x3943),f62(x3942,x3943))
% 15.02/14.81 [395]~E(x3951,x3952)+E(f62(x3953,x3951),f62(x3953,x3952))
% 15.02/14.81 [396]~E(x3961,x3962)+E(f165(x3961),f165(x3962))
% 15.02/14.81 [397]~E(x3971,x3972)+E(f561(x3971,x3973,x3974,x3975,x3976,x3977),f561(x3972,x3973,x3974,x3975,x3976,x3977))
% 15.02/14.81 [398]~E(x3981,x3982)+E(f561(x3983,x3981,x3984,x3985,x3986,x3987),f561(x3983,x3982,x3984,x3985,x3986,x3987))
% 15.02/14.81 [399]~E(x3991,x3992)+E(f561(x3993,x3994,x3991,x3995,x3996,x3997),f561(x3993,x3994,x3992,x3995,x3996,x3997))
% 15.02/14.81 [400]~E(x4001,x4002)+E(f561(x4003,x4004,x4005,x4001,x4006,x4007),f561(x4003,x4004,x4005,x4002,x4006,x4007))
% 15.02/14.81 [401]~E(x4011,x4012)+E(f561(x4013,x4014,x4015,x4016,x4011,x4017),f561(x4013,x4014,x4015,x4016,x4012,x4017))
% 15.02/14.81 [402]~E(x4021,x4022)+E(f561(x4023,x4024,x4025,x4026,x4027,x4021),f561(x4023,x4024,x4025,x4026,x4027,x4022))
% 15.02/14.81 [403]~E(x4031,x4032)+E(f17(x4031,x4033),f17(x4032,x4033))
% 15.02/14.81 [404]~E(x4041,x4042)+E(f17(x4043,x4041),f17(x4043,x4042))
% 15.02/14.81 [405]~E(x4051,x4052)+E(f119(x4051),f119(x4052))
% 15.02/14.81 [406]~E(x4061,x4062)+E(f120(x4061,x4063),f120(x4062,x4063))
% 15.02/14.81 [407]~E(x4071,x4072)+E(f120(x4073,x4071),f120(x4073,x4072))
% 15.02/14.81 [408]~E(x4081,x4082)+E(f799(x4081,x4083,x4084,x4085),f799(x4082,x4083,x4084,x4085))
% 15.02/14.81 [409]~E(x4091,x4092)+E(f799(x4093,x4091,x4094,x4095),f799(x4093,x4092,x4094,x4095))
% 15.02/14.81 [410]~E(x4101,x4102)+E(f799(x4103,x4104,x4101,x4105),f799(x4103,x4104,x4102,x4105))
% 15.02/14.81 [411]~E(x4111,x4112)+E(f799(x4113,x4114,x4115,x4111),f799(x4113,x4114,x4115,x4112))
% 15.02/14.81 [412]~E(x4121,x4122)+E(f48(x4121,x4123),f48(x4122,x4123))
% 15.02/14.81 [413]~E(x4131,x4132)+E(f48(x4133,x4131),f48(x4133,x4132))
% 15.02/14.81 [414]~E(x4141,x4142)+E(f516(x4141,x4143,x4144),f516(x4142,x4143,x4144))
% 15.02/14.81 [415]~E(x4151,x4152)+E(f516(x4153,x4151,x4154),f516(x4153,x4152,x4154))
% 15.02/14.81 [416]~E(x4161,x4162)+E(f516(x4163,x4164,x4161),f516(x4163,x4164,x4162))
% 15.02/14.81 [417]~E(x4171,x4172)+E(f315(x4171,x4173),f315(x4172,x4173))
% 15.02/14.81 [418]~E(x4181,x4182)+E(f315(x4183,x4181),f315(x4183,x4182))
% 15.02/14.81 [419]~E(x4191,x4192)+E(f84(x4191,x4193),f84(x4192,x4193))
% 15.02/14.81 [420]~E(x4201,x4202)+E(f84(x4203,x4201),f84(x4203,x4202))
% 15.02/14.81 [421]~E(x4211,x4212)+E(f367(x4211,x4213),f367(x4212,x4213))
% 15.02/14.81 [422]~E(x4221,x4222)+E(f367(x4223,x4221),f367(x4223,x4222))
% 15.02/14.81 [423]~E(x4231,x4232)+E(f89(x4231,x4233),f89(x4232,x4233))
% 15.02/14.81 [424]~E(x4241,x4242)+E(f89(x4243,x4241),f89(x4243,x4242))
% 15.02/14.81 [425]~E(x4251,x4252)+E(f58(x4251,x4253,x4254,x4255),f58(x4252,x4253,x4254,x4255))
% 15.02/14.81 [426]~E(x4261,x4262)+E(f58(x4263,x4261,x4264,x4265),f58(x4263,x4262,x4264,x4265))
% 15.02/14.81 [427]~E(x4271,x4272)+E(f58(x4273,x4274,x4271,x4275),f58(x4273,x4274,x4272,x4275))
% 15.02/14.81 [428]~E(x4281,x4282)+E(f58(x4283,x4284,x4285,x4281),f58(x4283,x4284,x4285,x4282))
% 15.02/14.81 [429]~E(x4291,x4292)+E(f153(x4291,x4293),f153(x4292,x4293))
% 15.02/14.81 [430]~E(x4301,x4302)+E(f153(x4303,x4301),f153(x4303,x4302))
% 15.02/14.81 [431]~E(x4311,x4312)+E(f262(x4311,x4313),f262(x4312,x4313))
% 15.02/14.81 [432]~E(x4321,x4322)+E(f262(x4323,x4321),f262(x4323,x4322))
% 15.02/14.81 [433]~E(x4331,x4332)+E(f700(x4331,x4333),f700(x4332,x4333))
% 15.02/14.81 [434]~E(x4341,x4342)+E(f700(x4343,x4341),f700(x4343,x4342))
% 15.02/14.81 [435]~E(x4351,x4352)+E(f394(x4351,x4353,x4354),f394(x4352,x4353,x4354))
% 15.02/14.81 [436]~E(x4361,x4362)+E(f394(x4363,x4361,x4364),f394(x4363,x4362,x4364))
% 15.02/14.81 [437]~E(x4371,x4372)+E(f394(x4373,x4374,x4371),f394(x4373,x4374,x4372))
% 15.02/14.81 [438]~E(x4381,x4382)+E(f732(x4381,x4383),f732(x4382,x4383))
% 15.02/14.81 [439]~E(x4391,x4392)+E(f732(x4393,x4391),f732(x4393,x4392))
% 15.02/14.81 [440]~E(x4401,x4402)+E(f47(x4401,x4403),f47(x4402,x4403))
% 15.02/14.81 [441]~E(x4411,x4412)+E(f47(x4413,x4411),f47(x4413,x4412))
% 15.02/14.81 [442]~E(x4421,x4422)+E(f11(x4421,x4423),f11(x4422,x4423))
% 15.02/14.81 [443]~E(x4431,x4432)+E(f11(x4433,x4431),f11(x4433,x4432))
% 15.02/14.81 [444]~E(x4441,x4442)+E(f720(x4441,x4443,x4444),f720(x4442,x4443,x4444))
% 15.02/14.81 [445]~E(x4451,x4452)+E(f720(x4453,x4451,x4454),f720(x4453,x4452,x4454))
% 15.02/14.81 [446]~E(x4461,x4462)+E(f720(x4463,x4464,x4461),f720(x4463,x4464,x4462))
% 15.02/14.81 [447]~E(x4471,x4472)+E(f803(x4471,x4473),f803(x4472,x4473))
% 15.02/14.81 [448]~E(x4481,x4482)+E(f803(x4483,x4481),f803(x4483,x4482))
% 15.02/14.81 [449]~E(x4491,x4492)+E(f476(x4491,x4493,x4494,x4495),f476(x4492,x4493,x4494,x4495))
% 15.02/14.81 [450]~E(x4501,x4502)+E(f476(x4503,x4501,x4504,x4505),f476(x4503,x4502,x4504,x4505))
% 15.02/14.81 [451]~E(x4511,x4512)+E(f476(x4513,x4514,x4511,x4515),f476(x4513,x4514,x4512,x4515))
% 15.02/14.81 [452]~E(x4521,x4522)+E(f476(x4523,x4524,x4525,x4521),f476(x4523,x4524,x4525,x4522))
% 15.02/14.81 [453]~E(x4531,x4532)+E(f86(x4531),f86(x4532))
% 15.02/14.81 [454]~E(x4541,x4542)+E(f678(x4541,x4543),f678(x4542,x4543))
% 15.02/14.81 [455]~E(x4551,x4552)+E(f678(x4553,x4551),f678(x4553,x4552))
% 15.02/14.81 [456]~E(x4561,x4562)+E(f221(x4561,x4563,x4564,x4565),f221(x4562,x4563,x4564,x4565))
% 15.02/14.81 [457]~E(x4571,x4572)+E(f221(x4573,x4571,x4574,x4575),f221(x4573,x4572,x4574,x4575))
% 15.02/14.81 [458]~E(x4581,x4582)+E(f221(x4583,x4584,x4581,x4585),f221(x4583,x4584,x4582,x4585))
% 15.02/14.81 [459]~E(x4591,x4592)+E(f221(x4593,x4594,x4595,x4591),f221(x4593,x4594,x4595,x4592))
% 15.02/14.81 [460]~E(x4601,x4602)+E(f260(x4601,x4603,x4604,x4605,x4606),f260(x4602,x4603,x4604,x4605,x4606))
% 15.02/14.81 [461]~E(x4611,x4612)+E(f260(x4613,x4611,x4614,x4615,x4616),f260(x4613,x4612,x4614,x4615,x4616))
% 15.02/14.81 [462]~E(x4621,x4622)+E(f260(x4623,x4624,x4621,x4625,x4626),f260(x4623,x4624,x4622,x4625,x4626))
% 15.02/14.81 [463]~E(x4631,x4632)+E(f260(x4633,x4634,x4635,x4631,x4636),f260(x4633,x4634,x4635,x4632,x4636))
% 15.02/14.81 [464]~E(x4641,x4642)+E(f260(x4643,x4644,x4645,x4646,x4641),f260(x4643,x4644,x4645,x4646,x4642))
% 15.02/14.81 [465]~E(x4651,x4652)+E(f724(x4651,x4653,x4654,x4655),f724(x4652,x4653,x4654,x4655))
% 15.02/14.81 [466]~E(x4661,x4662)+E(f724(x4663,x4661,x4664,x4665),f724(x4663,x4662,x4664,x4665))
% 15.02/14.81 [467]~E(x4671,x4672)+E(f724(x4673,x4674,x4671,x4675),f724(x4673,x4674,x4672,x4675))
% 15.02/14.81 [468]~E(x4681,x4682)+E(f724(x4683,x4684,x4685,x4681),f724(x4683,x4684,x4685,x4682))
% 15.02/14.81 [469]~E(x4691,x4692)+E(f137(x4691),f137(x4692))
% 15.02/14.81 [470]~E(x4701,x4702)+E(f833(x4701,x4703),f833(x4702,x4703))
% 15.02/14.81 [471]~E(x4711,x4712)+E(f833(x4713,x4711),f833(x4713,x4712))
% 15.02/14.81 [472]~E(x4721,x4722)+E(f403(x4721,x4723,x4724),f403(x4722,x4723,x4724))
% 15.02/14.81 [473]~E(x4731,x4732)+E(f403(x4733,x4731,x4734),f403(x4733,x4732,x4734))
% 15.02/14.81 [474]~E(x4741,x4742)+E(f403(x4743,x4744,x4741),f403(x4743,x4744,x4742))
% 15.02/14.81 [475]~E(x4751,x4752)+E(f845(x4751,x4753,x4754,x4755,x4756,x4757,x4758,x4759),f845(x4752,x4753,x4754,x4755,x4756,x4757,x4758,x4759))
% 15.02/14.81 [476]~E(x4761,x4762)+E(f845(x4763,x4761,x4764,x4765,x4766,x4767,x4768,x4769),f845(x4763,x4762,x4764,x4765,x4766,x4767,x4768,x4769))
% 15.02/14.81 [477]~E(x4771,x4772)+E(f845(x4773,x4774,x4771,x4775,x4776,x4777,x4778,x4779),f845(x4773,x4774,x4772,x4775,x4776,x4777,x4778,x4779))
% 15.02/14.81 [478]~E(x4781,x4782)+E(f845(x4783,x4784,x4785,x4781,x4786,x4787,x4788,x4789),f845(x4783,x4784,x4785,x4782,x4786,x4787,x4788,x4789))
% 15.02/14.81 [479]~E(x4791,x4792)+E(f845(x4793,x4794,x4795,x4796,x4791,x4797,x4798,x4799),f845(x4793,x4794,x4795,x4796,x4792,x4797,x4798,x4799))
% 15.02/14.81 [480]~E(x4801,x4802)+E(f845(x4803,x4804,x4805,x4806,x4807,x4801,x4808,x4809),f845(x4803,x4804,x4805,x4806,x4807,x4802,x4808,x4809))
% 15.02/14.81 [481]~E(x4811,x4812)+E(f845(x4813,x4814,x4815,x4816,x4817,x4818,x4811,x4819),f845(x4813,x4814,x4815,x4816,x4817,x4818,x4812,x4819))
% 15.02/14.81 [482]~E(x4821,x4822)+E(f845(x4823,x4824,x4825,x4826,x4827,x4828,x4829,x4821),f845(x4823,x4824,x4825,x4826,x4827,x4828,x4829,x4822))
% 15.02/14.81 [483]~E(x4831,x4832)+E(f778(x4831,x4833,x4834,x4835),f778(x4832,x4833,x4834,x4835))
% 15.02/14.81 [484]~E(x4841,x4842)+E(f778(x4843,x4841,x4844,x4845),f778(x4843,x4842,x4844,x4845))
% 15.02/14.81 [485]~E(x4851,x4852)+E(f778(x4853,x4854,x4851,x4855),f778(x4853,x4854,x4852,x4855))
% 15.02/14.81 [486]~E(x4861,x4862)+E(f778(x4863,x4864,x4865,x4861),f778(x4863,x4864,x4865,x4862))
% 15.02/14.81 [487]~E(x4871,x4872)+E(f391(x4871,x4873,x4874),f391(x4872,x4873,x4874))
% 15.02/14.81 [488]~E(x4881,x4882)+E(f391(x4883,x4881,x4884),f391(x4883,x4882,x4884))
% 15.02/14.81 [489]~E(x4891,x4892)+E(f391(x4893,x4894,x4891),f391(x4893,x4894,x4892))
% 15.02/14.81 [490]~E(x4901,x4902)+E(f842(x4901,x4903),f842(x4902,x4903))
% 15.02/14.81 [491]~E(x4911,x4912)+E(f842(x4913,x4911),f842(x4913,x4912))
% 15.02/14.81 [492]~E(x4921,x4922)+E(f399(x4921,x4923,x4924,x4925),f399(x4922,x4923,x4924,x4925))
% 15.02/14.81 [493]~E(x4931,x4932)+E(f399(x4933,x4931,x4934,x4935),f399(x4933,x4932,x4934,x4935))
% 15.02/14.81 [494]~E(x4941,x4942)+E(f399(x4943,x4944,x4941,x4945),f399(x4943,x4944,x4942,x4945))
% 15.02/14.81 [495]~E(x4951,x4952)+E(f399(x4953,x4954,x4955,x4951),f399(x4953,x4954,x4955,x4952))
% 15.02/14.81 [496]~E(x4961,x4962)+E(f263(x4961,x4963),f263(x4962,x4963))
% 15.02/14.81 [497]~E(x4971,x4972)+E(f263(x4973,x4971),f263(x4973,x4972))
% 15.02/14.81 [498]~E(x4981,x4982)+E(f147(x4981,x4983),f147(x4982,x4983))
% 15.02/14.81 [499]~E(x4991,x4992)+E(f147(x4993,x4991),f147(x4993,x4992))
% 15.02/14.81 [500]~E(x5001,x5002)+E(f883(x5001,x5003,x5004,x5005),f883(x5002,x5003,x5004,x5005))
% 15.02/14.81 [501]~E(x5011,x5012)+E(f883(x5013,x5011,x5014,x5015),f883(x5013,x5012,x5014,x5015))
% 15.02/14.81 [502]~E(x5021,x5022)+E(f883(x5023,x5024,x5021,x5025),f883(x5023,x5024,x5022,x5025))
% 15.02/14.81 [503]~E(x5031,x5032)+E(f883(x5033,x5034,x5035,x5031),f883(x5033,x5034,x5035,x5032))
% 15.02/14.81 [504]~E(x5041,x5042)+E(f179(x5041,x5043),f179(x5042,x5043))
% 15.02/14.81 [505]~E(x5051,x5052)+E(f179(x5053,x5051),f179(x5053,x5052))
% 15.02/14.81 [506]~E(x5061,x5062)+E(f436(x5061,x5063,x5064,x5065,x5066),f436(x5062,x5063,x5064,x5065,x5066))
% 15.02/14.81 [507]~E(x5071,x5072)+E(f436(x5073,x5071,x5074,x5075,x5076),f436(x5073,x5072,x5074,x5075,x5076))
% 15.02/14.81 [508]~E(x5081,x5082)+E(f436(x5083,x5084,x5081,x5085,x5086),f436(x5083,x5084,x5082,x5085,x5086))
% 15.02/14.81 [509]~E(x5091,x5092)+E(f436(x5093,x5094,x5095,x5091,x5096),f436(x5093,x5094,x5095,x5092,x5096))
% 15.02/14.81 [510]~E(x5101,x5102)+E(f436(x5103,x5104,x5105,x5106,x5101),f436(x5103,x5104,x5105,x5106,x5102))
% 15.02/14.81 [511]~E(x5111,x5112)+E(f65(x5111,x5113,x5114,x5115,x5116),f65(x5112,x5113,x5114,x5115,x5116))
% 15.02/14.81 [512]~E(x5121,x5122)+E(f65(x5123,x5121,x5124,x5125,x5126),f65(x5123,x5122,x5124,x5125,x5126))
% 15.02/14.81 [513]~E(x5131,x5132)+E(f65(x5133,x5134,x5131,x5135,x5136),f65(x5133,x5134,x5132,x5135,x5136))
% 15.02/14.81 [514]~E(x5141,x5142)+E(f65(x5143,x5144,x5145,x5141,x5146),f65(x5143,x5144,x5145,x5142,x5146))
% 15.02/14.81 [515]~E(x5151,x5152)+E(f65(x5153,x5154,x5155,x5156,x5151),f65(x5153,x5154,x5155,x5156,x5152))
% 15.02/14.81 [516]~E(x5161,x5162)+E(f92(x5161,x5163,x5164),f92(x5162,x5163,x5164))
% 15.02/14.81 [517]~E(x5171,x5172)+E(f92(x5173,x5171,x5174),f92(x5173,x5172,x5174))
% 15.02/14.81 [518]~E(x5181,x5182)+E(f92(x5183,x5184,x5181),f92(x5183,x5184,x5182))
% 15.02/14.81 [519]~E(x5191,x5192)+E(f313(x5191),f313(x5192))
% 15.02/14.81 [520]~E(x5201,x5202)+E(f175(x5201),f175(x5202))
% 15.02/14.81 [521]~E(x5211,x5212)+E(f506(x5211,x5213,x5214,x5215),f506(x5212,x5213,x5214,x5215))
% 15.02/14.81 [522]~E(x5221,x5222)+E(f506(x5223,x5221,x5224,x5225),f506(x5223,x5222,x5224,x5225))
% 15.02/14.81 [523]~E(x5231,x5232)+E(f506(x5233,x5234,x5231,x5235),f506(x5233,x5234,x5232,x5235))
% 15.02/14.81 [524]~E(x5241,x5242)+E(f506(x5243,x5244,x5245,x5241),f506(x5243,x5244,x5245,x5242))
% 15.02/14.81 [525]~E(x5251,x5252)+E(f73(x5251,x5253),f73(x5252,x5253))
% 15.02/14.81 [526]~E(x5261,x5262)+E(f73(x5263,x5261),f73(x5263,x5262))
% 15.02/14.81 [527]~E(x5271,x5272)+E(f303(x5271),f303(x5272))
% 15.02/14.81 [528]~E(x5281,x5282)+E(f30(x5281,x5283),f30(x5282,x5283))
% 15.02/14.81 [529]~E(x5291,x5292)+E(f30(x5293,x5291),f30(x5293,x5292))
% 15.02/14.81 [530]~E(x5301,x5302)+E(f752(x5301,x5303,x5304),f752(x5302,x5303,x5304))
% 15.02/14.81 [531]~E(x5311,x5312)+E(f752(x5313,x5311,x5314),f752(x5313,x5312,x5314))
% 15.02/14.81 [532]~E(x5321,x5322)+E(f752(x5323,x5324,x5321),f752(x5323,x5324,x5322))
% 15.02/14.81 [533]~E(x5331,x5332)+E(f161(x5331,x5333),f161(x5332,x5333))
% 15.02/14.81 [534]~E(x5341,x5342)+E(f161(x5343,x5341),f161(x5343,x5342))
% 15.02/14.81 [535]~E(x5351,x5352)+E(f593(x5351,x5353,x5354,x5355,x5356,x5357),f593(x5352,x5353,x5354,x5355,x5356,x5357))
% 15.02/14.81 [536]~E(x5361,x5362)+E(f593(x5363,x5361,x5364,x5365,x5366,x5367),f593(x5363,x5362,x5364,x5365,x5366,x5367))
% 15.02/14.81 [537]~E(x5371,x5372)+E(f593(x5373,x5374,x5371,x5375,x5376,x5377),f593(x5373,x5374,x5372,x5375,x5376,x5377))
% 15.02/14.81 [538]~E(x5381,x5382)+E(f593(x5383,x5384,x5385,x5381,x5386,x5387),f593(x5383,x5384,x5385,x5382,x5386,x5387))
% 15.02/14.81 [539]~E(x5391,x5392)+E(f593(x5393,x5394,x5395,x5396,x5391,x5397),f593(x5393,x5394,x5395,x5396,x5392,x5397))
% 15.02/14.81 [540]~E(x5401,x5402)+E(f593(x5403,x5404,x5405,x5406,x5407,x5401),f593(x5403,x5404,x5405,x5406,x5407,x5402))
% 15.02/14.81 [541]~E(x5411,x5412)+E(f281(x5411),f281(x5412))
% 15.02/14.81 [542]~E(x5421,x5422)+E(f139(x5421,x5423),f139(x5422,x5423))
% 15.02/14.81 [543]~E(x5431,x5432)+E(f139(x5433,x5431),f139(x5433,x5432))
% 15.02/14.81 [544]~E(x5441,x5442)+E(f774(x5441,x5443,x5444,x5445,x5446),f774(x5442,x5443,x5444,x5445,x5446))
% 15.02/14.81 [545]~E(x5451,x5452)+E(f774(x5453,x5451,x5454,x5455,x5456),f774(x5453,x5452,x5454,x5455,x5456))
% 15.02/14.81 [546]~E(x5461,x5462)+E(f774(x5463,x5464,x5461,x5465,x5466),f774(x5463,x5464,x5462,x5465,x5466))
% 15.02/14.81 [547]~E(x5471,x5472)+E(f774(x5473,x5474,x5475,x5471,x5476),f774(x5473,x5474,x5475,x5472,x5476))
% 15.02/14.81 [548]~E(x5481,x5482)+E(f774(x5483,x5484,x5485,x5486,x5481),f774(x5483,x5484,x5485,x5486,x5482))
% 15.02/14.81 [549]~E(x5491,x5492)+E(f14(x5491,x5493,x5494),f14(x5492,x5493,x5494))
% 15.02/14.81 [550]~E(x5501,x5502)+E(f14(x5503,x5501,x5504),f14(x5503,x5502,x5504))
% 15.02/14.81 [551]~E(x5511,x5512)+E(f14(x5513,x5514,x5511),f14(x5513,x5514,x5512))
% 15.02/14.81 [552]~E(x5521,x5522)+E(f522(x5521,x5523,x5524),f522(x5522,x5523,x5524))
% 15.02/14.81 [553]~E(x5531,x5532)+E(f522(x5533,x5531,x5534),f522(x5533,x5532,x5534))
% 15.02/14.81 [554]~E(x5541,x5542)+E(f522(x5543,x5544,x5541),f522(x5543,x5544,x5542))
% 15.02/14.81 [555]~E(x5551,x5552)+E(f282(x5551),f282(x5552))
% 15.02/14.81 [556]~E(x5561,x5562)+E(f892(x5561,x5563,x5564),f892(x5562,x5563,x5564))
% 15.02/14.81 [557]~E(x5571,x5572)+E(f892(x5573,x5571,x5574),f892(x5573,x5572,x5574))
% 15.02/14.81 [558]~E(x5581,x5582)+E(f892(x5583,x5584,x5581),f892(x5583,x5584,x5582))
% 15.02/14.81 [559]~E(x5591,x5592)+E(f669(x5591,x5593,x5594,x5595),f669(x5592,x5593,x5594,x5595))
% 15.02/14.81 [560]~E(x5601,x5602)+E(f669(x5603,x5601,x5604,x5605),f669(x5603,x5602,x5604,x5605))
% 15.02/14.81 [561]~E(x5611,x5612)+E(f669(x5613,x5614,x5611,x5615),f669(x5613,x5614,x5612,x5615))
% 15.02/14.81 [562]~E(x5621,x5622)+E(f669(x5623,x5624,x5625,x5621),f669(x5623,x5624,x5625,x5622))
% 15.02/14.81 [563]~E(x5631,x5632)+E(f867(x5631,x5633,x5634),f867(x5632,x5633,x5634))
% 15.02/14.81 [564]~E(x5641,x5642)+E(f867(x5643,x5641,x5644),f867(x5643,x5642,x5644))
% 15.02/14.81 [565]~E(x5651,x5652)+E(f867(x5653,x5654,x5651),f867(x5653,x5654,x5652))
% 15.02/14.81 [566]~E(x5661,x5662)+E(f266(x5661),f266(x5662))
% 15.02/14.81 [567]~E(x5671,x5672)+E(f683(x5671,x5673,x5674,x5675,x5676),f683(x5672,x5673,x5674,x5675,x5676))
% 15.02/14.81 [568]~E(x5681,x5682)+E(f683(x5683,x5681,x5684,x5685,x5686),f683(x5683,x5682,x5684,x5685,x5686))
% 15.02/14.81 [569]~E(x5691,x5692)+E(f683(x5693,x5694,x5691,x5695,x5696),f683(x5693,x5694,x5692,x5695,x5696))
% 15.02/14.81 [570]~E(x5701,x5702)+E(f683(x5703,x5704,x5705,x5701,x5706),f683(x5703,x5704,x5705,x5702,x5706))
% 15.02/14.81 [571]~E(x5711,x5712)+E(f683(x5713,x5714,x5715,x5716,x5711),f683(x5713,x5714,x5715,x5716,x5712))
% 15.02/14.81 [572]~E(x5721,x5722)+E(f91(x5721,x5723,x5724,x5725),f91(x5722,x5723,x5724,x5725))
% 15.02/14.81 [573]~E(x5731,x5732)+E(f91(x5733,x5731,x5734,x5735),f91(x5733,x5732,x5734,x5735))
% 15.02/14.81 [574]~E(x5741,x5742)+E(f91(x5743,x5744,x5741,x5745),f91(x5743,x5744,x5742,x5745))
% 15.02/14.81 [575]~E(x5751,x5752)+E(f91(x5753,x5754,x5755,x5751),f91(x5753,x5754,x5755,x5752))
% 15.02/14.81 [576]~E(x5761,x5762)+E(f128(x5761,x5763),f128(x5762,x5763))
% 15.02/14.81 [577]~E(x5771,x5772)+E(f128(x5773,x5771),f128(x5773,x5772))
% 15.02/14.81 [578]~E(x5781,x5782)+E(f482(x5781),f482(x5782))
% 15.02/14.81 [579]~E(x5791,x5792)+E(f594(x5791,x5793,x5794,x5795,x5796,x5797),f594(x5792,x5793,x5794,x5795,x5796,x5797))
% 15.02/14.81 [580]~E(x5801,x5802)+E(f594(x5803,x5801,x5804,x5805,x5806,x5807),f594(x5803,x5802,x5804,x5805,x5806,x5807))
% 15.02/14.81 [581]~E(x5811,x5812)+E(f594(x5813,x5814,x5811,x5815,x5816,x5817),f594(x5813,x5814,x5812,x5815,x5816,x5817))
% 15.02/14.81 [582]~E(x5821,x5822)+E(f594(x5823,x5824,x5825,x5821,x5826,x5827),f594(x5823,x5824,x5825,x5822,x5826,x5827))
% 15.02/14.81 [583]~E(x5831,x5832)+E(f594(x5833,x5834,x5835,x5836,x5831,x5837),f594(x5833,x5834,x5835,x5836,x5832,x5837))
% 15.02/14.81 [584]~E(x5841,x5842)+E(f594(x5843,x5844,x5845,x5846,x5847,x5841),f594(x5843,x5844,x5845,x5846,x5847,x5842))
% 15.02/14.81 [585]~E(x5851,x5852)+E(f140(x5851,x5853,x5854),f140(x5852,x5853,x5854))
% 15.02/14.81 [586]~E(x5861,x5862)+E(f140(x5863,x5861,x5864),f140(x5863,x5862,x5864))
% 15.02/14.81 [587]~E(x5871,x5872)+E(f140(x5873,x5874,x5871),f140(x5873,x5874,x5872))
% 15.02/14.81 [588]~E(x5881,x5882)+E(f582(x5881,x5883),f582(x5882,x5883))
% 15.02/14.81 [589]~E(x5891,x5892)+E(f582(x5893,x5891),f582(x5893,x5892))
% 15.02/14.81 [590]~E(x5901,x5902)+E(f49(x5901,x5903),f49(x5902,x5903))
% 15.02/14.81 [591]~E(x5911,x5912)+E(f49(x5913,x5911),f49(x5913,x5912))
% 15.02/14.81 [592]~E(x5921,x5922)+E(f661(x5921,x5923,x5924,x5925),f661(x5922,x5923,x5924,x5925))
% 15.02/14.81 [593]~E(x5931,x5932)+E(f661(x5933,x5931,x5934,x5935),f661(x5933,x5932,x5934,x5935))
% 15.02/14.81 [594]~E(x5941,x5942)+E(f661(x5943,x5944,x5941,x5945),f661(x5943,x5944,x5942,x5945))
% 15.02/14.81 [595]~E(x5951,x5952)+E(f661(x5953,x5954,x5955,x5951),f661(x5953,x5954,x5955,x5952))
% 15.02/14.81 [596]~E(x5961,x5962)+E(f125(x5961,x5963),f125(x5962,x5963))
% 15.02/14.81 [597]~E(x5971,x5972)+E(f125(x5973,x5971),f125(x5973,x5972))
% 15.02/14.81 [598]~E(x5981,x5982)+E(f258(x5981,x5983,x5984,x5985),f258(x5982,x5983,x5984,x5985))
% 15.02/14.81 [599]~E(x5991,x5992)+E(f258(x5993,x5991,x5994,x5995),f258(x5993,x5992,x5994,x5995))
% 15.02/14.81 [600]~E(x6001,x6002)+E(f258(x6003,x6004,x6001,x6005),f258(x6003,x6004,x6002,x6005))
% 15.02/14.81 [601]~E(x6011,x6012)+E(f258(x6013,x6014,x6015,x6011),f258(x6013,x6014,x6015,x6012))
% 15.02/14.81 [602]~E(x6021,x6022)+E(f216(x6021,x6023),f216(x6022,x6023))
% 15.02/14.81 [603]~E(x6031,x6032)+E(f216(x6033,x6031),f216(x6033,x6032))
% 15.02/14.81 [604]~E(x6041,x6042)+E(f804(x6041,x6043),f804(x6042,x6043))
% 15.02/14.81 [605]~E(x6051,x6052)+E(f804(x6053,x6051),f804(x6053,x6052))
% 15.02/14.81 [606]~E(x6061,x6062)+E(f679(x6061,x6063,x6064),f679(x6062,x6063,x6064))
% 15.02/14.81 [607]~E(x6071,x6072)+E(f679(x6073,x6071,x6074),f679(x6073,x6072,x6074))
% 15.02/14.81 [608]~E(x6081,x6082)+E(f679(x6083,x6084,x6081),f679(x6083,x6084,x6082))
% 15.02/14.81 [609]~E(x6091,x6092)+E(f185(x6091,x6093,x6094,x6095),f185(x6092,x6093,x6094,x6095))
% 15.02/14.81 [610]~E(x6101,x6102)+E(f185(x6103,x6101,x6104,x6105),f185(x6103,x6102,x6104,x6105))
% 15.02/14.81 [611]~E(x6111,x6112)+E(f185(x6113,x6114,x6111,x6115),f185(x6113,x6114,x6112,x6115))
% 15.02/14.81 [612]~E(x6121,x6122)+E(f185(x6123,x6124,x6125,x6121),f185(x6123,x6124,x6125,x6122))
% 15.02/14.81 [613]~E(x6131,x6132)+E(f871(x6131,x6133,x6134,x6135,x6136),f871(x6132,x6133,x6134,x6135,x6136))
% 15.02/14.81 [614]~E(x6141,x6142)+E(f871(x6143,x6141,x6144,x6145,x6146),f871(x6143,x6142,x6144,x6145,x6146))
% 15.02/14.81 [615]~E(x6151,x6152)+E(f871(x6153,x6154,x6151,x6155,x6156),f871(x6153,x6154,x6152,x6155,x6156))
% 15.02/14.81 [616]~E(x6161,x6162)+E(f871(x6163,x6164,x6165,x6161,x6166),f871(x6163,x6164,x6165,x6162,x6166))
% 15.02/14.81 [617]~E(x6171,x6172)+E(f871(x6173,x6174,x6175,x6176,x6171),f871(x6173,x6174,x6175,x6176,x6172))
% 15.02/14.81 [618]~E(x6181,x6182)+E(f526(x6181,x6183),f526(x6182,x6183))
% 15.02/14.81 [619]~E(x6191,x6192)+E(f526(x6193,x6191),f526(x6193,x6192))
% 15.02/14.81 [620]~E(x6201,x6202)+E(f886(x6201,x6203,x6204),f886(x6202,x6203,x6204))
% 15.02/14.81 [621]~E(x6211,x6212)+E(f886(x6213,x6211,x6214),f886(x6213,x6212,x6214))
% 15.02/14.81 [622]~E(x6221,x6222)+E(f886(x6223,x6224,x6221),f886(x6223,x6224,x6222))
% 15.02/14.81 [623]~E(x6231,x6232)+E(f76(x6231,x6233,x6234,x6235),f76(x6232,x6233,x6234,x6235))
% 15.02/14.81 [624]~E(x6241,x6242)+E(f76(x6243,x6241,x6244,x6245),f76(x6243,x6242,x6244,x6245))
% 15.02/14.81 [625]~E(x6251,x6252)+E(f76(x6253,x6254,x6251,x6255),f76(x6253,x6254,x6252,x6255))
% 15.02/14.81 [626]~E(x6261,x6262)+E(f76(x6263,x6264,x6265,x6261),f76(x6263,x6264,x6265,x6262))
% 15.02/14.81 [627]~E(x6271,x6272)+E(f232(x6271,x6273,x6274,x6275),f232(x6272,x6273,x6274,x6275))
% 15.02/14.81 [628]~E(x6281,x6282)+E(f232(x6283,x6281,x6284,x6285),f232(x6283,x6282,x6284,x6285))
% 15.02/14.81 [629]~E(x6291,x6292)+E(f232(x6293,x6294,x6291,x6295),f232(x6293,x6294,x6292,x6295))
% 15.02/14.81 [630]~E(x6301,x6302)+E(f232(x6303,x6304,x6305,x6301),f232(x6303,x6304,x6305,x6302))
% 15.02/14.81 [631]~E(x6311,x6312)+E(f484(x6311,x6313,x6314),f484(x6312,x6313,x6314))
% 15.02/14.81 [632]~E(x6321,x6322)+E(f484(x6323,x6321,x6324),f484(x6323,x6322,x6324))
% 15.02/14.81 [633]~E(x6331,x6332)+E(f484(x6333,x6334,x6331),f484(x6333,x6334,x6332))
% 15.02/14.81 [634]~E(x6341,x6342)+E(f550(x6341,x6343,x6344,x6345,x6346),f550(x6342,x6343,x6344,x6345,x6346))
% 15.02/14.81 [635]~E(x6351,x6352)+E(f550(x6353,x6351,x6354,x6355,x6356),f550(x6353,x6352,x6354,x6355,x6356))
% 15.02/14.81 [636]~E(x6361,x6362)+E(f550(x6363,x6364,x6361,x6365,x6366),f550(x6363,x6364,x6362,x6365,x6366))
% 15.02/14.81 [637]~E(x6371,x6372)+E(f550(x6373,x6374,x6375,x6371,x6376),f550(x6373,x6374,x6375,x6372,x6376))
% 15.02/14.81 [638]~E(x6381,x6382)+E(f550(x6383,x6384,x6385,x6386,x6381),f550(x6383,x6384,x6385,x6386,x6382))
% 15.02/14.81 [639]~E(x6391,x6392)+E(f680(x6391,x6393,x6394,x6395,x6396),f680(x6392,x6393,x6394,x6395,x6396))
% 15.02/14.81 [640]~E(x6401,x6402)+E(f680(x6403,x6401,x6404,x6405,x6406),f680(x6403,x6402,x6404,x6405,x6406))
% 15.02/14.81 [641]~E(x6411,x6412)+E(f680(x6413,x6414,x6411,x6415,x6416),f680(x6413,x6414,x6412,x6415,x6416))
% 15.02/14.81 [642]~E(x6421,x6422)+E(f680(x6423,x6424,x6425,x6421,x6426),f680(x6423,x6424,x6425,x6422,x6426))
% 15.02/14.81 [643]~E(x6431,x6432)+E(f680(x6433,x6434,x6435,x6436,x6431),f680(x6433,x6434,x6435,x6436,x6432))
% 15.02/14.81 [644]~E(x6441,x6442)+E(f55(x6441),f55(x6442))
% 15.02/14.81 [645]~E(x6451,x6452)+E(f642(x6451,x6453),f642(x6452,x6453))
% 15.02/14.81 [646]~E(x6461,x6462)+E(f642(x6463,x6461),f642(x6463,x6462))
% 15.02/14.81 [647]~E(x6471,x6472)+E(f40(x6471),f40(x6472))
% 15.02/14.81 [648]~E(x6481,x6482)+E(f614(x6481,x6483,x6484),f614(x6482,x6483,x6484))
% 15.02/14.81 [649]~E(x6491,x6492)+E(f614(x6493,x6491,x6494),f614(x6493,x6492,x6494))
% 15.02/14.81 [650]~E(x6501,x6502)+E(f614(x6503,x6504,x6501),f614(x6503,x6504,x6502))
% 15.02/14.81 [651]~E(x6511,x6512)+E(f560(x6511,x6513,x6514,x6515,x6516,x6517),f560(x6512,x6513,x6514,x6515,x6516,x6517))
% 15.02/14.81 [652]~E(x6521,x6522)+E(f560(x6523,x6521,x6524,x6525,x6526,x6527),f560(x6523,x6522,x6524,x6525,x6526,x6527))
% 15.02/14.81 [653]~E(x6531,x6532)+E(f560(x6533,x6534,x6531,x6535,x6536,x6537),f560(x6533,x6534,x6532,x6535,x6536,x6537))
% 15.02/14.81 [654]~E(x6541,x6542)+E(f560(x6543,x6544,x6545,x6541,x6546,x6547),f560(x6543,x6544,x6545,x6542,x6546,x6547))
% 15.02/14.81 [655]~E(x6551,x6552)+E(f560(x6553,x6554,x6555,x6556,x6551,x6557),f560(x6553,x6554,x6555,x6556,x6552,x6557))
% 15.02/14.81 [656]~E(x6561,x6562)+E(f560(x6563,x6564,x6565,x6566,x6567,x6561),f560(x6563,x6564,x6565,x6566,x6567,x6562))
% 15.02/14.81 [657]~E(x6571,x6572)+E(f816(x6571,x6573,x6574,x6575,x6576,x6577),f816(x6572,x6573,x6574,x6575,x6576,x6577))
% 15.02/14.81 [658]~E(x6581,x6582)+E(f816(x6583,x6581,x6584,x6585,x6586,x6587),f816(x6583,x6582,x6584,x6585,x6586,x6587))
% 15.02/14.81 [659]~E(x6591,x6592)+E(f816(x6593,x6594,x6591,x6595,x6596,x6597),f816(x6593,x6594,x6592,x6595,x6596,x6597))
% 15.02/14.81 [660]~E(x6601,x6602)+E(f816(x6603,x6604,x6605,x6601,x6606,x6607),f816(x6603,x6604,x6605,x6602,x6606,x6607))
% 15.02/14.81 [661]~E(x6611,x6612)+E(f816(x6613,x6614,x6615,x6616,x6611,x6617),f816(x6613,x6614,x6615,x6616,x6612,x6617))
% 15.02/14.81 [662]~E(x6621,x6622)+E(f816(x6623,x6624,x6625,x6626,x6627,x6621),f816(x6623,x6624,x6625,x6626,x6627,x6622))
% 15.02/14.81 [663]~E(x6631,x6632)+E(f197(x6631,x6633,x6634,x6635),f197(x6632,x6633,x6634,x6635))
% 15.02/14.81 [664]~E(x6641,x6642)+E(f197(x6643,x6641,x6644,x6645),f197(x6643,x6642,x6644,x6645))
% 15.02/14.81 [665]~E(x6651,x6652)+E(f197(x6653,x6654,x6651,x6655),f197(x6653,x6654,x6652,x6655))
% 15.02/14.81 [666]~E(x6661,x6662)+E(f197(x6663,x6664,x6665,x6661),f197(x6663,x6664,x6665,x6662))
% 15.02/14.81 [667]~E(x6671,x6672)+E(f503(x6671,x6673,x6674,x6675,x6676),f503(x6672,x6673,x6674,x6675,x6676))
% 15.02/14.81 [668]~E(x6681,x6682)+E(f503(x6683,x6681,x6684,x6685,x6686),f503(x6683,x6682,x6684,x6685,x6686))
% 15.02/14.81 [669]~E(x6691,x6692)+E(f503(x6693,x6694,x6691,x6695,x6696),f503(x6693,x6694,x6692,x6695,x6696))
% 15.02/14.81 [670]~E(x6701,x6702)+E(f503(x6703,x6704,x6705,x6701,x6706),f503(x6703,x6704,x6705,x6702,x6706))
% 15.02/14.81 [671]~E(x6711,x6712)+E(f503(x6713,x6714,x6715,x6716,x6711),f503(x6713,x6714,x6715,x6716,x6712))
% 15.02/14.81 [672]~E(x6721,x6722)+E(f371(x6721,x6723,x6724),f371(x6722,x6723,x6724))
% 15.02/14.81 [673]~E(x6731,x6732)+E(f371(x6733,x6731,x6734),f371(x6733,x6732,x6734))
% 15.02/14.81 [674]~E(x6741,x6742)+E(f371(x6743,x6744,x6741),f371(x6743,x6744,x6742))
% 15.02/14.81 [675]~E(x6751,x6752)+E(f890(x6751,x6753,x6754),f890(x6752,x6753,x6754))
% 15.02/14.81 [676]~E(x6761,x6762)+E(f890(x6763,x6761,x6764),f890(x6763,x6762,x6764))
% 15.02/14.81 [677]~E(x6771,x6772)+E(f890(x6773,x6774,x6771),f890(x6773,x6774,x6772))
% 15.02/14.81 [678]~E(x6781,x6782)+E(f183(x6781,x6783),f183(x6782,x6783))
% 15.02/14.81 [679]~E(x6791,x6792)+E(f183(x6793,x6791),f183(x6793,x6792))
% 15.02/14.81 [680]~E(x6801,x6802)+E(f311(x6801,x6803),f311(x6802,x6803))
% 15.02/14.81 [681]~E(x6811,x6812)+E(f311(x6813,x6811),f311(x6813,x6812))
% 15.02/14.81 [682]~E(x6821,x6822)+E(f145(x6821,x6823),f145(x6822,x6823))
% 15.02/14.81 [683]~E(x6831,x6832)+E(f145(x6833,x6831),f145(x6833,x6832))
% 15.02/14.81 [684]~E(x6841,x6842)+E(f45(x6841,x6843),f45(x6842,x6843))
% 15.02/14.81 [685]~E(x6851,x6852)+E(f45(x6853,x6851),f45(x6853,x6852))
% 15.02/14.81 [686]~E(x6861,x6862)+E(f344(x6861,x6863,x6864,x6865),f344(x6862,x6863,x6864,x6865))
% 15.02/14.81 [687]~E(x6871,x6872)+E(f344(x6873,x6871,x6874,x6875),f344(x6873,x6872,x6874,x6875))
% 15.02/14.81 [688]~E(x6881,x6882)+E(f344(x6883,x6884,x6881,x6885),f344(x6883,x6884,x6882,x6885))
% 15.02/14.81 [689]~E(x6891,x6892)+E(f344(x6893,x6894,x6895,x6891),f344(x6893,x6894,x6895,x6892))
% 15.02/14.81 [690]~E(x6901,x6902)+E(f646(x6901,x6903,x6904,x6905,x6906,x6907),f646(x6902,x6903,x6904,x6905,x6906,x6907))
% 15.02/14.81 [691]~E(x6911,x6912)+E(f646(x6913,x6911,x6914,x6915,x6916,x6917),f646(x6913,x6912,x6914,x6915,x6916,x6917))
% 15.02/14.81 [692]~E(x6921,x6922)+E(f646(x6923,x6924,x6921,x6925,x6926,x6927),f646(x6923,x6924,x6922,x6925,x6926,x6927))
% 15.02/14.81 [693]~E(x6931,x6932)+E(f646(x6933,x6934,x6935,x6931,x6936,x6937),f646(x6933,x6934,x6935,x6932,x6936,x6937))
% 15.02/14.81 [694]~E(x6941,x6942)+E(f646(x6943,x6944,x6945,x6946,x6941,x6947),f646(x6943,x6944,x6945,x6946,x6942,x6947))
% 15.02/14.81 [695]~E(x6951,x6952)+E(f646(x6953,x6954,x6955,x6956,x6957,x6951),f646(x6953,x6954,x6955,x6956,x6957,x6952))
% 15.02/14.81 [696]~E(x6961,x6962)+E(f215(x6961,x6963),f215(x6962,x6963))
% 15.02/14.81 [697]~E(x6971,x6972)+E(f215(x6973,x6971),f215(x6973,x6972))
% 15.02/14.81 [698]~E(x6981,x6982)+E(f146(x6981,x6983),f146(x6982,x6983))
% 15.02/14.81 [699]~E(x6991,x6992)+E(f146(x6993,x6991),f146(x6993,x6992))
% 15.02/14.81 [700]~E(x7001,x7002)+E(f469(x7001,x7003,x7004,x7005),f469(x7002,x7003,x7004,x7005))
% 15.02/14.81 [701]~E(x7011,x7012)+E(f469(x7013,x7011,x7014,x7015),f469(x7013,x7012,x7014,x7015))
% 15.02/14.81 [702]~E(x7021,x7022)+E(f469(x7023,x7024,x7021,x7025),f469(x7023,x7024,x7022,x7025))
% 15.02/14.81 [703]~E(x7031,x7032)+E(f469(x7033,x7034,x7035,x7031),f469(x7033,x7034,x7035,x7032))
% 15.02/14.81 [704]~E(x7041,x7042)+E(f150(x7041,x7043,x7044,x7045),f150(x7042,x7043,x7044,x7045))
% 15.02/14.81 [705]~E(x7051,x7052)+E(f150(x7053,x7051,x7054,x7055),f150(x7053,x7052,x7054,x7055))
% 15.02/14.81 [706]~E(x7061,x7062)+E(f150(x7063,x7064,x7061,x7065),f150(x7063,x7064,x7062,x7065))
% 15.02/14.81 [707]~E(x7071,x7072)+E(f150(x7073,x7074,x7075,x7071),f150(x7073,x7074,x7075,x7072))
% 15.02/14.81 [708]~E(x7081,x7082)+E(f249(x7081,x7083,x7084),f249(x7082,x7083,x7084))
% 15.02/14.81 [709]~E(x7091,x7092)+E(f249(x7093,x7091,x7094),f249(x7093,x7092,x7094))
% 15.02/14.81 [710]~E(x7101,x7102)+E(f249(x7103,x7104,x7101),f249(x7103,x7104,x7102))
% 15.02/14.81 [711]~E(x7111,x7112)+E(f130(x7111,x7113,x7114,x7115),f130(x7112,x7113,x7114,x7115))
% 15.02/14.81 [712]~E(x7121,x7122)+E(f130(x7123,x7121,x7124,x7125),f130(x7123,x7122,x7124,x7125))
% 15.02/14.81 [713]~E(x7131,x7132)+E(f130(x7133,x7134,x7131,x7135),f130(x7133,x7134,x7132,x7135))
% 15.02/14.81 [714]~E(x7141,x7142)+E(f130(x7143,x7144,x7145,x7141),f130(x7143,x7144,x7145,x7142))
% 15.02/14.81 [715]~E(x7151,x7152)+E(f479(x7151,x7153,x7154,x7155),f479(x7152,x7153,x7154,x7155))
% 15.02/14.81 [716]~E(x7161,x7162)+E(f479(x7163,x7161,x7164,x7165),f479(x7163,x7162,x7164,x7165))
% 15.02/14.81 [717]~E(x7171,x7172)+E(f479(x7173,x7174,x7171,x7175),f479(x7173,x7174,x7172,x7175))
% 15.02/14.81 [718]~E(x7181,x7182)+E(f479(x7183,x7184,x7185,x7181),f479(x7183,x7184,x7185,x7182))
% 15.02/14.81 [719]~E(x7191,x7192)+E(f776(x7191,x7193,x7194,x7195),f776(x7192,x7193,x7194,x7195))
% 15.02/14.81 [720]~E(x7201,x7202)+E(f776(x7203,x7201,x7204,x7205),f776(x7203,x7202,x7204,x7205))
% 15.02/14.81 [721]~E(x7211,x7212)+E(f776(x7213,x7214,x7211,x7215),f776(x7213,x7214,x7212,x7215))
% 15.02/14.81 [722]~E(x7221,x7222)+E(f776(x7223,x7224,x7225,x7221),f776(x7223,x7224,x7225,x7222))
% 15.02/14.81 [723]~E(x7231,x7232)+E(f830(x7231,x7233,x7234,x7235),f830(x7232,x7233,x7234,x7235))
% 15.02/14.81 [724]~E(x7241,x7242)+E(f830(x7243,x7241,x7244,x7245),f830(x7243,x7242,x7244,x7245))
% 15.02/14.81 [725]~E(x7251,x7252)+E(f830(x7253,x7254,x7251,x7255),f830(x7253,x7254,x7252,x7255))
% 15.02/14.81 [726]~E(x7261,x7262)+E(f830(x7263,x7264,x7265,x7261),f830(x7263,x7264,x7265,x7262))
% 15.02/14.81 [727]~E(x7271,x7272)+E(f586(x7271,x7273,x7274),f586(x7272,x7273,x7274))
% 15.02/14.81 [728]~E(x7281,x7282)+E(f586(x7283,x7281,x7284),f586(x7283,x7282,x7284))
% 15.02/14.81 [729]~E(x7291,x7292)+E(f586(x7293,x7294,x7291),f586(x7293,x7294,x7292))
% 15.02/14.81 [730]~E(x7301,x7302)+E(f908(x7301,x7303,x7304,x7305,x7306),f908(x7302,x7303,x7304,x7305,x7306))
% 15.02/14.81 [731]~E(x7311,x7312)+E(f908(x7313,x7311,x7314,x7315,x7316),f908(x7313,x7312,x7314,x7315,x7316))
% 15.02/14.81 [732]~E(x7321,x7322)+E(f908(x7323,x7324,x7321,x7325,x7326),f908(x7323,x7324,x7322,x7325,x7326))
% 15.02/14.81 [733]~E(x7331,x7332)+E(f908(x7333,x7334,x7335,x7331,x7336),f908(x7333,x7334,x7335,x7332,x7336))
% 15.02/14.81 [734]~E(x7341,x7342)+E(f908(x7343,x7344,x7345,x7346,x7341),f908(x7343,x7344,x7345,x7346,x7342))
% 15.02/14.81 [735]~E(x7351,x7352)+E(f135(x7351),f135(x7352))
% 15.02/14.81 [736]~E(x7361,x7362)+E(f806(x7361),f806(x7362))
% 15.02/14.81 [737]~E(x7371,x7372)+E(f500(x7371,x7373,x7374,x7375,x7376),f500(x7372,x7373,x7374,x7375,x7376))
% 15.02/14.81 [738]~E(x7381,x7382)+E(f500(x7383,x7381,x7384,x7385,x7386),f500(x7383,x7382,x7384,x7385,x7386))
% 15.02/14.81 [739]~E(x7391,x7392)+E(f500(x7393,x7394,x7391,x7395,x7396),f500(x7393,x7394,x7392,x7395,x7396))
% 15.02/14.81 [740]~E(x7401,x7402)+E(f500(x7403,x7404,x7405,x7401,x7406),f500(x7403,x7404,x7405,x7402,x7406))
% 15.02/14.81 [741]~E(x7411,x7412)+E(f500(x7413,x7414,x7415,x7416,x7411),f500(x7413,x7414,x7415,x7416,x7412))
% 15.02/14.81 [742]~E(x7421,x7422)+E(f129(x7421),f129(x7422))
% 15.02/14.81 [743]~E(x7431,x7432)+E(f896(x7431,x7433,x7434),f896(x7432,x7433,x7434))
% 15.02/14.81 [744]~E(x7441,x7442)+E(f896(x7443,x7441,x7444),f896(x7443,x7442,x7444))
% 15.02/14.81 [745]~E(x7451,x7452)+E(f896(x7453,x7454,x7451),f896(x7453,x7454,x7452))
% 15.02/14.81 [746]~E(x7461,x7462)+E(f814(x7461,x7463,x7464,x7465,x7466,x7467),f814(x7462,x7463,x7464,x7465,x7466,x7467))
% 15.02/14.81 [747]~E(x7471,x7472)+E(f814(x7473,x7471,x7474,x7475,x7476,x7477),f814(x7473,x7472,x7474,x7475,x7476,x7477))
% 15.02/14.81 [748]~E(x7481,x7482)+E(f814(x7483,x7484,x7481,x7485,x7486,x7487),f814(x7483,x7484,x7482,x7485,x7486,x7487))
% 15.02/14.81 [749]~E(x7491,x7492)+E(f814(x7493,x7494,x7495,x7491,x7496,x7497),f814(x7493,x7494,x7495,x7492,x7496,x7497))
% 15.02/14.81 [750]~E(x7501,x7502)+E(f814(x7503,x7504,x7505,x7506,x7501,x7507),f814(x7503,x7504,x7505,x7506,x7502,x7507))
% 15.02/14.81 [751]~E(x7511,x7512)+E(f814(x7513,x7514,x7515,x7516,x7517,x7511),f814(x7513,x7514,x7515,x7516,x7517,x7512))
% 15.02/14.81 [752]~E(x7521,x7522)+E(f362(x7521,x7523,x7524,x7525),f362(x7522,x7523,x7524,x7525))
% 15.02/14.81 [753]~E(x7531,x7532)+E(f362(x7533,x7531,x7534,x7535),f362(x7533,x7532,x7534,x7535))
% 15.02/14.81 [754]~E(x7541,x7542)+E(f362(x7543,x7544,x7541,x7545),f362(x7543,x7544,x7542,x7545))
% 15.02/14.81 [755]~E(x7551,x7552)+E(f362(x7553,x7554,x7555,x7551),f362(x7553,x7554,x7555,x7552))
% 15.02/14.81 [756]~E(x7561,x7562)+E(f440(x7561,x7563,x7564,x7565,x7566),f440(x7562,x7563,x7564,x7565,x7566))
% 15.02/14.81 [757]~E(x7571,x7572)+E(f440(x7573,x7571,x7574,x7575,x7576),f440(x7573,x7572,x7574,x7575,x7576))
% 15.02/14.81 [758]~E(x7581,x7582)+E(f440(x7583,x7584,x7581,x7585,x7586),f440(x7583,x7584,x7582,x7585,x7586))
% 15.02/14.81 [759]~E(x7591,x7592)+E(f440(x7593,x7594,x7595,x7591,x7596),f440(x7593,x7594,x7595,x7592,x7596))
% 15.02/14.81 [760]~E(x7601,x7602)+E(f440(x7603,x7604,x7605,x7606,x7601),f440(x7603,x7604,x7605,x7606,x7602))
% 15.02/14.81 [761]~E(x7611,x7612)+E(f703(x7611,x7613,x7614,x7615,x7616),f703(x7612,x7613,x7614,x7615,x7616))
% 15.02/14.81 [762]~E(x7621,x7622)+E(f703(x7623,x7621,x7624,x7625,x7626),f703(x7623,x7622,x7624,x7625,x7626))
% 15.02/14.81 [763]~E(x7631,x7632)+E(f703(x7633,x7634,x7631,x7635,x7636),f703(x7633,x7634,x7632,x7635,x7636))
% 15.02/14.81 [764]~E(x7641,x7642)+E(f703(x7643,x7644,x7645,x7641,x7646),f703(x7643,x7644,x7645,x7642,x7646))
% 15.02/14.81 [765]~E(x7651,x7652)+E(f703(x7653,x7654,x7655,x7656,x7651),f703(x7653,x7654,x7655,x7656,x7652))
% 15.02/14.81 [766]~E(x7661,x7662)+E(f296(x7661,x7663,x7664,x7665,x7666),f296(x7662,x7663,x7664,x7665,x7666))
% 15.02/14.81 [767]~E(x7671,x7672)+E(f296(x7673,x7671,x7674,x7675,x7676),f296(x7673,x7672,x7674,x7675,x7676))
% 15.02/14.81 [768]~E(x7681,x7682)+E(f296(x7683,x7684,x7681,x7685,x7686),f296(x7683,x7684,x7682,x7685,x7686))
% 15.02/14.81 [769]~E(x7691,x7692)+E(f296(x7693,x7694,x7695,x7691,x7696),f296(x7693,x7694,x7695,x7692,x7696))
% 15.02/14.81 [770]~E(x7701,x7702)+E(f296(x7703,x7704,x7705,x7706,x7701),f296(x7703,x7704,x7705,x7706,x7702))
% 15.02/14.81 [771]~E(x7711,x7712)+E(f280(x7711),f280(x7712))
% 15.02/14.81 [772]~E(x7721,x7722)+E(f155(x7721,x7723,x7724),f155(x7722,x7723,x7724))
% 15.02/14.81 [773]~E(x7731,x7732)+E(f155(x7733,x7731,x7734),f155(x7733,x7732,x7734))
% 15.02/14.81 [774]~E(x7741,x7742)+E(f155(x7743,x7744,x7741),f155(x7743,x7744,x7742))
% 15.02/14.81 [775]~E(x7751,x7752)+E(f815(x7751,x7753,x7754,x7755,x7756,x7757),f815(x7752,x7753,x7754,x7755,x7756,x7757))
% 15.02/14.81 [776]~E(x7761,x7762)+E(f815(x7763,x7761,x7764,x7765,x7766,x7767),f815(x7763,x7762,x7764,x7765,x7766,x7767))
% 15.02/14.81 [777]~E(x7771,x7772)+E(f815(x7773,x7774,x7771,x7775,x7776,x7777),f815(x7773,x7774,x7772,x7775,x7776,x7777))
% 15.02/14.81 [778]~E(x7781,x7782)+E(f815(x7783,x7784,x7785,x7781,x7786,x7787),f815(x7783,x7784,x7785,x7782,x7786,x7787))
% 15.02/14.81 [779]~E(x7791,x7792)+E(f815(x7793,x7794,x7795,x7796,x7791,x7797),f815(x7793,x7794,x7795,x7796,x7792,x7797))
% 15.02/14.81 [780]~E(x7801,x7802)+E(f815(x7803,x7804,x7805,x7806,x7807,x7801),f815(x7803,x7804,x7805,x7806,x7807,x7802))
% 15.02/14.81 [781]~E(x7811,x7812)+E(f361(x7811,x7813,x7814,x7815),f361(x7812,x7813,x7814,x7815))
% 15.02/14.81 [782]~E(x7821,x7822)+E(f361(x7823,x7821,x7824,x7825),f361(x7823,x7822,x7824,x7825))
% 15.02/14.81 [783]~E(x7831,x7832)+E(f361(x7833,x7834,x7831,x7835),f361(x7833,x7834,x7832,x7835))
% 15.02/14.81 [784]~E(x7841,x7842)+E(f361(x7843,x7844,x7845,x7841),f361(x7843,x7844,x7845,x7842))
% 15.02/14.81 [785]~E(x7851,x7852)+E(f90(x7851),f90(x7852))
% 15.02/14.81 [786]~E(x7861,x7862)+E(f67(x7861,x7863,x7864),f67(x7862,x7863,x7864))
% 15.02/14.81 [787]~E(x7871,x7872)+E(f67(x7873,x7871,x7874),f67(x7873,x7872,x7874))
% 15.02/14.81 [788]~E(x7881,x7882)+E(f67(x7883,x7884,x7881),f67(x7883,x7884,x7882))
% 15.02/14.81 [789]~E(x7891,x7892)+E(f300(x7891),f300(x7892))
% 15.02/14.81 [790]~E(x7901,x7902)+E(f170(x7901,x7903,x7904),f170(x7902,x7903,x7904))
% 15.02/14.81 [791]~E(x7911,x7912)+E(f170(x7913,x7911,x7914),f170(x7913,x7912,x7914))
% 15.02/14.81 [792]~E(x7921,x7922)+E(f170(x7923,x7924,x7921),f170(x7923,x7924,x7922))
% 15.02/14.81 [793]~E(x7931,x7932)+E(f885(x7931,x7933,x7934),f885(x7932,x7933,x7934))
% 15.02/14.81 [794]~E(x7941,x7942)+E(f885(x7943,x7941,x7944),f885(x7943,x7942,x7944))
% 15.02/14.81 [795]~E(x7951,x7952)+E(f885(x7953,x7954,x7951),f885(x7953,x7954,x7952))
% 15.02/14.81 [796]~E(x7961,x7962)+E(f224(x7961,x7963,x7964,x7965,x7966),f224(x7962,x7963,x7964,x7965,x7966))
% 15.02/14.81 [797]~E(x7971,x7972)+E(f224(x7973,x7971,x7974,x7975,x7976),f224(x7973,x7972,x7974,x7975,x7976))
% 15.02/14.81 [798]~E(x7981,x7982)+E(f224(x7983,x7984,x7981,x7985,x7986),f224(x7983,x7984,x7982,x7985,x7986))
% 15.02/14.81 [799]~E(x7991,x7992)+E(f224(x7993,x7994,x7995,x7991,x7996),f224(x7993,x7994,x7995,x7992,x7996))
% 15.02/14.81 [800]~E(x8001,x8002)+E(f224(x8003,x8004,x8005,x8006,x8001),f224(x8003,x8004,x8005,x8006,x8002))
% 15.02/14.81 [801]~E(x8011,x8012)+E(f460(x8011,x8013,x8014,x8015),f460(x8012,x8013,x8014,x8015))
% 15.02/14.81 [802]~E(x8021,x8022)+E(f460(x8023,x8021,x8024,x8025),f460(x8023,x8022,x8024,x8025))
% 15.02/14.81 [803]~E(x8031,x8032)+E(f460(x8033,x8034,x8031,x8035),f460(x8033,x8034,x8032,x8035))
% 15.02/14.81 [804]~E(x8041,x8042)+E(f460(x8043,x8044,x8045,x8041),f460(x8043,x8044,x8045,x8042))
% 15.02/14.81 [805]~E(x8051,x8052)+E(f578(x8051,x8053,x8054,x8055),f578(x8052,x8053,x8054,x8055))
% 15.02/14.81 [806]~E(x8061,x8062)+E(f578(x8063,x8061,x8064,x8065),f578(x8063,x8062,x8064,x8065))
% 15.02/14.81 [807]~E(x8071,x8072)+E(f578(x8073,x8074,x8071,x8075),f578(x8073,x8074,x8072,x8075))
% 15.02/14.81 [808]~E(x8081,x8082)+E(f578(x8083,x8084,x8085,x8081),f578(x8083,x8084,x8085,x8082))
% 15.02/14.81 [809]~E(x8091,x8092)+E(f166(x8091,x8093,x8094),f166(x8092,x8093,x8094))
% 15.02/14.81 [810]~E(x8101,x8102)+E(f166(x8103,x8101,x8104),f166(x8103,x8102,x8104))
% 15.02/14.81 [811]~E(x8111,x8112)+E(f166(x8113,x8114,x8111),f166(x8113,x8114,x8112))
% 15.02/14.81 [812]~E(x8121,x8122)+E(f355(x8121,x8123,x8124),f355(x8122,x8123,x8124))
% 15.02/14.81 [813]~E(x8131,x8132)+E(f355(x8133,x8131,x8134),f355(x8133,x8132,x8134))
% 15.02/14.81 [814]~E(x8141,x8142)+E(f355(x8143,x8144,x8141),f355(x8143,x8144,x8142))
% 15.02/14.81 [815]~E(x8151,x8152)+E(f269(x8151,x8153),f269(x8152,x8153))
% 15.02/14.81 [816]~E(x8161,x8162)+E(f269(x8163,x8161),f269(x8163,x8162))
% 15.02/14.81 [817]~E(x8171,x8172)+E(f771(x8171,x8173,x8174,x8175),f771(x8172,x8173,x8174,x8175))
% 15.02/14.81 [818]~E(x8181,x8182)+E(f771(x8183,x8181,x8184,x8185),f771(x8183,x8182,x8184,x8185))
% 15.02/14.81 [819]~E(x8191,x8192)+E(f771(x8193,x8194,x8191,x8195),f771(x8193,x8194,x8192,x8195))
% 15.02/14.81 [820]~E(x8201,x8202)+E(f771(x8203,x8204,x8205,x8201),f771(x8203,x8204,x8205,x8202))
% 15.02/14.81 [821]~E(x8211,x8212)+E(f463(x8211,x8213,x8214,x8215),f463(x8212,x8213,x8214,x8215))
% 15.02/14.81 [822]~E(x8221,x8222)+E(f463(x8223,x8221,x8224,x8225),f463(x8223,x8222,x8224,x8225))
% 15.02/14.81 [823]~E(x8231,x8232)+E(f463(x8233,x8234,x8231,x8235),f463(x8233,x8234,x8232,x8235))
% 15.02/14.81 [824]~E(x8241,x8242)+E(f463(x8243,x8244,x8245,x8241),f463(x8243,x8244,x8245,x8242))
% 15.02/14.81 [825]~E(x8251,x8252)+E(f201(x8251),f201(x8252))
% 15.02/14.81 [826]~E(x8261,x8262)+E(f731(x8261,x8263),f731(x8262,x8263))
% 15.02/14.81 [827]~E(x8271,x8272)+E(f731(x8273,x8271),f731(x8273,x8272))
% 15.02/14.81 [828]~E(x8281,x8282)+E(f257(x8281,x8283,x8284,x8285,x8286,x8287),f257(x8282,x8283,x8284,x8285,x8286,x8287))
% 15.02/14.81 [829]~E(x8291,x8292)+E(f257(x8293,x8291,x8294,x8295,x8296,x8297),f257(x8293,x8292,x8294,x8295,x8296,x8297))
% 15.02/14.81 [830]~E(x8301,x8302)+E(f257(x8303,x8304,x8301,x8305,x8306,x8307),f257(x8303,x8304,x8302,x8305,x8306,x8307))
% 15.02/14.81 [831]~E(x8311,x8312)+E(f257(x8313,x8314,x8315,x8311,x8316,x8317),f257(x8313,x8314,x8315,x8312,x8316,x8317))
% 15.02/14.81 [832]~E(x8321,x8322)+E(f257(x8323,x8324,x8325,x8326,x8321,x8327),f257(x8323,x8324,x8325,x8326,x8322,x8327))
% 15.02/14.81 [833]~E(x8331,x8332)+E(f257(x8333,x8334,x8335,x8336,x8337,x8331),f257(x8333,x8334,x8335,x8336,x8337,x8332))
% 15.02/14.81 [834]~E(x8341,x8342)+E(f148(x8341,x8343,x8344),f148(x8342,x8343,x8344))
% 15.02/14.81 [835]~E(x8351,x8352)+E(f148(x8353,x8351,x8354),f148(x8353,x8352,x8354))
% 15.02/14.81 [836]~E(x8361,x8362)+E(f148(x8363,x8364,x8361),f148(x8363,x8364,x8362))
% 15.02/14.81 [837]~E(x8371,x8372)+E(f807(x8371),f807(x8372))
% 15.02/14.81 [838]~E(x8381,x8382)+E(f85(x8381,x8383),f85(x8382,x8383))
% 15.02/14.81 [839]~E(x8391,x8392)+E(f85(x8393,x8391),f85(x8393,x8392))
% 15.02/14.81 [840]~E(x8401,x8402)+E(f696(x8401,x8403,x8404,x8405,x8406),f696(x8402,x8403,x8404,x8405,x8406))
% 15.02/14.81 [841]~E(x8411,x8412)+E(f696(x8413,x8411,x8414,x8415,x8416),f696(x8413,x8412,x8414,x8415,x8416))
% 15.02/14.81 [842]~E(x8421,x8422)+E(f696(x8423,x8424,x8421,x8425,x8426),f696(x8423,x8424,x8422,x8425,x8426))
% 15.02/14.81 [843]~E(x8431,x8432)+E(f696(x8433,x8434,x8435,x8431,x8436),f696(x8433,x8434,x8435,x8432,x8436))
% 15.02/14.81 [844]~E(x8441,x8442)+E(f696(x8443,x8444,x8445,x8446,x8441),f696(x8443,x8444,x8445,x8446,x8442))
% 15.02/14.81 [845]~E(x8451,x8452)+E(f904(x8451,x8453,x8454,x8455,x8456,x8457,x8458),f904(x8452,x8453,x8454,x8455,x8456,x8457,x8458))
% 15.02/14.81 [846]~E(x8461,x8462)+E(f904(x8463,x8461,x8464,x8465,x8466,x8467,x8468),f904(x8463,x8462,x8464,x8465,x8466,x8467,x8468))
% 15.02/14.81 [847]~E(x8471,x8472)+E(f904(x8473,x8474,x8471,x8475,x8476,x8477,x8478),f904(x8473,x8474,x8472,x8475,x8476,x8477,x8478))
% 15.02/14.81 [848]~E(x8481,x8482)+E(f904(x8483,x8484,x8485,x8481,x8486,x8487,x8488),f904(x8483,x8484,x8485,x8482,x8486,x8487,x8488))
% 15.02/14.81 [849]~E(x8491,x8492)+E(f904(x8493,x8494,x8495,x8496,x8491,x8497,x8498),f904(x8493,x8494,x8495,x8496,x8492,x8497,x8498))
% 15.02/14.81 [850]~E(x8501,x8502)+E(f904(x8503,x8504,x8505,x8506,x8507,x8501,x8508),f904(x8503,x8504,x8505,x8506,x8507,x8502,x8508))
% 15.02/14.81 [851]~E(x8511,x8512)+E(f904(x8513,x8514,x8515,x8516,x8517,x8518,x8511),f904(x8513,x8514,x8515,x8516,x8517,x8518,x8512))
% 15.02/14.81 [852]~E(x8521,x8522)+E(f54(x8521,x8523,x8524),f54(x8522,x8523,x8524))
% 15.02/14.81 [853]~E(x8531,x8532)+E(f54(x8533,x8531,x8534),f54(x8533,x8532,x8534))
% 15.02/14.81 [854]~E(x8541,x8542)+E(f54(x8543,x8544,x8541),f54(x8543,x8544,x8542))
% 15.02/14.81 [855]~E(x8551,x8552)+E(f718(x8551,x8553,x8554),f718(x8552,x8553,x8554))
% 15.02/14.81 [856]~E(x8561,x8562)+E(f718(x8563,x8561,x8564),f718(x8563,x8562,x8564))
% 15.02/14.81 [857]~E(x8571,x8572)+E(f718(x8573,x8574,x8571),f718(x8573,x8574,x8572))
% 15.02/14.81 [858]~E(x8581,x8582)+E(f27(x8581,x8583,x8584),f27(x8582,x8583,x8584))
% 15.02/14.81 [859]~E(x8591,x8592)+E(f27(x8593,x8591,x8594),f27(x8593,x8592,x8594))
% 15.02/14.81 [860]~E(x8601,x8602)+E(f27(x8603,x8604,x8601),f27(x8603,x8604,x8602))
% 15.02/14.81 [861]~E(x8611,x8612)+E(f701(x8611,x8613,x8614,x8615),f701(x8612,x8613,x8614,x8615))
% 15.02/14.81 [862]~E(x8621,x8622)+E(f701(x8623,x8621,x8624,x8625),f701(x8623,x8622,x8624,x8625))
% 15.02/14.81 [863]~E(x8631,x8632)+E(f701(x8633,x8634,x8631,x8635),f701(x8633,x8634,x8632,x8635))
% 15.02/14.81 [864]~E(x8641,x8642)+E(f701(x8643,x8644,x8645,x8641),f701(x8643,x8644,x8645,x8642))
% 15.02/14.81 [865]~E(x8651,x8652)+E(f392(x8651,x8653,x8654),f392(x8652,x8653,x8654))
% 15.02/14.81 [866]~E(x8661,x8662)+E(f392(x8663,x8661,x8664),f392(x8663,x8662,x8664))
% 15.02/14.81 [867]~E(x8671,x8672)+E(f392(x8673,x8674,x8671),f392(x8673,x8674,x8672))
% 15.02/14.81 [868]~E(x8681,x8682)+E(f662(x8681,x8683,x8684),f662(x8682,x8683,x8684))
% 15.02/14.81 [869]~E(x8691,x8692)+E(f662(x8693,x8691,x8694),f662(x8693,x8692,x8694))
% 15.02/14.81 [870]~E(x8701,x8702)+E(f662(x8703,x8704,x8701),f662(x8703,x8704,x8702))
% 15.02/14.81 [871]~E(x8711,x8712)+E(f248(x8711,x8713,x8714),f248(x8712,x8713,x8714))
% 15.02/14.81 [872]~E(x8721,x8722)+E(f248(x8723,x8721,x8724),f248(x8723,x8722,x8724))
% 15.02/14.81 [873]~E(x8731,x8732)+E(f248(x8733,x8734,x8731),f248(x8733,x8734,x8732))
% 15.02/14.81 [874]~E(x8741,x8742)+E(f213(x8741),f213(x8742))
% 15.02/14.81 [875]~E(x8751,x8752)+E(f217(x8751,x8753),f217(x8752,x8753))
% 15.02/14.81 [876]~E(x8761,x8762)+E(f217(x8763,x8761),f217(x8763,x8762))
% 15.02/14.81 [877]~E(x8771,x8772)+E(f846(x8771,x8773,x8774,x8775,x8776,x8777,x8778,x8779),f846(x8772,x8773,x8774,x8775,x8776,x8777,x8778,x8779))
% 15.02/14.81 [878]~E(x8781,x8782)+E(f846(x8783,x8781,x8784,x8785,x8786,x8787,x8788,x8789),f846(x8783,x8782,x8784,x8785,x8786,x8787,x8788,x8789))
% 15.02/14.81 [879]~E(x8791,x8792)+E(f846(x8793,x8794,x8791,x8795,x8796,x8797,x8798,x8799),f846(x8793,x8794,x8792,x8795,x8796,x8797,x8798,x8799))
% 15.02/14.81 [880]~E(x8801,x8802)+E(f846(x8803,x8804,x8805,x8801,x8806,x8807,x8808,x8809),f846(x8803,x8804,x8805,x8802,x8806,x8807,x8808,x8809))
% 15.02/14.81 [881]~E(x8811,x8812)+E(f846(x8813,x8814,x8815,x8816,x8811,x8817,x8818,x8819),f846(x8813,x8814,x8815,x8816,x8812,x8817,x8818,x8819))
% 15.02/14.81 [882]~E(x8821,x8822)+E(f846(x8823,x8824,x8825,x8826,x8827,x8821,x8828,x8829),f846(x8823,x8824,x8825,x8826,x8827,x8822,x8828,x8829))
% 15.02/14.81 [883]~E(x8831,x8832)+E(f846(x8833,x8834,x8835,x8836,x8837,x8838,x8831,x8839),f846(x8833,x8834,x8835,x8836,x8837,x8838,x8832,x8839))
% 15.02/14.81 [884]~E(x8841,x8842)+E(f846(x8843,x8844,x8845,x8846,x8847,x8848,x8849,x8841),f846(x8843,x8844,x8845,x8846,x8847,x8848,x8849,x8842))
% 15.02/14.81 [885]~E(x8851,x8852)+E(f492(x8851,x8853),f492(x8852,x8853))
% 15.02/14.81 [886]~E(x8861,x8862)+E(f492(x8863,x8861),f492(x8863,x8862))
% 15.02/14.81 [887]~E(x8871,x8872)+E(f888(x8871,x8873,x8874,x8875),f888(x8872,x8873,x8874,x8875))
% 15.02/14.81 [888]~E(x8881,x8882)+E(f888(x8883,x8881,x8884,x8885),f888(x8883,x8882,x8884,x8885))
% 15.02/14.81 [889]~E(x8891,x8892)+E(f888(x8893,x8894,x8891,x8895),f888(x8893,x8894,x8892,x8895))
% 15.02/14.81 [890]~E(x8901,x8902)+E(f888(x8903,x8904,x8905,x8901),f888(x8903,x8904,x8905,x8902))
% 15.02/14.81 [891]~E(x8911,x8912)+E(f714(x8911,x8913,x8914),f714(x8912,x8913,x8914))
% 15.02/14.81 [892]~E(x8921,x8922)+E(f714(x8923,x8921,x8924),f714(x8923,x8922,x8924))
% 15.02/14.81 [893]~E(x8931,x8932)+E(f714(x8933,x8934,x8931),f714(x8933,x8934,x8932))
% 15.02/14.81 [894]~E(x8941,x8942)+E(f200(x8941,x8943),f200(x8942,x8943))
% 15.02/14.81 [895]~E(x8951,x8952)+E(f200(x8953,x8951),f200(x8953,x8952))
% 15.02/14.81 [896]~E(x8961,x8962)+E(f789(x8961,x8963,x8964,x8965,x8966,x8967,x8968),f789(x8962,x8963,x8964,x8965,x8966,x8967,x8968))
% 15.02/14.81 [897]~E(x8971,x8972)+E(f789(x8973,x8971,x8974,x8975,x8976,x8977,x8978),f789(x8973,x8972,x8974,x8975,x8976,x8977,x8978))
% 15.02/14.81 [898]~E(x8981,x8982)+E(f789(x8983,x8984,x8981,x8985,x8986,x8987,x8988),f789(x8983,x8984,x8982,x8985,x8986,x8987,x8988))
% 15.02/14.81 [899]~E(x8991,x8992)+E(f789(x8993,x8994,x8995,x8991,x8996,x8997,x8998),f789(x8993,x8994,x8995,x8992,x8996,x8997,x8998))
% 15.02/14.81 [900]~E(x9001,x9002)+E(f789(x9003,x9004,x9005,x9006,x9001,x9007,x9008),f789(x9003,x9004,x9005,x9006,x9002,x9007,x9008))
% 15.02/14.81 [901]~E(x9011,x9012)+E(f789(x9013,x9014,x9015,x9016,x9017,x9011,x9018),f789(x9013,x9014,x9015,x9016,x9017,x9012,x9018))
% 15.02/14.81 [902]~E(x9021,x9022)+E(f789(x9023,x9024,x9025,x9026,x9027,x9028,x9021),f789(x9023,x9024,x9025,x9026,x9027,x9028,x9022))
% 15.02/14.81 [903]~E(x9031,x9032)+E(f779(x9031,x9033,x9034,x9035),f779(x9032,x9033,x9034,x9035))
% 15.02/14.81 [904]~E(x9041,x9042)+E(f779(x9043,x9041,x9044,x9045),f779(x9043,x9042,x9044,x9045))
% 15.02/14.81 [905]~E(x9051,x9052)+E(f779(x9053,x9054,x9051,x9055),f779(x9053,x9054,x9052,x9055))
% 15.02/14.81 [906]~E(x9061,x9062)+E(f779(x9063,x9064,x9065,x9061),f779(x9063,x9064,x9065,x9062))
% 15.02/14.81 [907]~E(x9071,x9072)+E(f766(x9071,x9073,x9074),f766(x9072,x9073,x9074))
% 15.02/14.81 [908]~E(x9081,x9082)+E(f766(x9083,x9081,x9084),f766(x9083,x9082,x9084))
% 15.02/14.81 [909]~E(x9091,x9092)+E(f766(x9093,x9094,x9091),f766(x9093,x9094,x9092))
% 15.02/14.81 [910]~E(x9101,x9102)+E(f553(x9101),f553(x9102))
% 15.02/14.81 [911]~E(x9111,x9112)+E(f373(x9111,x9113,x9114),f373(x9112,x9113,x9114))
% 15.02/14.81 [912]~E(x9121,x9122)+E(f373(x9123,x9121,x9124),f373(x9123,x9122,x9124))
% 15.02/14.81 [913]~E(x9131,x9132)+E(f373(x9133,x9134,x9131),f373(x9133,x9134,x9132))
% 15.02/14.81 [914]~E(x9141,x9142)+E(f407(x9141,x9143),f407(x9142,x9143))
% 15.02/14.81 [915]~E(x9151,x9152)+E(f407(x9153,x9151),f407(x9153,x9152))
% 15.02/14.81 [916]~E(x9161,x9162)+E(f618(x9161,x9163,x9164),f618(x9162,x9163,x9164))
% 15.02/14.81 [917]~E(x9171,x9172)+E(f618(x9173,x9171,x9174),f618(x9173,x9172,x9174))
% 15.02/14.81 [918]~E(x9181,x9182)+E(f618(x9183,x9184,x9181),f618(x9183,x9184,x9182))
% 15.02/14.81 [919]~E(x9191,x9192)+E(f353(x9191,x9193,x9194),f353(x9192,x9193,x9194))
% 15.02/14.81 [920]~E(x9201,x9202)+E(f353(x9203,x9201,x9204),f353(x9203,x9202,x9204))
% 15.02/14.81 [921]~E(x9211,x9212)+E(f353(x9213,x9214,x9211),f353(x9213,x9214,x9212))
% 15.02/14.81 [922]~E(x9221,x9222)+E(f193(x9221,x9223),f193(x9222,x9223))
% 15.02/14.81 [923]~E(x9231,x9232)+E(f193(x9233,x9231),f193(x9233,x9232))
% 15.02/14.81 [924]~E(x9241,x9242)+E(f632(x9241,x9243,x9244,x9245,x9246),f632(x9242,x9243,x9244,x9245,x9246))
% 15.02/14.81 [925]~E(x9251,x9252)+E(f632(x9253,x9251,x9254,x9255,x9256),f632(x9253,x9252,x9254,x9255,x9256))
% 15.02/14.81 [926]~E(x9261,x9262)+E(f632(x9263,x9264,x9261,x9265,x9266),f632(x9263,x9264,x9262,x9265,x9266))
% 15.02/14.81 [927]~E(x9271,x9272)+E(f632(x9273,x9274,x9275,x9271,x9276),f632(x9273,x9274,x9275,x9272,x9276))
% 15.02/14.81 [928]~E(x9281,x9282)+E(f632(x9283,x9284,x9285,x9286,x9281),f632(x9283,x9284,x9285,x9286,x9282))
% 15.02/14.81 [929]~E(x9291,x9292)+E(f121(x9291,x9293),f121(x9292,x9293))
% 15.02/14.81 [930]~E(x9301,x9302)+E(f121(x9303,x9301),f121(x9303,x9302))
% 15.02/14.81 [931]~E(x9311,x9312)+E(f672(x9311,x9313),f672(x9312,x9313))
% 15.02/14.81 [932]~E(x9321,x9322)+E(f672(x9323,x9321),f672(x9323,x9322))
% 15.02/14.81 [933]~E(x9331,x9332)+E(f891(x9331,x9333,x9334),f891(x9332,x9333,x9334))
% 15.02/14.81 [934]~E(x9341,x9342)+E(f891(x9343,x9341,x9344),f891(x9343,x9342,x9344))
% 15.02/14.81 [935]~E(x9351,x9352)+E(f891(x9353,x9354,x9351),f891(x9353,x9354,x9352))
% 15.02/14.81 [936]~E(x9361,x9362)+E(f782(x9361,x9363,x9364,x9365),f782(x9362,x9363,x9364,x9365))
% 15.02/14.81 [937]~E(x9371,x9372)+E(f782(x9373,x9371,x9374,x9375),f782(x9373,x9372,x9374,x9375))
% 15.02/14.81 [938]~E(x9381,x9382)+E(f782(x9383,x9384,x9381,x9385),f782(x9383,x9384,x9382,x9385))
% 15.02/14.81 [939]~E(x9391,x9392)+E(f782(x9393,x9394,x9395,x9391),f782(x9393,x9394,x9395,x9392))
% 15.02/14.81 [940]~E(x9401,x9402)+E(f780(x9401,x9403,x9404,x9405,x9406,x9407),f780(x9402,x9403,x9404,x9405,x9406,x9407))
% 15.02/14.81 [941]~E(x9411,x9412)+E(f780(x9413,x9411,x9414,x9415,x9416,x9417),f780(x9413,x9412,x9414,x9415,x9416,x9417))
% 15.02/14.81 [942]~E(x9421,x9422)+E(f780(x9423,x9424,x9421,x9425,x9426,x9427),f780(x9423,x9424,x9422,x9425,x9426,x9427))
% 15.02/14.81 [943]~E(x9431,x9432)+E(f780(x9433,x9434,x9435,x9431,x9436,x9437),f780(x9433,x9434,x9435,x9432,x9436,x9437))
% 15.02/14.81 [944]~E(x9441,x9442)+E(f780(x9443,x9444,x9445,x9446,x9441,x9447),f780(x9443,x9444,x9445,x9446,x9442,x9447))
% 15.02/14.81 [945]~E(x9451,x9452)+E(f780(x9453,x9454,x9455,x9456,x9457,x9451),f780(x9453,x9454,x9455,x9456,x9457,x9452))
% 15.02/14.81 [946]~E(x9461,x9462)+E(f203(x9461,x9463),f203(x9462,x9463))
% 15.02/14.81 [947]~E(x9471,x9472)+E(f203(x9473,x9471),f203(x9473,x9472))
% 15.02/14.81 [948]~E(x9481,x9482)+E(f149(x9481,x9483,x9484,x9485,x9486),f149(x9482,x9483,x9484,x9485,x9486))
% 15.02/14.81 [949]~E(x9491,x9492)+E(f149(x9493,x9491,x9494,x9495,x9496),f149(x9493,x9492,x9494,x9495,x9496))
% 15.02/14.81 [950]~E(x9501,x9502)+E(f149(x9503,x9504,x9501,x9505,x9506),f149(x9503,x9504,x9502,x9505,x9506))
% 15.02/14.81 [951]~E(x9511,x9512)+E(f149(x9513,x9514,x9515,x9511,x9516),f149(x9513,x9514,x9515,x9512,x9516))
% 15.02/14.81 [952]~E(x9521,x9522)+E(f149(x9523,x9524,x9525,x9526,x9521),f149(x9523,x9524,x9525,x9526,x9522))
% 15.02/14.81 [953]~E(x9531,x9532)+E(f430(x9531,x9533,x9534,x9535),f430(x9532,x9533,x9534,x9535))
% 15.02/14.81 [954]~E(x9541,x9542)+E(f430(x9543,x9541,x9544,x9545),f430(x9543,x9542,x9544,x9545))
% 15.02/14.81 [955]~E(x9551,x9552)+E(f430(x9553,x9554,x9551,x9555),f430(x9553,x9554,x9552,x9555))
% 15.02/14.81 [956]~E(x9561,x9562)+E(f430(x9563,x9564,x9565,x9561),f430(x9563,x9564,x9565,x9562))
% 15.02/14.81 [957]~E(x9571,x9572)+E(f478(x9571,x9573,x9574,x9575),f478(x9572,x9573,x9574,x9575))
% 15.02/14.81 [958]~E(x9581,x9582)+E(f478(x9583,x9581,x9584,x9585),f478(x9583,x9582,x9584,x9585))
% 15.02/14.81 [959]~E(x9591,x9592)+E(f478(x9593,x9594,x9591,x9595),f478(x9593,x9594,x9592,x9595))
% 15.02/14.81 [960]~E(x9601,x9602)+E(f478(x9603,x9604,x9605,x9601),f478(x9603,x9604,x9605,x9602))
% 15.02/14.81 [961]~E(x9611,x9612)+E(f29(x9611,x9613),f29(x9612,x9613))
% 15.02/14.81 [962]~E(x9621,x9622)+E(f29(x9623,x9621),f29(x9623,x9622))
% 15.02/14.81 [963]~E(x9631,x9632)+E(f468(x9631,x9633,x9634,x9635),f468(x9632,x9633,x9634,x9635))
% 15.02/14.81 [964]~E(x9641,x9642)+E(f468(x9643,x9641,x9644,x9645),f468(x9643,x9642,x9644,x9645))
% 15.02/14.81 [965]~E(x9651,x9652)+E(f468(x9653,x9654,x9651,x9655),f468(x9653,x9654,x9652,x9655))
% 15.02/14.81 [966]~E(x9661,x9662)+E(f468(x9663,x9664,x9665,x9661),f468(x9663,x9664,x9665,x9662))
% 15.02/14.81 [967]~E(x9671,x9672)+E(f143(x9671,x9673),f143(x9672,x9673))
% 15.02/14.81 [968]~E(x9681,x9682)+E(f143(x9683,x9681),f143(x9683,x9682))
% 15.02/14.81 [969]~E(x9691,x9692)+E(f439(x9691,x9693),f439(x9692,x9693))
% 15.02/14.81 [970]~E(x9701,x9702)+E(f439(x9703,x9701),f439(x9703,x9702))
% 15.02/14.81 [971]~E(x9711,x9712)+E(f819(x9711,x9713,x9714),f819(x9712,x9713,x9714))
% 15.02/14.81 [972]~E(x9721,x9722)+E(f819(x9723,x9721,x9724),f819(x9723,x9722,x9724))
% 15.02/14.81 [973]~E(x9731,x9732)+E(f819(x9733,x9734,x9731),f819(x9733,x9734,x9732))
% 15.02/14.81 [974]~E(x9741,x9742)+E(f868(x9741,x9743,x9744),f868(x9742,x9743,x9744))
% 15.02/14.81 [975]~E(x9751,x9752)+E(f868(x9753,x9751,x9754),f868(x9753,x9752,x9754))
% 15.02/14.81 [976]~E(x9761,x9762)+E(f868(x9763,x9764,x9761),f868(x9763,x9764,x9762))
% 15.02/14.81 [977]~E(x9771,x9772)+E(f612(x9771,x9773,x9774),f612(x9772,x9773,x9774))
% 15.02/14.81 [978]~E(x9781,x9782)+E(f612(x9783,x9781,x9784),f612(x9783,x9782,x9784))
% 15.02/14.81 [979]~E(x9791,x9792)+E(f612(x9793,x9794,x9791),f612(x9793,x9794,x9792))
% 15.02/14.81 [980]~E(x9801,x9802)+E(f839(x9801,x9803,x9804,x9805,x9806,x9807,x9808,x9809),f839(x9802,x9803,x9804,x9805,x9806,x9807,x9808,x9809))
% 15.02/14.81 [981]~E(x9811,x9812)+E(f839(x9813,x9811,x9814,x9815,x9816,x9817,x9818,x9819),f839(x9813,x9812,x9814,x9815,x9816,x9817,x9818,x9819))
% 15.02/14.81 [982]~E(x9821,x9822)+E(f839(x9823,x9824,x9821,x9825,x9826,x9827,x9828,x9829),f839(x9823,x9824,x9822,x9825,x9826,x9827,x9828,x9829))
% 15.02/14.81 [983]~E(x9831,x9832)+E(f839(x9833,x9834,x9835,x9831,x9836,x9837,x9838,x9839),f839(x9833,x9834,x9835,x9832,x9836,x9837,x9838,x9839))
% 15.02/14.81 [984]~E(x9841,x9842)+E(f839(x9843,x9844,x9845,x9846,x9841,x9847,x9848,x9849),f839(x9843,x9844,x9845,x9846,x9842,x9847,x9848,x9849))
% 15.02/14.81 [985]~E(x9851,x9852)+E(f839(x9853,x9854,x9855,x9856,x9857,x9851,x9858,x9859),f839(x9853,x9854,x9855,x9856,x9857,x9852,x9858,x9859))
% 15.02/14.81 [986]~E(x9861,x9862)+E(f839(x9863,x9864,x9865,x9866,x9867,x9868,x9861,x9869),f839(x9863,x9864,x9865,x9866,x9867,x9868,x9862,x9869))
% 15.02/14.81 [987]~E(x9871,x9872)+E(f839(x9873,x9874,x9875,x9876,x9877,x9878,x9879,x9871),f839(x9873,x9874,x9875,x9876,x9877,x9878,x9879,x9872))
% 15.02/14.81 [988]~E(x9881,x9882)+E(f320(x9881,x9883,x9884),f320(x9882,x9883,x9884))
% 15.02/14.81 [989]~E(x9891,x9892)+E(f320(x9893,x9891,x9894),f320(x9893,x9892,x9894))
% 15.02/14.81 [990]~E(x9901,x9902)+E(f320(x9903,x9904,x9901),f320(x9903,x9904,x9902))
% 15.02/14.81 [991]~E(x9911,x9912)+E(f721(x9911,x9913,x9914,x9915,x9916),f721(x9912,x9913,x9914,x9915,x9916))
% 15.02/14.81 [992]~E(x9921,x9922)+E(f721(x9923,x9921,x9924,x9925,x9926),f721(x9923,x9922,x9924,x9925,x9926))
% 15.02/14.81 [993]~E(x9931,x9932)+E(f721(x9933,x9934,x9931,x9935,x9936),f721(x9933,x9934,x9932,x9935,x9936))
% 15.02/14.81 [994]~E(x9941,x9942)+E(f721(x9943,x9944,x9945,x9941,x9946),f721(x9943,x9944,x9945,x9942,x9946))
% 15.02/14.81 [995]~E(x9951,x9952)+E(f721(x9953,x9954,x9955,x9956,x9951),f721(x9953,x9954,x9955,x9956,x9952))
% 15.02/14.81 [996]~E(x9961,x9962)+E(f754(x9961,x9963,x9964),f754(x9962,x9963,x9964))
% 15.02/14.81 [997]~E(x9971,x9972)+E(f754(x9973,x9971,x9974),f754(x9973,x9972,x9974))
% 15.02/14.81 [998]~E(x9981,x9982)+E(f754(x9983,x9984,x9981),f754(x9983,x9984,x9982))
% 15.02/14.81 [999]~E(x9991,x9992)+E(f676(x9991,x9993,x9994),f676(x9992,x9993,x9994))
% 15.02/14.81 [1000]~E(x10001,x10002)+E(f676(x10003,x10001,x10004),f676(x10003,x10002,x10004))
% 15.02/14.81 [1001]~E(x10011,x10012)+E(f676(x10013,x10014,x10011),f676(x10013,x10014,x10012))
% 15.02/14.81 [1002]~E(x10021,x10022)+E(f610(x10021,x10023),f610(x10022,x10023))
% 15.02/14.81 [1003]~E(x10031,x10032)+E(f610(x10033,x10031),f610(x10033,x10032))
% 15.02/14.81 [1004]~E(x10041,x10042)+E(f796(x10041,x10043,x10044),f796(x10042,x10043,x10044))
% 15.02/14.81 [1005]~E(x10051,x10052)+E(f796(x10053,x10051,x10054),f796(x10053,x10052,x10054))
% 15.02/14.81 [1006]~E(x10061,x10062)+E(f796(x10063,x10064,x10061),f796(x10063,x10064,x10062))
% 15.02/14.81 [1007]~E(x10071,x10072)+E(f267(x10071,x10073),f267(x10072,x10073))
% 15.02/14.81 [1008]~E(x10081,x10082)+E(f267(x10083,x10081),f267(x10083,x10082))
% 15.02/14.81 [1009]~E(x10091,x10092)+E(f717(x10091,x10093),f717(x10092,x10093))
% 15.02/14.81 [1010]~E(x10101,x10102)+E(f717(x10103,x10101),f717(x10103,x10102))
% 15.02/14.81 [1011]~E(x10111,x10112)+E(f225(x10111,x10113,x10114,x10115,x10116),f225(x10112,x10113,x10114,x10115,x10116))
% 15.02/14.81 [1012]~E(x10121,x10122)+E(f225(x10123,x10121,x10124,x10125,x10126),f225(x10123,x10122,x10124,x10125,x10126))
% 15.02/14.81 [1013]~E(x10131,x10132)+E(f225(x10133,x10134,x10131,x10135,x10136),f225(x10133,x10134,x10132,x10135,x10136))
% 15.02/14.81 [1014]~E(x10141,x10142)+E(f225(x10143,x10144,x10145,x10141,x10146),f225(x10143,x10144,x10145,x10142,x10146))
% 15.02/14.81 [1015]~E(x10151,x10152)+E(f225(x10153,x10154,x10155,x10156,x10151),f225(x10153,x10154,x10155,x10156,x10152))
% 15.02/14.81 [1016]~E(x10161,x10162)+E(f822(x10161,x10163),f822(x10162,x10163))
% 15.02/14.81 [1017]~E(x10171,x10172)+E(f822(x10173,x10171),f822(x10173,x10172))
% 15.02/14.81 [1018]~E(x10181,x10182)+E(f775(x10181,x10183,x10184,x10185),f775(x10182,x10183,x10184,x10185))
% 15.02/14.81 [1019]~E(x10191,x10192)+E(f775(x10193,x10191,x10194,x10195),f775(x10193,x10192,x10194,x10195))
% 15.02/14.81 [1020]~E(x10201,x10202)+E(f775(x10203,x10204,x10201,x10205),f775(x10203,x10204,x10202,x10205))
% 15.02/14.81 [1021]~E(x10211,x10212)+E(f775(x10213,x10214,x10215,x10211),f775(x10213,x10214,x10215,x10212))
% 15.02/14.81 [1022]~E(x10221,x10222)+E(f615(x10221,x10223,x10224),f615(x10222,x10223,x10224))
% 15.02/14.81 [1023]~E(x10231,x10232)+E(f615(x10233,x10231,x10234),f615(x10233,x10232,x10234))
% 15.02/14.81 [1024]~E(x10241,x10242)+E(f615(x10243,x10244,x10241),f615(x10243,x10244,x10242))
% 15.02/14.81 [1025]~E(x10251,x10252)+E(f832(x10251,x10253,x10254,x10255),f832(x10252,x10253,x10254,x10255))
% 15.02/14.81 [1026]~E(x10261,x10262)+E(f832(x10263,x10261,x10264,x10265),f832(x10263,x10262,x10264,x10265))
% 15.02/14.81 [1027]~E(x10271,x10272)+E(f832(x10273,x10274,x10271,x10275),f832(x10273,x10274,x10272,x10275))
% 15.02/14.81 [1028]~E(x10281,x10282)+E(f832(x10283,x10284,x10285,x10281),f832(x10283,x10284,x10285,x10282))
% 15.02/14.81 [1029]~E(x10291,x10292)+E(f56(x10291),f56(x10292))
% 15.02/14.81 [1030]~E(x10301,x10302)+E(f872(x10301,x10303,x10304,x10305,x10306),f872(x10302,x10303,x10304,x10305,x10306))
% 15.02/14.81 [1031]~E(x10311,x10312)+E(f872(x10313,x10311,x10314,x10315,x10316),f872(x10313,x10312,x10314,x10315,x10316))
% 15.02/14.81 [1032]~E(x10321,x10322)+E(f872(x10323,x10324,x10321,x10325,x10326),f872(x10323,x10324,x10322,x10325,x10326))
% 15.02/14.81 [1033]~E(x10331,x10332)+E(f872(x10333,x10334,x10335,x10331,x10336),f872(x10333,x10334,x10335,x10332,x10336))
% 15.02/14.81 [1034]~E(x10341,x10342)+E(f872(x10343,x10344,x10345,x10346,x10341),f872(x10343,x10344,x10345,x10346,x10342))
% 15.02/14.81 [1035]~E(x10351,x10352)+E(f357(x10351,x10353,x10354),f357(x10352,x10353,x10354))
% 15.02/14.81 [1036]~E(x10361,x10362)+E(f357(x10363,x10361,x10364),f357(x10363,x10362,x10364))
% 15.02/14.81 [1037]~E(x10371,x10372)+E(f357(x10373,x10374,x10371),f357(x10373,x10374,x10372))
% 15.02/14.81 [1038]~E(x10381,x10382)+E(f465(x10381,x10383,x10384),f465(x10382,x10383,x10384))
% 15.02/14.81 [1039]~E(x10391,x10392)+E(f465(x10393,x10391,x10394),f465(x10393,x10392,x10394))
% 15.02/14.81 [1040]~E(x10401,x10402)+E(f465(x10403,x10404,x10401),f465(x10403,x10404,x10402))
% 15.02/14.81 [1041]~E(x10411,x10412)+E(f768(x10411,x10413,x10414),f768(x10412,x10413,x10414))
% 15.02/14.81 [1042]~E(x10421,x10422)+E(f768(x10423,x10421,x10424),f768(x10423,x10422,x10424))
% 15.02/14.81 [1043]~E(x10431,x10432)+E(f768(x10433,x10434,x10431),f768(x10433,x10434,x10432))
% 15.02/14.81 [1044]~E(x10441,x10442)+E(f733(x10441,x10443),f733(x10442,x10443))
% 15.02/14.81 [1045]~E(x10451,x10452)+E(f733(x10453,x10451),f733(x10453,x10452))
% 15.02/14.81 [1046]~E(x10461,x10462)+E(f299(x10461,x10463,x10464,x10465,x10466),f299(x10462,x10463,x10464,x10465,x10466))
% 15.02/14.81 [1047]~E(x10471,x10472)+E(f299(x10473,x10471,x10474,x10475,x10476),f299(x10473,x10472,x10474,x10475,x10476))
% 15.02/14.81 [1048]~E(x10481,x10482)+E(f299(x10483,x10484,x10481,x10485,x10486),f299(x10483,x10484,x10482,x10485,x10486))
% 15.02/14.81 [1049]~E(x10491,x10492)+E(f299(x10493,x10494,x10495,x10491,x10496),f299(x10493,x10494,x10495,x10492,x10496))
% 15.02/14.81 [1050]~E(x10501,x10502)+E(f299(x10503,x10504,x10505,x10506,x10501),f299(x10503,x10504,x10505,x10506,x10502))
% 15.02/14.81 [1051]~E(x10511,x10512)+E(f298(x10511,x10513,x10514,x10515),f298(x10512,x10513,x10514,x10515))
% 15.02/14.81 [1052]~E(x10521,x10522)+E(f298(x10523,x10521,x10524,x10525),f298(x10523,x10522,x10524,x10525))
% 15.02/14.81 [1053]~E(x10531,x10532)+E(f298(x10533,x10534,x10531,x10535),f298(x10533,x10534,x10532,x10535))
% 15.02/14.81 [1054]~E(x10541,x10542)+E(f298(x10543,x10544,x10545,x10541),f298(x10543,x10544,x10545,x10542))
% 15.02/14.81 [1055]~E(x10551,x10552)+E(f237(x10551,x10553),f237(x10552,x10553))
% 15.02/14.81 [1056]~E(x10561,x10562)+E(f237(x10563,x10561),f237(x10563,x10562))
% 15.02/14.81 [1057]~E(x10571,x10572)+E(f273(x10571,x10573,x10574),f273(x10572,x10573,x10574))
% 15.02/14.81 [1058]~E(x10581,x10582)+E(f273(x10583,x10581,x10584),f273(x10583,x10582,x10584))
% 15.02/14.81 [1059]~E(x10591,x10592)+E(f273(x10593,x10594,x10591),f273(x10593,x10594,x10592))
% 15.02/14.81 [1060]~E(x10601,x10602)+E(f573(x10601,x10603,x10604),f573(x10602,x10603,x10604))
% 15.02/14.81 [1061]~E(x10611,x10612)+E(f573(x10613,x10611,x10614),f573(x10613,x10612,x10614))
% 15.02/14.81 [1062]~E(x10621,x10622)+E(f573(x10623,x10624,x10621),f573(x10623,x10624,x10622))
% 15.02/14.81 [1063]~E(x10631,x10632)+E(f488(x10631,x10633,x10634,x10635,x10636,x10637,x10638),f488(x10632,x10633,x10634,x10635,x10636,x10637,x10638))
% 15.02/14.81 [1064]~E(x10641,x10642)+E(f488(x10643,x10641,x10644,x10645,x10646,x10647,x10648),f488(x10643,x10642,x10644,x10645,x10646,x10647,x10648))
% 15.02/14.81 [1065]~E(x10651,x10652)+E(f488(x10653,x10654,x10651,x10655,x10656,x10657,x10658),f488(x10653,x10654,x10652,x10655,x10656,x10657,x10658))
% 15.02/14.81 [1066]~E(x10661,x10662)+E(f488(x10663,x10664,x10665,x10661,x10666,x10667,x10668),f488(x10663,x10664,x10665,x10662,x10666,x10667,x10668))
% 15.02/14.81 [1067]~E(x10671,x10672)+E(f488(x10673,x10674,x10675,x10676,x10671,x10677,x10678),f488(x10673,x10674,x10675,x10676,x10672,x10677,x10678))
% 15.02/14.81 [1068]~E(x10681,x10682)+E(f488(x10683,x10684,x10685,x10686,x10687,x10681,x10688),f488(x10683,x10684,x10685,x10686,x10687,x10682,x10688))
% 15.02/14.81 [1069]~E(x10691,x10692)+E(f488(x10693,x10694,x10695,x10696,x10697,x10698,x10691),f488(x10693,x10694,x10695,x10696,x10697,x10698,x10692))
% 15.02/14.81 [1070]~E(x10701,x10702)+E(f466(x10701,x10703),f466(x10702,x10703))
% 15.02/14.81 [1071]~E(x10711,x10712)+E(f466(x10713,x10711),f466(x10713,x10712))
% 15.02/14.81 [1072]~E(x10721,x10722)+E(f52(x10721,x10723),f52(x10722,x10723))
% 15.02/14.81 [1073]~E(x10731,x10732)+E(f52(x10733,x10731),f52(x10733,x10732))
% 15.02/14.81 [1074]~E(x10741,x10742)+E(f499(x10741,x10743,x10744,x10745),f499(x10742,x10743,x10744,x10745))
% 15.02/14.81 [1075]~E(x10751,x10752)+E(f499(x10753,x10751,x10754,x10755),f499(x10753,x10752,x10754,x10755))
% 15.02/14.81 [1076]~E(x10761,x10762)+E(f499(x10763,x10764,x10761,x10765),f499(x10763,x10764,x10762,x10765))
% 15.02/14.81 [1077]~E(x10771,x10772)+E(f499(x10773,x10774,x10775,x10771),f499(x10773,x10774,x10775,x10772))
% 15.02/14.81 [1078]~E(x10781,x10782)+E(f445(x10781,x10783,x10784,x10785),f445(x10782,x10783,x10784,x10785))
% 15.02/14.81 [1079]~E(x10791,x10792)+E(f445(x10793,x10791,x10794,x10795),f445(x10793,x10792,x10794,x10795))
% 15.02/14.81 [1080]~E(x10801,x10802)+E(f445(x10803,x10804,x10801,x10805),f445(x10803,x10804,x10802,x10805))
% 15.02/14.81 [1081]~E(x10811,x10812)+E(f445(x10813,x10814,x10815,x10811),f445(x10813,x10814,x10815,x10812))
% 15.02/14.81 [1082]~E(x10821,x10822)+E(f539(x10821,x10823,x10824),f539(x10822,x10823,x10824))
% 15.02/14.81 [1083]~E(x10831,x10832)+E(f539(x10833,x10831,x10834),f539(x10833,x10832,x10834))
% 15.02/14.81 [1084]~E(x10841,x10842)+E(f539(x10843,x10844,x10841),f539(x10843,x10844,x10842))
% 15.02/14.81 [1085]~E(x10851,x10852)+E(f748(x10851,x10853,x10854,x10855,x10856,x10857,x10858),f748(x10852,x10853,x10854,x10855,x10856,x10857,x10858))
% 15.02/14.81 [1086]~E(x10861,x10862)+E(f748(x10863,x10861,x10864,x10865,x10866,x10867,x10868),f748(x10863,x10862,x10864,x10865,x10866,x10867,x10868))
% 15.02/14.81 [1087]~E(x10871,x10872)+E(f748(x10873,x10874,x10871,x10875,x10876,x10877,x10878),f748(x10873,x10874,x10872,x10875,x10876,x10877,x10878))
% 15.02/14.81 [1088]~E(x10881,x10882)+E(f748(x10883,x10884,x10885,x10881,x10886,x10887,x10888),f748(x10883,x10884,x10885,x10882,x10886,x10887,x10888))
% 15.02/14.81 [1089]~E(x10891,x10892)+E(f748(x10893,x10894,x10895,x10896,x10891,x10897,x10898),f748(x10893,x10894,x10895,x10896,x10892,x10897,x10898))
% 15.02/14.81 [1090]~E(x10901,x10902)+E(f748(x10903,x10904,x10905,x10906,x10907,x10901,x10908),f748(x10903,x10904,x10905,x10906,x10907,x10902,x10908))
% 15.02/14.81 [1091]~E(x10911,x10912)+E(f748(x10913,x10914,x10915,x10916,x10917,x10918,x10911),f748(x10913,x10914,x10915,x10916,x10917,x10918,x10912))
% 15.02/14.81 [1092]~E(x10921,x10922)+E(f626(x10921,x10923,x10924,x10925,x10926),f626(x10922,x10923,x10924,x10925,x10926))
% 15.02/14.81 [1093]~E(x10931,x10932)+E(f626(x10933,x10931,x10934,x10935,x10936),f626(x10933,x10932,x10934,x10935,x10936))
% 15.02/14.81 [1094]~E(x10941,x10942)+E(f626(x10943,x10944,x10941,x10945,x10946),f626(x10943,x10944,x10942,x10945,x10946))
% 15.02/14.81 [1095]~E(x10951,x10952)+E(f626(x10953,x10954,x10955,x10951,x10956),f626(x10953,x10954,x10955,x10952,x10956))
% 15.02/14.81 [1096]~E(x10961,x10962)+E(f626(x10963,x10964,x10965,x10966,x10961),f626(x10963,x10964,x10965,x10966,x10962))
% 15.02/14.81 [1097]~E(x10971,x10972)+E(f707(x10971,x10973),f707(x10972,x10973))
% 15.02/14.81 [1098]~E(x10981,x10982)+E(f707(x10983,x10981),f707(x10983,x10982))
% 15.02/14.81 [1099]~E(x10991,x10992)+E(f543(x10991,x10993,x10994,x10995,x10996,x10997),f543(x10992,x10993,x10994,x10995,x10996,x10997))
% 15.02/14.81 [1100]~E(x11001,x11002)+E(f543(x11003,x11001,x11004,x11005,x11006,x11007),f543(x11003,x11002,x11004,x11005,x11006,x11007))
% 15.02/14.81 [1101]~E(x11011,x11012)+E(f543(x11013,x11014,x11011,x11015,x11016,x11017),f543(x11013,x11014,x11012,x11015,x11016,x11017))
% 15.02/14.81 [1102]~E(x11021,x11022)+E(f543(x11023,x11024,x11025,x11021,x11026,x11027),f543(x11023,x11024,x11025,x11022,x11026,x11027))
% 15.02/14.81 [1103]~E(x11031,x11032)+E(f543(x11033,x11034,x11035,x11036,x11031,x11037),f543(x11033,x11034,x11035,x11036,x11032,x11037))
% 15.02/14.81 [1104]~E(x11041,x11042)+E(f543(x11043,x11044,x11045,x11046,x11047,x11041),f543(x11043,x11044,x11045,x11046,x11047,x11042))
% 15.02/14.81 [1105]~E(x11051,x11052)+E(f574(x11051,x11053,x11054),f574(x11052,x11053,x11054))
% 15.02/14.81 [1106]~E(x11061,x11062)+E(f574(x11063,x11061,x11064),f574(x11063,x11062,x11064))
% 15.02/14.81 [1107]~E(x11071,x11072)+E(f574(x11073,x11074,x11071),f574(x11073,x11074,x11072))
% 15.02/14.81 [1108]~E(x11081,x11082)+E(f675(x11081,x11083),f675(x11082,x11083))
% 15.02/14.81 [1109]~E(x11091,x11092)+E(f675(x11093,x11091),f675(x11093,x11092))
% 15.02/14.81 [1110]~E(x11101,x11102)+E(f512(x11101,x11103,x11104),f512(x11102,x11103,x11104))
% 15.02/14.81 [1111]~E(x11111,x11112)+E(f512(x11113,x11111,x11114),f512(x11113,x11112,x11114))
% 15.02/14.81 [1112]~E(x11121,x11122)+E(f512(x11123,x11124,x11121),f512(x11123,x11124,x11122))
% 15.02/14.81 [1113]~E(x11131,x11132)+E(f219(x11131,x11133),f219(x11132,x11133))
% 15.02/14.81 [1114]~E(x11141,x11142)+E(f219(x11143,x11141),f219(x11143,x11142))
% 15.02/14.81 [1115]~E(x11151,x11152)+E(f41(x11151),f41(x11152))
% 15.02/14.81 [1116]~E(x11161,x11162)+E(f385(x11161,x11163,x11164),f385(x11162,x11163,x11164))
% 15.02/14.81 [1117]~E(x11171,x11172)+E(f385(x11173,x11171,x11174),f385(x11173,x11172,x11174))
% 15.02/14.81 [1118]~E(x11181,x11182)+E(f385(x11183,x11184,x11181),f385(x11183,x11184,x11182))
% 15.02/14.81 [1119]~E(x11191,x11192)+E(f401(x11191,x11193,x11194,x11195,x11196),f401(x11192,x11193,x11194,x11195,x11196))
% 15.02/14.81 [1120]~E(x11201,x11202)+E(f401(x11203,x11201,x11204,x11205,x11206),f401(x11203,x11202,x11204,x11205,x11206))
% 15.02/14.81 [1121]~E(x11211,x11212)+E(f401(x11213,x11214,x11211,x11215,x11216),f401(x11213,x11214,x11212,x11215,x11216))
% 15.02/14.81 [1122]~E(x11221,x11222)+E(f401(x11223,x11224,x11225,x11221,x11226),f401(x11223,x11224,x11225,x11222,x11226))
% 15.02/14.81 [1123]~E(x11231,x11232)+E(f401(x11233,x11234,x11235,x11236,x11231),f401(x11233,x11234,x11235,x11236,x11232))
% 15.02/14.81 [1124]~E(x11241,x11242)+E(f813(x11241,x11243,x11244,x11245,x11246),f813(x11242,x11243,x11244,x11245,x11246))
% 15.02/14.81 [1125]~E(x11251,x11252)+E(f813(x11253,x11251,x11254,x11255,x11256),f813(x11253,x11252,x11254,x11255,x11256))
% 15.02/14.81 [1126]~E(x11261,x11262)+E(f813(x11263,x11264,x11261,x11265,x11266),f813(x11263,x11264,x11262,x11265,x11266))
% 15.02/14.81 [1127]~E(x11271,x11272)+E(f813(x11273,x11274,x11275,x11271,x11276),f813(x11273,x11274,x11275,x11272,x11276))
% 15.02/14.81 [1128]~E(x11281,x11282)+E(f813(x11283,x11284,x11285,x11286,x11281),f813(x11283,x11284,x11285,x11286,x11282))
% 15.02/14.81 [1129]~E(x11291,x11292)+E(f464(x11291,x11293,x11294),f464(x11292,x11293,x11294))
% 15.02/14.81 [1130]~E(x11301,x11302)+E(f464(x11303,x11301,x11304),f464(x11303,x11302,x11304))
% 15.02/14.81 [1131]~E(x11311,x11312)+E(f464(x11313,x11314,x11311),f464(x11313,x11314,x11312))
% 15.02/14.81 [1132]~E(x11321,x11322)+E(f876(x11321,x11323,x11324),f876(x11322,x11323,x11324))
% 15.02/14.81 [1133]~E(x11331,x11332)+E(f876(x11333,x11331,x11334),f876(x11333,x11332,x11334))
% 15.02/14.81 [1134]~E(x11341,x11342)+E(f876(x11343,x11344,x11341),f876(x11343,x11344,x11342))
% 15.02/14.81 [1135]~E(x11351,x11352)+E(f567(x11351,x11353),f567(x11352,x11353))
% 15.02/14.81 [1136]~E(x11361,x11362)+E(f567(x11363,x11361),f567(x11363,x11362))
% 15.02/14.81 [1137]~E(x11371,x11372)+E(f749(x11371,x11373,x11374,x11375,x11376,x11377,x11378),f749(x11372,x11373,x11374,x11375,x11376,x11377,x11378))
% 15.02/14.81 [1138]~E(x11381,x11382)+E(f749(x11383,x11381,x11384,x11385,x11386,x11387,x11388),f749(x11383,x11382,x11384,x11385,x11386,x11387,x11388))
% 15.02/14.81 [1139]~E(x11391,x11392)+E(f749(x11393,x11394,x11391,x11395,x11396,x11397,x11398),f749(x11393,x11394,x11392,x11395,x11396,x11397,x11398))
% 15.02/14.81 [1140]~E(x11401,x11402)+E(f749(x11403,x11404,x11405,x11401,x11406,x11407,x11408),f749(x11403,x11404,x11405,x11402,x11406,x11407,x11408))
% 15.02/14.81 [1141]~E(x11411,x11412)+E(f749(x11413,x11414,x11415,x11416,x11411,x11417,x11418),f749(x11413,x11414,x11415,x11416,x11412,x11417,x11418))
% 15.02/14.81 [1142]~E(x11421,x11422)+E(f749(x11423,x11424,x11425,x11426,x11427,x11421,x11428),f749(x11423,x11424,x11425,x11426,x11427,x11422,x11428))
% 15.02/14.81 [1143]~E(x11431,x11432)+E(f749(x11433,x11434,x11435,x11436,x11437,x11438,x11431),f749(x11433,x11434,x11435,x11436,x11437,x11438,x11432))
% 15.02/14.81 [1144]~E(x11441,x11442)+E(f514(x11441,x11443,x11444),f514(x11442,x11443,x11444))
% 15.02/14.81 [1145]~E(x11451,x11452)+E(f514(x11453,x11451,x11454),f514(x11453,x11452,x11454))
% 15.02/14.81 [1146]~E(x11461,x11462)+E(f514(x11463,x11464,x11461),f514(x11463,x11464,x11462))
% 15.02/14.81 [1147]~E(x11471,x11472)+E(f880(x11471,x11473,x11474),f880(x11472,x11473,x11474))
% 15.02/14.81 [1148]~E(x11481,x11482)+E(f880(x11483,x11481,x11484),f880(x11483,x11482,x11484))
% 15.02/14.81 [1149]~E(x11491,x11492)+E(f880(x11493,x11494,x11491),f880(x11493,x11494,x11492))
% 15.02/14.81 [1150]~E(x11501,x11502)+E(f132(x11501,x11503),f132(x11502,x11503))
% 15.02/14.81 [1151]~E(x11511,x11512)+E(f132(x11513,x11511),f132(x11513,x11512))
% 15.02/14.81 [1152]~E(x11521,x11522)+E(f659(x11521,x11523,x11524),f659(x11522,x11523,x11524))
% 15.02/14.81 [1153]~E(x11531,x11532)+E(f659(x11533,x11531,x11534),f659(x11533,x11532,x11534))
% 15.02/14.81 [1154]~E(x11541,x11542)+E(f659(x11543,x11544,x11541),f659(x11543,x11544,x11542))
% 15.02/14.81 [1155]~E(x11551,x11552)+E(f580(x11551),f580(x11552))
% 15.02/14.81 [1156]~E(x11561,x11562)+E(f882(x11561,x11563,x11564),f882(x11562,x11563,x11564))
% 15.02/14.81 [1157]~E(x11571,x11572)+E(f882(x11573,x11571,x11574),f882(x11573,x11572,x11574))
% 15.02/14.81 [1158]~E(x11581,x11582)+E(f882(x11583,x11584,x11581),f882(x11583,x11584,x11582))
% 15.02/14.81 [1159]~E(x11591,x11592)+E(f874(x11591,x11593,x11594,x11595,x11596,x11597),f874(x11592,x11593,x11594,x11595,x11596,x11597))
% 15.02/14.81 [1160]~E(x11601,x11602)+E(f874(x11603,x11601,x11604,x11605,x11606,x11607),f874(x11603,x11602,x11604,x11605,x11606,x11607))
% 15.02/14.81 [1161]~E(x11611,x11612)+E(f874(x11613,x11614,x11611,x11615,x11616,x11617),f874(x11613,x11614,x11612,x11615,x11616,x11617))
% 15.02/14.81 [1162]~E(x11621,x11622)+E(f874(x11623,x11624,x11625,x11621,x11626,x11627),f874(x11623,x11624,x11625,x11622,x11626,x11627))
% 15.02/14.81 [1163]~E(x11631,x11632)+E(f874(x11633,x11634,x11635,x11636,x11631,x11637),f874(x11633,x11634,x11635,x11636,x11632,x11637))
% 15.02/14.81 [1164]~E(x11641,x11642)+E(f874(x11643,x11644,x11645,x11646,x11647,x11641),f874(x11643,x11644,x11645,x11646,x11647,x11642))
% 15.02/14.81 [1165]~E(x11651,x11652)+E(f911(x11651,x11653,x11654),f911(x11652,x11653,x11654))
% 15.02/14.81 [1166]~E(x11661,x11662)+E(f911(x11663,x11661,x11664),f911(x11663,x11662,x11664))
% 15.02/14.81 [1167]~E(x11671,x11672)+E(f911(x11673,x11674,x11671),f911(x11673,x11674,x11672))
% 15.02/14.81 [1168]~E(x11681,x11682)+E(f866(x11681,x11683,x11684,x11685,x11686),f866(x11682,x11683,x11684,x11685,x11686))
% 15.02/14.81 [1169]~E(x11691,x11692)+E(f866(x11693,x11691,x11694,x11695,x11696),f866(x11693,x11692,x11694,x11695,x11696))
% 15.02/14.81 [1170]~E(x11701,x11702)+E(f866(x11703,x11704,x11701,x11705,x11706),f866(x11703,x11704,x11702,x11705,x11706))
% 15.02/14.81 [1171]~E(x11711,x11712)+E(f866(x11713,x11714,x11715,x11711,x11716),f866(x11713,x11714,x11715,x11712,x11716))
% 15.02/14.81 [1172]~E(x11721,x11722)+E(f866(x11723,x11724,x11725,x11726,x11721),f866(x11723,x11724,x11725,x11726,x11722))
% 15.02/14.81 [1173]~E(x11731,x11732)+E(f534(x11731,x11733,x11734,x11735,x11736),f534(x11732,x11733,x11734,x11735,x11736))
% 15.02/14.81 [1174]~E(x11741,x11742)+E(f534(x11743,x11741,x11744,x11745,x11746),f534(x11743,x11742,x11744,x11745,x11746))
% 15.02/14.81 [1175]~E(x11751,x11752)+E(f534(x11753,x11754,x11751,x11755,x11756),f534(x11753,x11754,x11752,x11755,x11756))
% 15.02/14.81 [1176]~E(x11761,x11762)+E(f534(x11763,x11764,x11765,x11761,x11766),f534(x11763,x11764,x11765,x11762,x11766))
% 15.02/14.81 [1177]~E(x11771,x11772)+E(f534(x11773,x11774,x11775,x11776,x11771),f534(x11773,x11774,x11775,x11776,x11772))
% 15.02/14.81 [1178]~E(x11781,x11782)+E(f657(x11781,x11783,x11784,x11785),f657(x11782,x11783,x11784,x11785))
% 15.02/14.81 [1179]~E(x11791,x11792)+E(f657(x11793,x11791,x11794,x11795),f657(x11793,x11792,x11794,x11795))
% 15.02/14.81 [1180]~E(x11801,x11802)+E(f657(x11803,x11804,x11801,x11805),f657(x11803,x11804,x11802,x11805))
% 15.02/14.81 [1181]~E(x11811,x11812)+E(f657(x11813,x11814,x11815,x11811),f657(x11813,x11814,x11815,x11812))
% 15.02/14.81 [1182]~E(x11821,x11822)+E(f656(x11821,x11823,x11824,x11825,x11826),f656(x11822,x11823,x11824,x11825,x11826))
% 15.02/14.81 [1183]~E(x11831,x11832)+E(f656(x11833,x11831,x11834,x11835,x11836),f656(x11833,x11832,x11834,x11835,x11836))
% 15.02/14.81 [1184]~E(x11841,x11842)+E(f656(x11843,x11844,x11841,x11845,x11846),f656(x11843,x11844,x11842,x11845,x11846))
% 15.02/14.81 [1185]~E(x11851,x11852)+E(f656(x11853,x11854,x11855,x11851,x11856),f656(x11853,x11854,x11855,x11852,x11856))
% 15.02/14.81 [1186]~E(x11861,x11862)+E(f656(x11863,x11864,x11865,x11866,x11861),f656(x11863,x11864,x11865,x11866,x11862))
% 15.02/14.81 [1187]~E(x11871,x11872)+E(f417(x11871,x11873,x11874),f417(x11872,x11873,x11874))
% 15.02/14.81 [1188]~E(x11881,x11882)+E(f417(x11883,x11881,x11884),f417(x11883,x11882,x11884))
% 15.02/14.81 [1189]~E(x11891,x11892)+E(f417(x11893,x11894,x11891),f417(x11893,x11894,x11892))
% 15.02/14.81 [1190]~E(x11901,x11902)+E(f126(x11901,x11903,x11904),f126(x11902,x11903,x11904))
% 15.02/14.81 [1191]~E(x11911,x11912)+E(f126(x11913,x11911,x11914),f126(x11913,x11912,x11914))
% 15.02/14.81 [1192]~E(x11921,x11922)+E(f126(x11923,x11924,x11921),f126(x11923,x11924,x11922))
% 15.02/14.81 [1193]~E(x11931,x11932)+E(f668(x11931,x11933),f668(x11932,x11933))
% 15.02/14.81 [1194]~E(x11941,x11942)+E(f668(x11943,x11941),f668(x11943,x11942))
% 15.02/14.81 [1195]~E(x11951,x11952)+E(f370(x11951,x11953,x11954),f370(x11952,x11953,x11954))
% 15.02/14.81 [1196]~E(x11961,x11962)+E(f370(x11963,x11961,x11964),f370(x11963,x11962,x11964))
% 15.02/14.81 [1197]~E(x11971,x11972)+E(f370(x11973,x11974,x11971),f370(x11973,x11974,x11972))
% 15.02/14.81 [1198]~E(x11981,x11982)+E(f378(x11981,x11983,x11984),f378(x11982,x11983,x11984))
% 15.02/14.81 [1199]~E(x11991,x11992)+E(f378(x11993,x11991,x11994),f378(x11993,x11992,x11994))
% 15.02/14.81 [1200]~E(x12001,x12002)+E(f378(x12003,x12004,x12001),f378(x12003,x12004,x12002))
% 15.02/14.81 [1201]~E(x12011,x12012)+E(f548(x12011,x12013),f548(x12012,x12013))
% 15.02/14.81 [1202]~E(x12021,x12022)+E(f548(x12023,x12021),f548(x12023,x12022))
% 15.02/14.81 [1203]~E(x12031,x12032)+E(f42(x12031),f42(x12032))
% 15.02/14.81 [1204]~E(x12041,x12042)+E(f348(x12041,x12043,x12044,x12045),f348(x12042,x12043,x12044,x12045))
% 15.02/14.81 [1205]~E(x12051,x12052)+E(f348(x12053,x12051,x12054,x12055),f348(x12053,x12052,x12054,x12055))
% 15.02/14.81 [1206]~E(x12061,x12062)+E(f348(x12063,x12064,x12061,x12065),f348(x12063,x12064,x12062,x12065))
% 15.02/14.81 [1207]~E(x12071,x12072)+E(f348(x12073,x12074,x12075,x12071),f348(x12073,x12074,x12075,x12072))
% 15.02/14.81 [1208]~E(x12081,x12082)+E(f913(x12081,x12083,x12084,x12085),f913(x12082,x12083,x12084,x12085))
% 15.02/14.81 [1209]~E(x12091,x12092)+E(f913(x12093,x12091,x12094,x12095),f913(x12093,x12092,x12094,x12095))
% 15.02/14.81 [1210]~E(x12101,x12102)+E(f913(x12103,x12104,x12101,x12105),f913(x12103,x12104,x12102,x12105))
% 15.02/14.81 [1211]~E(x12111,x12112)+E(f913(x12113,x12114,x12115,x12111),f913(x12113,x12114,x12115,x12112))
% 15.02/14.81 [1212]~E(x12121,x12122)+E(f836(x12121,x12123,x12124),f836(x12122,x12123,x12124))
% 15.02/14.81 [1213]~E(x12131,x12132)+E(f836(x12133,x12131,x12134),f836(x12133,x12132,x12134))
% 15.02/14.81 [1214]~E(x12141,x12142)+E(f836(x12143,x12144,x12141),f836(x12143,x12144,x12142))
% 15.02/14.81 [1215]~E(x12151,x12152)+E(f160(x12151,x12153),f160(x12152,x12153))
% 15.02/14.81 [1216]~E(x12161,x12162)+E(f160(x12163,x12161),f160(x12163,x12162))
% 15.02/14.81 [1217]~E(x12171,x12172)+E(f162(x12171,x12173),f162(x12172,x12173))
% 15.02/14.81 [1218]~E(x12181,x12182)+E(f162(x12183,x12181),f162(x12183,x12182))
% 15.02/14.81 [1219]~E(x12191,x12192)+E(f702(x12191,x12193,x12194,x12195,x12196),f702(x12192,x12193,x12194,x12195,x12196))
% 15.02/14.81 [1220]~E(x12201,x12202)+E(f702(x12203,x12201,x12204,x12205,x12206),f702(x12203,x12202,x12204,x12205,x12206))
% 15.02/14.81 [1221]~E(x12211,x12212)+E(f702(x12213,x12214,x12211,x12215,x12216),f702(x12213,x12214,x12212,x12215,x12216))
% 15.02/14.81 [1222]~E(x12221,x12222)+E(f702(x12223,x12224,x12225,x12221,x12226),f702(x12223,x12224,x12225,x12222,x12226))
% 15.02/14.81 [1223]~E(x12231,x12232)+E(f702(x12233,x12234,x12235,x12236,x12231),f702(x12233,x12234,x12235,x12236,x12232))
% 15.02/14.81 [1224]~E(x12241,x12242)+E(f236(x12241,x12243),f236(x12242,x12243))
% 15.02/14.81 [1225]~E(x12251,x12252)+E(f236(x12253,x12251),f236(x12253,x12252))
% 15.02/14.81 [1226]~E(x12261,x12262)+E(f415(x12261,x12263),f415(x12262,x12263))
% 15.02/14.81 [1227]~E(x12271,x12272)+E(f415(x12273,x12271),f415(x12273,x12272))
% 15.02/14.81 [1228]~E(x12281,x12282)+E(f421(x12281,x12283),f421(x12282,x12283))
% 15.02/14.81 [1229]~E(x12291,x12292)+E(f421(x12293,x12291),f421(x12293,x12292))
% 15.02/14.81 [1230]~E(x12301,x12302)+E(f600(x12301,x12303,x12304),f600(x12302,x12303,x12304))
% 15.02/14.81 [1231]~E(x12311,x12312)+E(f600(x12313,x12311,x12314),f600(x12313,x12312,x12314))
% 15.02/14.81 [1232]~E(x12321,x12322)+E(f600(x12323,x12324,x12321),f600(x12323,x12324,x12322))
% 15.02/14.81 [1233]~E(x12331,x12332)+E(f346(x12331,x12333,x12334,x12335),f346(x12332,x12333,x12334,x12335))
% 15.02/14.81 [1234]~E(x12341,x12342)+E(f346(x12343,x12341,x12344,x12345),f346(x12343,x12342,x12344,x12345))
% 15.02/14.81 [1235]~E(x12351,x12352)+E(f346(x12353,x12354,x12351,x12355),f346(x12353,x12354,x12352,x12355))
% 15.02/14.81 [1236]~E(x12361,x12362)+E(f346(x12363,x12364,x12365,x12361),f346(x12363,x12364,x12365,x12362))
% 15.02/14.81 [1237]~E(x12371,x12372)+E(f174(x12371,x12373,x12374),f174(x12372,x12373,x12374))
% 15.02/14.81 [1238]~E(x12381,x12382)+E(f174(x12383,x12381,x12384),f174(x12383,x12382,x12384))
% 15.02/14.81 [1239]~E(x12391,x12392)+E(f174(x12393,x12394,x12391),f174(x12393,x12394,x12392))
% 15.02/14.81 [1240]~E(x12401,x12402)+E(f173(x12401,x12403,x12404),f173(x12402,x12403,x12404))
% 15.02/14.81 [1241]~E(x12411,x12412)+E(f173(x12413,x12411,x12414),f173(x12413,x12412,x12414))
% 15.02/14.81 [1242]~E(x12421,x12422)+E(f173(x12423,x12424,x12421),f173(x12423,x12424,x12422))
% 15.02/14.81 [1243]~E(x12431,x12432)+E(f206(x12431,x12433,x12434,x12435),f206(x12432,x12433,x12434,x12435))
% 15.02/14.81 [1244]~E(x12441,x12442)+E(f206(x12443,x12441,x12444,x12445),f206(x12443,x12442,x12444,x12445))
% 15.02/14.81 [1245]~E(x12451,x12452)+E(f206(x12453,x12454,x12451,x12455),f206(x12453,x12454,x12452,x12455))
% 15.02/14.81 [1246]~E(x12461,x12462)+E(f206(x12463,x12464,x12465,x12461),f206(x12463,x12464,x12465,x12462))
% 15.02/14.81 [1247]~E(x12471,x12472)+E(f653(x12471,x12473,x12474,x12475,x12476),f653(x12472,x12473,x12474,x12475,x12476))
% 15.02/14.81 [1248]~E(x12481,x12482)+E(f653(x12483,x12481,x12484,x12485,x12486),f653(x12483,x12482,x12484,x12485,x12486))
% 15.02/14.81 [1249]~E(x12491,x12492)+E(f653(x12493,x12494,x12491,x12495,x12496),f653(x12493,x12494,x12492,x12495,x12496))
% 15.02/14.81 [1250]~E(x12501,x12502)+E(f653(x12503,x12504,x12505,x12501,x12506),f653(x12503,x12504,x12505,x12502,x12506))
% 15.02/14.81 [1251]~E(x12511,x12512)+E(f653(x12513,x12514,x12515,x12516,x12511),f653(x12513,x12514,x12515,x12516,x12512))
% 15.02/14.81 [1252]~E(x12521,x12522)+E(f318(x12521,x12523,x12524,x12525),f318(x12522,x12523,x12524,x12525))
% 15.02/14.81 [1253]~E(x12531,x12532)+E(f318(x12533,x12531,x12534,x12535),f318(x12533,x12532,x12534,x12535))
% 15.02/14.81 [1254]~E(x12541,x12542)+E(f318(x12543,x12544,x12541,x12545),f318(x12543,x12544,x12542,x12545))
% 15.02/14.81 [1255]~E(x12551,x12552)+E(f318(x12553,x12554,x12555,x12551),f318(x12553,x12554,x12555,x12552))
% 15.02/14.81 [1256]~E(x12561,x12562)+E(f116(x12561,x12563,x12564),f116(x12562,x12563,x12564))
% 15.02/14.81 [1257]~E(x12571,x12572)+E(f116(x12573,x12571,x12574),f116(x12573,x12572,x12574))
% 15.02/14.81 [1258]~E(x12581,x12582)+E(f116(x12583,x12584,x12581),f116(x12583,x12584,x12582))
% 15.02/14.81 [1259]~E(x12591,x12592)+E(f745(x12591,x12593,x12594,x12595,x12596),f745(x12592,x12593,x12594,x12595,x12596))
% 15.02/14.81 [1260]~E(x12601,x12602)+E(f745(x12603,x12601,x12604,x12605,x12606),f745(x12603,x12602,x12604,x12605,x12606))
% 15.02/14.81 [1261]~E(x12611,x12612)+E(f745(x12613,x12614,x12611,x12615,x12616),f745(x12613,x12614,x12612,x12615,x12616))
% 15.02/14.81 [1262]~E(x12621,x12622)+E(f745(x12623,x12624,x12625,x12621,x12626),f745(x12623,x12624,x12625,x12622,x12626))
% 15.02/14.81 [1263]~E(x12631,x12632)+E(f745(x12633,x12634,x12635,x12636,x12631),f745(x12633,x12634,x12635,x12636,x12632))
% 15.02/14.81 [1264]~E(x12641,x12642)+E(f423(x12641,x12643,x12644,x12645),f423(x12642,x12643,x12644,x12645))
% 15.02/14.81 [1265]~E(x12651,x12652)+E(f423(x12653,x12651,x12654,x12655),f423(x12653,x12652,x12654,x12655))
% 15.02/14.81 [1266]~E(x12661,x12662)+E(f423(x12663,x12664,x12661,x12665),f423(x12663,x12664,x12662,x12665))
% 15.02/14.81 [1267]~E(x12671,x12672)+E(f423(x12673,x12674,x12675,x12671),f423(x12673,x12674,x12675,x12672))
% 15.02/14.81 [1268]~E(x12681,x12682)+E(f585(x12681,x12683,x12684),f585(x12682,x12683,x12684))
% 15.02/14.81 [1269]~E(x12691,x12692)+E(f585(x12693,x12691,x12694),f585(x12693,x12692,x12694))
% 15.02/14.81 [1270]~E(x12701,x12702)+E(f585(x12703,x12704,x12701),f585(x12703,x12704,x12702))
% 15.02/14.81 [1271]~E(x12711,x12712)+E(f472(x12711,x12713),f472(x12712,x12713))
% 15.02/14.81 [1272]~E(x12721,x12722)+E(f472(x12723,x12721),f472(x12723,x12722))
% 15.02/14.81 [1273]~E(x12731,x12732)+E(f648(x12731,x12733,x12734,x12735,x12736,x12737),f648(x12732,x12733,x12734,x12735,x12736,x12737))
% 15.02/14.81 [1274]~E(x12741,x12742)+E(f648(x12743,x12741,x12744,x12745,x12746,x12747),f648(x12743,x12742,x12744,x12745,x12746,x12747))
% 15.02/14.81 [1275]~E(x12751,x12752)+E(f648(x12753,x12754,x12751,x12755,x12756,x12757),f648(x12753,x12754,x12752,x12755,x12756,x12757))
% 15.02/14.81 [1276]~E(x12761,x12762)+E(f648(x12763,x12764,x12765,x12761,x12766,x12767),f648(x12763,x12764,x12765,x12762,x12766,x12767))
% 15.02/14.81 [1277]~E(x12771,x12772)+E(f648(x12773,x12774,x12775,x12776,x12771,x12777),f648(x12773,x12774,x12775,x12776,x12772,x12777))
% 15.02/14.81 [1278]~E(x12781,x12782)+E(f648(x12783,x12784,x12785,x12786,x12787,x12781),f648(x12783,x12784,x12785,x12786,x12787,x12782))
% 15.02/14.81 [1279]~E(x12791,x12792)+E(f709(x12791,x12793),f709(x12792,x12793))
% 15.02/14.81 [1280]~E(x12801,x12802)+E(f709(x12803,x12801),f709(x12803,x12802))
% 15.02/14.81 [1281]~E(x12811,x12812)+E(f334(x12811,x12813),f334(x12812,x12813))
% 15.02/14.81 [1282]~E(x12821,x12822)+E(f334(x12823,x12821),f334(x12823,x12822))
% 15.02/14.81 [1283]~E(x12831,x12832)+E(f470(x12831,x12833,x12834,x12835),f470(x12832,x12833,x12834,x12835))
% 15.02/14.81 [1284]~E(x12841,x12842)+E(f470(x12843,x12841,x12844,x12845),f470(x12843,x12842,x12844,x12845))
% 15.02/14.81 [1285]~E(x12851,x12852)+E(f470(x12853,x12854,x12851,x12855),f470(x12853,x12854,x12852,x12855))
% 15.02/14.81 [1286]~E(x12861,x12862)+E(f470(x12863,x12864,x12865,x12861),f470(x12863,x12864,x12865,x12862))
% 15.02/14.81 [1287]~E(x12871,x12872)+E(f861(x12871,x12873),f861(x12872,x12873))
% 15.02/14.81 [1288]~E(x12881,x12882)+E(f861(x12883,x12881),f861(x12883,x12882))
% 15.02/14.81 [1289]~E(x12891,x12892)+E(f228(x12891,x12893),f228(x12892,x12893))
% 15.02/14.81 [1290]~E(x12901,x12902)+E(f228(x12903,x12901),f228(x12903,x12902))
% 15.02/14.81 [1291]~E(x12911,x12912)+E(f760(x12911,x12913,x12914),f760(x12912,x12913,x12914))
% 15.02/14.81 [1292]~E(x12921,x12922)+E(f760(x12923,x12921,x12924),f760(x12923,x12922,x12924))
% 15.02/14.81 [1293]~E(x12931,x12932)+E(f760(x12933,x12934,x12931),f760(x12933,x12934,x12932))
% 15.02/14.81 [1294]~E(x12941,x12942)+E(f294(x12941,x12943,x12944),f294(x12942,x12943,x12944))
% 15.02/14.81 [1295]~E(x12951,x12952)+E(f294(x12953,x12951,x12954),f294(x12953,x12952,x12954))
% 15.02/14.81 [1296]~E(x12961,x12962)+E(f294(x12963,x12964,x12961),f294(x12963,x12964,x12962))
% 15.02/14.81 [1297]~E(x12971,x12972)+E(f658(x12971,x12973,x12974,x12975),f658(x12972,x12973,x12974,x12975))
% 15.02/14.81 [1298]~E(x12981,x12982)+E(f658(x12983,x12981,x12984,x12985),f658(x12983,x12982,x12984,x12985))
% 15.02/14.81 [1299]~E(x12991,x12992)+E(f658(x12993,x12994,x12991,x12995),f658(x12993,x12994,x12992,x12995))
% 15.02/14.81 [1300]~E(x13001,x13002)+E(f658(x13003,x13004,x13005,x13001),f658(x13003,x13004,x13005,x13002))
% 15.02/14.81 [1301]~E(x13011,x13012)+E(f654(x13011,x13013,x13014,x13015,x13016),f654(x13012,x13013,x13014,x13015,x13016))
% 15.02/14.81 [1302]~E(x13021,x13022)+E(f654(x13023,x13021,x13024,x13025,x13026),f654(x13023,x13022,x13024,x13025,x13026))
% 15.02/14.81 [1303]~E(x13031,x13032)+E(f654(x13033,x13034,x13031,x13035,x13036),f654(x13033,x13034,x13032,x13035,x13036))
% 15.02/14.81 [1304]~E(x13041,x13042)+E(f654(x13043,x13044,x13045,x13041,x13046),f654(x13043,x13044,x13045,x13042,x13046))
% 15.02/14.81 [1305]~E(x13051,x13052)+E(f654(x13053,x13054,x13055,x13056,x13051),f654(x13053,x13054,x13055,x13056,x13052))
% 15.02/14.81 [1306]~E(x13061,x13062)+E(f544(x13061,x13063,x13064,x13065,x13066),f544(x13062,x13063,x13064,x13065,x13066))
% 15.02/14.81 [1307]~E(x13071,x13072)+E(f544(x13073,x13071,x13074,x13075,x13076),f544(x13073,x13072,x13074,x13075,x13076))
% 15.02/14.81 [1308]~E(x13081,x13082)+E(f544(x13083,x13084,x13081,x13085,x13086),f544(x13083,x13084,x13082,x13085,x13086))
% 15.02/14.81 [1309]~E(x13091,x13092)+E(f544(x13093,x13094,x13095,x13091,x13096),f544(x13093,x13094,x13095,x13092,x13096))
% 15.02/14.81 [1310]~E(x13101,x13102)+E(f544(x13103,x13104,x13105,x13106,x13101),f544(x13103,x13104,x13105,x13106,x13102))
% 15.02/14.81 [1311]~E(x13111,x13112)+E(f899(x13111,x13113,x13114),f899(x13112,x13113,x13114))
% 15.02/14.81 [1312]~E(x13121,x13122)+E(f899(x13123,x13121,x13124),f899(x13123,x13122,x13124))
% 15.02/14.81 [1313]~E(x13131,x13132)+E(f899(x13133,x13134,x13131),f899(x13133,x13134,x13132))
% 15.02/14.81 [1314]~E(x13141,x13142)+E(f831(x13141,x13143),f831(x13142,x13143))
% 15.02/14.81 [1315]~E(x13151,x13152)+E(f831(x13153,x13151),f831(x13153,x13152))
% 15.02/14.81 [1316]~E(x13161,x13162)+E(f551(x13161,x13163,x13164,x13165,x13166,x13167),f551(x13162,x13163,x13164,x13165,x13166,x13167))
% 15.02/14.81 [1317]~E(x13171,x13172)+E(f551(x13173,x13171,x13174,x13175,x13176,x13177),f551(x13173,x13172,x13174,x13175,x13176,x13177))
% 15.02/14.81 [1318]~E(x13181,x13182)+E(f551(x13183,x13184,x13181,x13185,x13186,x13187),f551(x13183,x13184,x13182,x13185,x13186,x13187))
% 15.02/14.81 [1319]~E(x13191,x13192)+E(f551(x13193,x13194,x13195,x13191,x13196,x13197),f551(x13193,x13194,x13195,x13192,x13196,x13197))
% 15.02/14.81 [1320]~E(x13201,x13202)+E(f551(x13203,x13204,x13205,x13206,x13201,x13207),f551(x13203,x13204,x13205,x13206,x13202,x13207))
% 15.02/14.81 [1321]~E(x13211,x13212)+E(f551(x13213,x13214,x13215,x13216,x13217,x13211),f551(x13213,x13214,x13215,x13216,x13217,x13212))
% 15.02/14.81 [1322]~E(x13221,x13222)+E(f685(x13221,x13223,x13224,x13225),f685(x13222,x13223,x13224,x13225))
% 15.02/14.81 [1323]~E(x13231,x13232)+E(f685(x13233,x13231,x13234,x13235),f685(x13233,x13232,x13234,x13235))
% 15.02/14.81 [1324]~E(x13241,x13242)+E(f685(x13243,x13244,x13241,x13245),f685(x13243,x13244,x13242,x13245))
% 15.02/14.81 [1325]~E(x13251,x13252)+E(f685(x13253,x13254,x13255,x13251),f685(x13253,x13254,x13255,x13252))
% 15.02/14.81 [1326]~E(x13261,x13262)+E(f843(x13261,x13263,x13264,x13265,x13266,x13267),f843(x13262,x13263,x13264,x13265,x13266,x13267))
% 15.02/14.81 [1327]~E(x13271,x13272)+E(f843(x13273,x13271,x13274,x13275,x13276,x13277),f843(x13273,x13272,x13274,x13275,x13276,x13277))
% 15.02/14.81 [1328]~E(x13281,x13282)+E(f843(x13283,x13284,x13281,x13285,x13286,x13287),f843(x13283,x13284,x13282,x13285,x13286,x13287))
% 15.02/14.81 [1329]~E(x13291,x13292)+E(f843(x13293,x13294,x13295,x13291,x13296,x13297),f843(x13293,x13294,x13295,x13292,x13296,x13297))
% 15.02/14.81 [1330]~E(x13301,x13302)+E(f843(x13303,x13304,x13305,x13306,x13301,x13307),f843(x13303,x13304,x13305,x13306,x13302,x13307))
% 15.02/14.81 [1331]~E(x13311,x13312)+E(f843(x13313,x13314,x13315,x13316,x13317,x13311),f843(x13313,x13314,x13315,x13316,x13317,x13312))
% 15.02/14.81 [1332]~E(x13321,x13322)+E(f446(x13321,x13323,x13324,x13325),f446(x13322,x13323,x13324,x13325))
% 15.02/14.81 [1333]~E(x13331,x13332)+E(f446(x13333,x13331,x13334,x13335),f446(x13333,x13332,x13334,x13335))
% 15.02/14.81 [1334]~E(x13341,x13342)+E(f446(x13343,x13344,x13341,x13345),f446(x13343,x13344,x13342,x13345))
% 15.02/14.81 [1335]~E(x13351,x13352)+E(f446(x13353,x13354,x13355,x13351),f446(x13353,x13354,x13355,x13352))
% 15.02/14.81 [1336]~E(x13361,x13362)+E(f156(x13361,x13363,x13364,x13365),f156(x13362,x13363,x13364,x13365))
% 15.02/14.81 [1337]~E(x13371,x13372)+E(f156(x13373,x13371,x13374,x13375),f156(x13373,x13372,x13374,x13375))
% 15.02/14.81 [1338]~E(x13381,x13382)+E(f156(x13383,x13384,x13381,x13385),f156(x13383,x13384,x13382,x13385))
% 15.02/14.81 [1339]~E(x13391,x13392)+E(f156(x13393,x13394,x13395,x13391),f156(x13393,x13394,x13395,x13392))
% 15.02/14.81 [1340]~E(x13401,x13402)+E(f336(x13401),f336(x13402))
% 15.02/14.81 [1341]~E(x13411,x13412)+E(f416(x13411,x13413),f416(x13412,x13413))
% 15.02/14.81 [1342]~E(x13421,x13422)+E(f416(x13423,x13421),f416(x13423,x13422))
% 15.02/14.81 [1343]~E(x13431,x13432)+E(f758(x13431,x13433,x13434),f758(x13432,x13433,x13434))
% 15.02/14.81 [1344]~E(x13441,x13442)+E(f758(x13443,x13441,x13444),f758(x13443,x13442,x13444))
% 15.02/14.81 [1345]~E(x13451,x13452)+E(f758(x13453,x13454,x13451),f758(x13453,x13454,x13452))
% 15.02/14.81 [1346]~E(x13461,x13462)+E(f426(x13461,x13463,x13464,x13465,x13466),f426(x13462,x13463,x13464,x13465,x13466))
% 15.02/14.81 [1347]~E(x13471,x13472)+E(f426(x13473,x13471,x13474,x13475,x13476),f426(x13473,x13472,x13474,x13475,x13476))
% 15.02/14.81 [1348]~E(x13481,x13482)+E(f426(x13483,x13484,x13481,x13485,x13486),f426(x13483,x13484,x13482,x13485,x13486))
% 15.02/14.81 [1349]~E(x13491,x13492)+E(f426(x13493,x13494,x13495,x13491,x13496),f426(x13493,x13494,x13495,x13492,x13496))
% 15.02/14.81 [1350]~E(x13501,x13502)+E(f426(x13503,x13504,x13505,x13506,x13501),f426(x13503,x13504,x13505,x13506,x13502))
% 15.02/14.81 [1351]~E(x13511,x13512)+E(f23(x13511,x13513),f23(x13512,x13513))
% 15.02/14.81 [1352]~E(x13521,x13522)+E(f23(x13523,x13521),f23(x13523,x13522))
% 15.02/14.81 [1353]~E(x13531,x13532)+E(f359(x13531,x13533,x13534),f359(x13532,x13533,x13534))
% 15.02/14.81 [1354]~E(x13541,x13542)+E(f359(x13543,x13541,x13544),f359(x13543,x13542,x13544))
% 15.02/14.81 [1355]~E(x13551,x13552)+E(f359(x13553,x13554,x13551),f359(x13553,x13554,x13552))
% 15.02/14.81 [1356]~E(x13561,x13562)+E(f434(x13561,x13563,x13564,x13565,x13566),f434(x13562,x13563,x13564,x13565,x13566))
% 15.02/14.81 [1357]~E(x13571,x13572)+E(f434(x13573,x13571,x13574,x13575,x13576),f434(x13573,x13572,x13574,x13575,x13576))
% 15.02/14.81 [1358]~E(x13581,x13582)+E(f434(x13583,x13584,x13581,x13585,x13586),f434(x13583,x13584,x13582,x13585,x13586))
% 15.02/14.81 [1359]~E(x13591,x13592)+E(f434(x13593,x13594,x13595,x13591,x13596),f434(x13593,x13594,x13595,x13592,x13596))
% 15.02/14.81 [1360]~E(x13601,x13602)+E(f434(x13603,x13604,x13605,x13606,x13601),f434(x13603,x13604,x13605,x13606,x13602))
% 15.02/14.81 [1361]~E(x13611,x13612)+E(f698(x13611,x13613,x13614),f698(x13612,x13613,x13614))
% 15.02/14.81 [1362]~E(x13621,x13622)+E(f698(x13623,x13621,x13624),f698(x13623,x13622,x13624))
% 15.02/14.81 [1363]~E(x13631,x13632)+E(f698(x13633,x13634,x13631),f698(x13633,x13634,x13632))
% 15.02/14.81 [1364]~E(x13641,x13642)+E(f374(x13641,x13643,x13644),f374(x13642,x13643,x13644))
% 15.02/14.81 [1365]~E(x13651,x13652)+E(f374(x13653,x13651,x13654),f374(x13653,x13652,x13654))
% 15.02/14.81 [1366]~E(x13661,x13662)+E(f374(x13663,x13664,x13661),f374(x13663,x13664,x13662))
% 15.02/14.81 [1367]~E(x13671,x13672)+E(f532(x13671,x13673,x13674,x13675),f532(x13672,x13673,x13674,x13675))
% 15.02/14.81 [1368]~E(x13681,x13682)+E(f532(x13683,x13681,x13684,x13685),f532(x13683,x13682,x13684,x13685))
% 15.02/14.81 [1369]~E(x13691,x13692)+E(f532(x13693,x13694,x13691,x13695),f532(x13693,x13694,x13692,x13695))
% 15.02/14.81 [1370]~E(x13701,x13702)+E(f532(x13703,x13704,x13705,x13701),f532(x13703,x13704,x13705,x13702))
% 15.02/14.81 [1371]~E(x13711,x13712)+E(f511(x13711,x13713,x13714),f511(x13712,x13713,x13714))
% 15.02/14.81 [1372]~E(x13721,x13722)+E(f511(x13723,x13721,x13724),f511(x13723,x13722,x13724))
% 15.02/14.81 [1373]~E(x13731,x13732)+E(f511(x13733,x13734,x13731),f511(x13733,x13734,x13732))
% 15.02/14.81 [1374]~E(x13741,x13742)+E(f442(x13741,x13743,x13744,x13745,x13746,x13747,x13748),f442(x13742,x13743,x13744,x13745,x13746,x13747,x13748))
% 15.02/14.81 [1375]~E(x13751,x13752)+E(f442(x13753,x13751,x13754,x13755,x13756,x13757,x13758),f442(x13753,x13752,x13754,x13755,x13756,x13757,x13758))
% 15.02/14.81 [1376]~E(x13761,x13762)+E(f442(x13763,x13764,x13761,x13765,x13766,x13767,x13768),f442(x13763,x13764,x13762,x13765,x13766,x13767,x13768))
% 15.02/14.81 [1377]~E(x13771,x13772)+E(f442(x13773,x13774,x13775,x13771,x13776,x13777,x13778),f442(x13773,x13774,x13775,x13772,x13776,x13777,x13778))
% 15.02/14.81 [1378]~E(x13781,x13782)+E(f442(x13783,x13784,x13785,x13786,x13781,x13787,x13788),f442(x13783,x13784,x13785,x13786,x13782,x13787,x13788))
% 15.02/14.81 [1379]~E(x13791,x13792)+E(f442(x13793,x13794,x13795,x13796,x13797,x13791,x13798),f442(x13793,x13794,x13795,x13796,x13797,x13792,x13798))
% 15.02/14.81 [1380]~E(x13801,x13802)+E(f442(x13803,x13804,x13805,x13806,x13807,x13808,x13801),f442(x13803,x13804,x13805,x13806,x13807,x13808,x13802))
% 15.02/14.81 [1381]~E(x13811,x13812)+E(f340(x13811,x13813,x13814),f340(x13812,x13813,x13814))
% 15.02/14.81 [1382]~E(x13821,x13822)+E(f340(x13823,x13821,x13824),f340(x13823,x13822,x13824))
% 15.02/14.81 [1383]~E(x13831,x13832)+E(f340(x13833,x13834,x13831),f340(x13833,x13834,x13832))
% 15.02/14.81 [1384]~E(x13841,x13842)+E(f274(x13841,x13843),f274(x13842,x13843))
% 15.02/14.81 [1385]~E(x13851,x13852)+E(f274(x13853,x13851),f274(x13853,x13852))
% 15.02/14.81 [1386]~E(x13861,x13862)+E(f639(x13861,x13863,x13864),f639(x13862,x13863,x13864))
% 15.02/14.81 [1387]~E(x13871,x13872)+E(f639(x13873,x13871,x13874),f639(x13873,x13872,x13874))
% 15.02/14.81 [1388]~E(x13881,x13882)+E(f639(x13883,x13884,x13881),f639(x13883,x13884,x13882))
% 15.02/14.81 [1389]~E(x13891,x13892)+E(f795(x13891,x13893,x13894),f795(x13892,x13893,x13894))
% 15.02/14.81 [1390]~E(x13901,x13902)+E(f795(x13903,x13901,x13904),f795(x13903,x13902,x13904))
% 15.02/14.81 [1391]~E(x13911,x13912)+E(f795(x13913,x13914,x13911),f795(x13913,x13914,x13912))
% 15.02/14.81 [1392]~E(x13921,x13922)+E(f640(x13921,x13923,x13924),f640(x13922,x13923,x13924))
% 15.02/14.81 [1393]~E(x13931,x13932)+E(f640(x13933,x13931,x13934),f640(x13933,x13932,x13934))
% 15.02/14.81 [1394]~E(x13941,x13942)+E(f640(x13943,x13944,x13941),f640(x13943,x13944,x13942))
% 15.02/14.81 [1395]~E(x13951,x13952)+E(f854(x13951,x13953,x13954,x13955,x13956,x13957,x13958),f854(x13952,x13953,x13954,x13955,x13956,x13957,x13958))
% 15.02/14.81 [1396]~E(x13961,x13962)+E(f854(x13963,x13961,x13964,x13965,x13966,x13967,x13968),f854(x13963,x13962,x13964,x13965,x13966,x13967,x13968))
% 15.02/14.81 [1397]~E(x13971,x13972)+E(f854(x13973,x13974,x13971,x13975,x13976,x13977,x13978),f854(x13973,x13974,x13972,x13975,x13976,x13977,x13978))
% 15.02/14.81 [1398]~E(x13981,x13982)+E(f854(x13983,x13984,x13985,x13981,x13986,x13987,x13988),f854(x13983,x13984,x13985,x13982,x13986,x13987,x13988))
% 15.02/14.81 [1399]~E(x13991,x13992)+E(f854(x13993,x13994,x13995,x13996,x13991,x13997,x13998),f854(x13993,x13994,x13995,x13996,x13992,x13997,x13998))
% 15.02/14.81 [1400]~E(x14001,x14002)+E(f854(x14003,x14004,x14005,x14006,x14007,x14001,x14008),f854(x14003,x14004,x14005,x14006,x14007,x14002,x14008))
% 15.02/14.81 [1401]~E(x14011,x14012)+E(f854(x14013,x14014,x14015,x14016,x14017,x14018,x14011),f854(x14013,x14014,x14015,x14016,x14017,x14018,x14012))
% 15.02/14.81 [1402]~E(x14021,x14022)+E(f884(x14021,x14023,x14024),f884(x14022,x14023,x14024))
% 15.02/14.81 [1403]~E(x14031,x14032)+E(f884(x14033,x14031,x14034),f884(x14033,x14032,x14034))
% 15.02/14.81 [1404]~E(x14041,x14042)+E(f884(x14043,x14044,x14041),f884(x14043,x14044,x14042))
% 15.02/14.81 [1405]~E(x14051,x14052)+E(f552(x14051,x14053,x14054,x14055,x14056,x14057),f552(x14052,x14053,x14054,x14055,x14056,x14057))
% 15.02/14.81 [1406]~E(x14061,x14062)+E(f552(x14063,x14061,x14064,x14065,x14066,x14067),f552(x14063,x14062,x14064,x14065,x14066,x14067))
% 15.02/14.81 [1407]~E(x14071,x14072)+E(f552(x14073,x14074,x14071,x14075,x14076,x14077),f552(x14073,x14074,x14072,x14075,x14076,x14077))
% 15.02/14.81 [1408]~E(x14081,x14082)+E(f552(x14083,x14084,x14085,x14081,x14086,x14087),f552(x14083,x14084,x14085,x14082,x14086,x14087))
% 15.02/14.81 [1409]~E(x14091,x14092)+E(f552(x14093,x14094,x14095,x14096,x14091,x14097),f552(x14093,x14094,x14095,x14096,x14092,x14097))
% 15.02/14.81 [1410]~E(x14101,x14102)+E(f552(x14103,x14104,x14105,x14106,x14107,x14101),f552(x14103,x14104,x14105,x14106,x14107,x14102))
% 15.02/14.81 [1411]~E(x14111,x14112)+E(f180(x14111),f180(x14112))
% 15.02/14.81 [1412]~E(x14121,x14122)+E(f252(x14121,x14123,x14124,x14125,x14126),f252(x14122,x14123,x14124,x14125,x14126))
% 15.02/14.81 [1413]~E(x14131,x14132)+E(f252(x14133,x14131,x14134,x14135,x14136),f252(x14133,x14132,x14134,x14135,x14136))
% 15.02/14.81 [1414]~E(x14141,x14142)+E(f252(x14143,x14144,x14141,x14145,x14146),f252(x14143,x14144,x14142,x14145,x14146))
% 15.02/14.81 [1415]~E(x14151,x14152)+E(f252(x14153,x14154,x14155,x14151,x14156),f252(x14153,x14154,x14155,x14152,x14156))
% 15.02/14.81 [1416]~E(x14161,x14162)+E(f252(x14163,x14164,x14165,x14166,x14161),f252(x14163,x14164,x14165,x14166,x14162))
% 15.02/14.81 [1417]~E(x14171,x14172)+E(f584(x14171,x14173,x14174,x14175),f584(x14172,x14173,x14174,x14175))
% 15.02/14.81 [1418]~E(x14181,x14182)+E(f584(x14183,x14181,x14184,x14185),f584(x14183,x14182,x14184,x14185))
% 15.02/14.81 [1419]~E(x14191,x14192)+E(f584(x14193,x14194,x14191,x14195),f584(x14193,x14194,x14192,x14195))
% 15.02/14.81 [1420]~E(x14201,x14202)+E(f584(x14203,x14204,x14205,x14201),f584(x14203,x14204,x14205,x14202))
% 15.02/14.81 [1421]~E(x14211,x14212)+E(f508(x14211,x14213,x14214,x14215,x14216,x14217,x14218,x14219,x142110),f508(x14212,x14213,x14214,x14215,x14216,x14217,x14218,x14219,x142110))
% 15.02/14.81 [1422]~E(x14221,x14222)+E(f508(x14223,x14221,x14224,x14225,x14226,x14227,x14228,x14229,x142210),f508(x14223,x14222,x14224,x14225,x14226,x14227,x14228,x14229,x142210))
% 15.02/14.81 [1423]~E(x14231,x14232)+E(f508(x14233,x14234,x14231,x14235,x14236,x14237,x14238,x14239,x142310),f508(x14233,x14234,x14232,x14235,x14236,x14237,x14238,x14239,x142310))
% 15.02/14.81 [1424]~E(x14241,x14242)+E(f508(x14243,x14244,x14245,x14241,x14246,x14247,x14248,x14249,x142410),f508(x14243,x14244,x14245,x14242,x14246,x14247,x14248,x14249,x142410))
% 15.02/14.81 [1425]~E(x14251,x14252)+E(f508(x14253,x14254,x14255,x14256,x14251,x14257,x14258,x14259,x142510),f508(x14253,x14254,x14255,x14256,x14252,x14257,x14258,x14259,x142510))
% 15.02/14.81 [1426]~E(x14261,x14262)+E(f508(x14263,x14264,x14265,x14266,x14267,x14261,x14268,x14269,x142610),f508(x14263,x14264,x14265,x14266,x14267,x14262,x14268,x14269,x142610))
% 15.02/14.81 [1427]~E(x14271,x14272)+E(f508(x14273,x14274,x14275,x14276,x14277,x14278,x14271,x14279,x142710),f508(x14273,x14274,x14275,x14276,x14277,x14278,x14272,x14279,x142710))
% 15.02/14.81 [1428]~E(x14281,x14282)+E(f508(x14283,x14284,x14285,x14286,x14287,x14288,x14289,x14281,x142810),f508(x14283,x14284,x14285,x14286,x14287,x14288,x14289,x14282,x142810))
% 15.02/14.81 [1429]~E(x14291,x14292)+E(f508(x14293,x14294,x14295,x14296,x14297,x14298,x14299,x142910,x14291),f508(x14293,x14294,x14295,x14296,x14297,x14298,x14299,x142910,x14292))
% 15.02/14.81 [1430]~E(x14301,x14302)+E(f688(x14301,x14303,x14304,x14305),f688(x14302,x14303,x14304,x14305))
% 15.02/14.81 [1431]~E(x14311,x14312)+E(f688(x14313,x14311,x14314,x14315),f688(x14313,x14312,x14314,x14315))
% 15.02/14.81 [1432]~E(x14321,x14322)+E(f688(x14323,x14324,x14321,x14325),f688(x14323,x14324,x14322,x14325))
% 15.02/14.81 [1433]~E(x14331,x14332)+E(f688(x14333,x14334,x14335,x14331),f688(x14333,x14334,x14335,x14332))
% 15.02/14.81 [1434]~E(x14341,x14342)+E(f781(x14341,x14343,x14344,x14345,x14346,x14347,x14348),f781(x14342,x14343,x14344,x14345,x14346,x14347,x14348))
% 15.02/14.81 [1435]~E(x14351,x14352)+E(f781(x14353,x14351,x14354,x14355,x14356,x14357,x14358),f781(x14353,x14352,x14354,x14355,x14356,x14357,x14358))
% 15.02/14.81 [1436]~E(x14361,x14362)+E(f781(x14363,x14364,x14361,x14365,x14366,x14367,x14368),f781(x14363,x14364,x14362,x14365,x14366,x14367,x14368))
% 15.02/14.81 [1437]~E(x14371,x14372)+E(f781(x14373,x14374,x14375,x14371,x14376,x14377,x14378),f781(x14373,x14374,x14375,x14372,x14376,x14377,x14378))
% 15.02/14.81 [1438]~E(x14381,x14382)+E(f781(x14383,x14384,x14385,x14386,x14381,x14387,x14388),f781(x14383,x14384,x14385,x14386,x14382,x14387,x14388))
% 15.02/14.81 [1439]~E(x14391,x14392)+E(f781(x14393,x14394,x14395,x14396,x14397,x14391,x14398),f781(x14393,x14394,x14395,x14396,x14397,x14392,x14398))
% 15.02/14.81 [1440]~E(x14401,x14402)+E(f781(x14403,x14404,x14405,x14406,x14407,x14408,x14401),f781(x14403,x14404,x14405,x14406,x14407,x14408,x14402))
% 15.02/14.81 [1441]~E(x14411,x14412)+E(f473(x14411,x14413),f473(x14412,x14413))
% 15.02/14.81 [1442]~E(x14421,x14422)+E(f473(x14423,x14421),f473(x14423,x14422))
% 15.02/14.81 [1443]~E(x14431,x14432)+E(f769(x14431,x14433,x14434,x14435),f769(x14432,x14433,x14434,x14435))
% 15.02/14.81 [1444]~E(x14441,x14442)+E(f769(x14443,x14441,x14444,x14445),f769(x14443,x14442,x14444,x14445))
% 15.02/14.81 [1445]~E(x14451,x14452)+E(f769(x14453,x14454,x14451,x14455),f769(x14453,x14454,x14452,x14455))
% 15.02/14.81 [1446]~E(x14461,x14462)+E(f769(x14463,x14464,x14465,x14461),f769(x14463,x14464,x14465,x14462))
% 15.02/14.81 [1447]~E(x14471,x14472)+E(f271(x14471,x14473),f271(x14472,x14473))
% 15.02/14.81 [1448]~E(x14481,x14482)+E(f271(x14483,x14481),f271(x14483,x14482))
% 15.02/14.81 [1449]~E(x14491,x14492)+E(f903(x14491,x14493,x14494,x14495,x14496),f903(x14492,x14493,x14494,x14495,x14496))
% 15.02/14.81 [1450]~E(x14501,x14502)+E(f903(x14503,x14501,x14504,x14505,x14506),f903(x14503,x14502,x14504,x14505,x14506))
% 15.02/14.81 [1451]~E(x14511,x14512)+E(f903(x14513,x14514,x14511,x14515,x14516),f903(x14513,x14514,x14512,x14515,x14516))
% 15.02/14.81 [1452]~E(x14521,x14522)+E(f903(x14523,x14524,x14525,x14521,x14526),f903(x14523,x14524,x14525,x14522,x14526))
% 15.02/14.81 [1453]~E(x14531,x14532)+E(f903(x14533,x14534,x14535,x14536,x14531),f903(x14533,x14534,x14535,x14536,x14532))
% 15.02/14.81 [1454]~E(x14541,x14542)+E(f66(x14541,x14543,x14544),f66(x14542,x14543,x14544))
% 15.02/14.81 [1455]~E(x14551,x14552)+E(f66(x14553,x14551,x14554),f66(x14553,x14552,x14554))
% 15.02/14.81 [1456]~E(x14561,x14562)+E(f66(x14563,x14564,x14561),f66(x14563,x14564,x14562))
% 15.02/14.81 [1457]~E(x14571,x14572)+E(f692(x14571,x14573,x14574),f692(x14572,x14573,x14574))
% 15.02/14.81 [1458]~E(x14581,x14582)+E(f692(x14583,x14581,x14584),f692(x14583,x14582,x14584))
% 15.02/14.81 [1459]~E(x14591,x14592)+E(f692(x14593,x14594,x14591),f692(x14593,x14594,x14592))
% 15.02/14.81 [1460]~E(x14601,x14602)+E(f590(x14601,x14603,x14604,x14605,x14606,x14607),f590(x14602,x14603,x14604,x14605,x14606,x14607))
% 15.02/14.81 [1461]~E(x14611,x14612)+E(f590(x14613,x14611,x14614,x14615,x14616,x14617),f590(x14613,x14612,x14614,x14615,x14616,x14617))
% 15.02/14.81 [1462]~E(x14621,x14622)+E(f590(x14623,x14624,x14621,x14625,x14626,x14627),f590(x14623,x14624,x14622,x14625,x14626,x14627))
% 15.02/14.81 [1463]~E(x14631,x14632)+E(f590(x14633,x14634,x14635,x14631,x14636,x14637),f590(x14633,x14634,x14635,x14632,x14636,x14637))
% 15.02/14.81 [1464]~E(x14641,x14642)+E(f590(x14643,x14644,x14645,x14646,x14641,x14647),f590(x14643,x14644,x14645,x14646,x14642,x14647))
% 15.02/14.81 [1465]~E(x14651,x14652)+E(f590(x14653,x14654,x14655,x14656,x14657,x14651),f590(x14653,x14654,x14655,x14656,x14657,x14652))
% 15.02/14.81 [1466]~E(x14661,x14662)+E(f568(x14661,x14663,x14664),f568(x14662,x14663,x14664))
% 15.02/14.81 [1467]~E(x14671,x14672)+E(f568(x14673,x14671,x14674),f568(x14673,x14672,x14674))
% 15.02/14.81 [1468]~E(x14681,x14682)+E(f568(x14683,x14684,x14681),f568(x14683,x14684,x14682))
% 15.02/14.81 [1469]~E(x14691,x14692)+E(f630(x14691,x14693,x14694,x14695,x14696),f630(x14692,x14693,x14694,x14695,x14696))
% 15.02/14.81 [1470]~E(x14701,x14702)+E(f630(x14703,x14701,x14704,x14705,x14706),f630(x14703,x14702,x14704,x14705,x14706))
% 15.02/14.81 [1471]~E(x14711,x14712)+E(f630(x14713,x14714,x14711,x14715,x14716),f630(x14713,x14714,x14712,x14715,x14716))
% 15.02/14.81 [1472]~E(x14721,x14722)+E(f630(x14723,x14724,x14725,x14721,x14726),f630(x14723,x14724,x14725,x14722,x14726))
% 15.02/14.81 [1473]~E(x14731,x14732)+E(f630(x14733,x14734,x14735,x14736,x14731),f630(x14733,x14734,x14735,x14736,x14732))
% 15.02/14.81 [1474]~E(x14741,x14742)+E(f761(x14741,x14743,x14744),f761(x14742,x14743,x14744))
% 15.02/14.81 [1475]~E(x14751,x14752)+E(f761(x14753,x14751,x14754),f761(x14753,x14752,x14754))
% 15.02/14.81 [1476]~E(x14761,x14762)+E(f761(x14763,x14764,x14761),f761(x14763,x14764,x14762))
% 15.02/14.81 [1477]~E(x14771,x14772)+E(f443(x14771),f443(x14772))
% 15.02/14.81 [1478]~E(x14781,x14782)+E(f493(x14781,x14783,x14784),f493(x14782,x14783,x14784))
% 15.02/14.81 [1479]~E(x14791,x14792)+E(f493(x14793,x14791,x14794),f493(x14793,x14792,x14794))
% 15.02/14.81 [1480]~E(x14801,x14802)+E(f493(x14803,x14804,x14801),f493(x14803,x14804,x14802))
% 15.02/14.81 [1481]~E(x14811,x14812)+E(f602(x14811,x14813,x14814),f602(x14812,x14813,x14814))
% 15.02/14.81 [1482]~E(x14821,x14822)+E(f602(x14823,x14821,x14824),f602(x14823,x14822,x14824))
% 15.02/14.81 [1483]~E(x14831,x14832)+E(f602(x14833,x14834,x14831),f602(x14833,x14834,x14832))
% 15.02/14.81 [1484]~E(x14841,x14842)+E(f122(x14841,x14843,x14844,x14845),f122(x14842,x14843,x14844,x14845))
% 15.02/14.81 [1485]~E(x14851,x14852)+E(f122(x14853,x14851,x14854,x14855),f122(x14853,x14852,x14854,x14855))
% 15.02/14.81 [1486]~E(x14861,x14862)+E(f122(x14863,x14864,x14861,x14865),f122(x14863,x14864,x14862,x14865))
% 15.02/14.81 [1487]~E(x14871,x14872)+E(f122(x14873,x14874,x14875,x14871),f122(x14873,x14874,x14875,x14872))
% 15.02/14.81 [1488]~E(x14881,x14882)+E(f704(x14881,x14883,x14884),f704(x14882,x14883,x14884))
% 15.02/14.81 [1489]~E(x14891,x14892)+E(f704(x14893,x14891,x14894),f704(x14893,x14892,x14894))
% 15.02/14.81 [1490]~E(x14901,x14902)+E(f704(x14903,x14904,x14901),f704(x14903,x14904,x14902))
% 15.02/14.81 [1491]~E(x14911,x14912)+E(f689(x14911,x14913,x14914,x14915,x14916),f689(x14912,x14913,x14914,x14915,x14916))
% 15.02/14.81 [1492]~E(x14921,x14922)+E(f689(x14923,x14921,x14924,x14925,x14926),f689(x14923,x14922,x14924,x14925,x14926))
% 15.02/14.81 [1493]~E(x14931,x14932)+E(f689(x14933,x14934,x14931,x14935,x14936),f689(x14933,x14934,x14932,x14935,x14936))
% 15.02/14.81 [1494]~E(x14941,x14942)+E(f689(x14943,x14944,x14945,x14941,x14946),f689(x14943,x14944,x14945,x14942,x14946))
% 15.02/14.81 [1495]~E(x14951,x14952)+E(f689(x14953,x14954,x14955,x14956,x14951),f689(x14953,x14954,x14955,x14956,x14952))
% 15.02/14.81 [1496]~E(x14961,x14962)+E(f598(x14961,x14963,x14964),f598(x14962,x14963,x14964))
% 15.02/14.81 [1497]~E(x14971,x14972)+E(f598(x14973,x14971,x14974),f598(x14973,x14972,x14974))
% 15.02/14.81 [1498]~E(x14981,x14982)+E(f598(x14983,x14984,x14981),f598(x14983,x14984,x14982))
% 15.02/14.81 [1499]~E(x14991,x14992)+E(f554(x14991,x14993),f554(x14992,x14993))
% 15.02/14.81 [1500]~E(x15001,x15002)+E(f554(x15003,x15001),f554(x15003,x15002))
% 15.02/14.81 [1501]~E(x15011,x15012)+E(f376(x15011,x15013,x15014),f376(x15012,x15013,x15014))
% 15.02/14.81 [1502]~E(x15021,x15022)+E(f376(x15023,x15021,x15024),f376(x15023,x15022,x15024))
% 15.02/14.81 [1503]~E(x15031,x15032)+E(f376(x15033,x15034,x15031),f376(x15033,x15034,x15032))
% 15.02/14.81 [1504]~E(x15041,x15042)+E(f444(x15041,x15043,x15044),f444(x15042,x15043,x15044))
% 15.02/14.81 [1505]~E(x15051,x15052)+E(f444(x15053,x15051,x15054),f444(x15053,x15052,x15054))
% 15.02/14.81 [1506]~E(x15061,x15062)+E(f444(x15063,x15064,x15061),f444(x15063,x15064,x15062))
% 15.02/14.81 [1507]~E(x15071,x15072)+E(f412(x15071,x15073),f412(x15072,x15073))
% 15.02/14.81 [1508]~E(x15081,x15082)+E(f412(x15083,x15081),f412(x15083,x15082))
% 15.02/14.81 [1509]~E(x15091,x15092)+E(f345(x15091,x15093,x15094,x15095),f345(x15092,x15093,x15094,x15095))
% 15.02/14.81 [1510]~E(x15101,x15102)+E(f345(x15103,x15101,x15104,x15105),f345(x15103,x15102,x15104,x15105))
% 15.02/14.81 [1511]~E(x15111,x15112)+E(f345(x15113,x15114,x15111,x15115),f345(x15113,x15114,x15112,x15115))
% 15.02/14.81 [1512]~E(x15121,x15122)+E(f345(x15123,x15124,x15125,x15121),f345(x15123,x15124,x15125,x15122))
% 15.02/14.81 [1513]~E(x15131,x15132)+E(f791(x15131,x15133,x15134,x15135,x15136,x15137,x15138),f791(x15132,x15133,x15134,x15135,x15136,x15137,x15138))
% 15.02/14.81 [1514]~E(x15141,x15142)+E(f791(x15143,x15141,x15144,x15145,x15146,x15147,x15148),f791(x15143,x15142,x15144,x15145,x15146,x15147,x15148))
% 15.02/14.81 [1515]~E(x15151,x15152)+E(f791(x15153,x15154,x15151,x15155,x15156,x15157,x15158),f791(x15153,x15154,x15152,x15155,x15156,x15157,x15158))
% 15.02/14.81 [1516]~E(x15161,x15162)+E(f791(x15163,x15164,x15165,x15161,x15166,x15167,x15168),f791(x15163,x15164,x15165,x15162,x15166,x15167,x15168))
% 15.02/14.81 [1517]~E(x15171,x15172)+E(f791(x15173,x15174,x15175,x15176,x15171,x15177,x15178),f791(x15173,x15174,x15175,x15176,x15172,x15177,x15178))
% 15.02/14.81 [1518]~E(x15181,x15182)+E(f791(x15183,x15184,x15185,x15186,x15187,x15181,x15188),f791(x15183,x15184,x15185,x15186,x15187,x15182,x15188))
% 15.02/14.81 [1519]~E(x15191,x15192)+E(f791(x15193,x15194,x15195,x15196,x15197,x15198,x15191),f791(x15193,x15194,x15195,x15196,x15197,x15198,x15192))
% 15.02/14.81 [1520]~E(x15201,x15202)+E(f619(x15201,x15203),f619(x15202,x15203))
% 15.02/14.81 [1521]~E(x15211,x15212)+E(f619(x15213,x15211),f619(x15213,x15212))
% 15.02/14.81 [1522]~E(x15221,x15222)+E(f513(x15221,x15223,x15224),f513(x15222,x15223,x15224))
% 15.02/14.81 [1523]~E(x15231,x15232)+E(f513(x15233,x15231,x15234),f513(x15233,x15232,x15234))
% 15.02/14.81 [1524]~E(x15241,x15242)+E(f513(x15243,x15244,x15241),f513(x15243,x15244,x15242))
% 15.02/14.81 [1525]~E(x15251,x15252)+E(f387(x15251,x15253,x15254),f387(x15252,x15253,x15254))
% 15.02/14.81 [1526]~E(x15261,x15262)+E(f387(x15263,x15261,x15264),f387(x15263,x15262,x15264))
% 15.02/14.81 [1527]~E(x15271,x15272)+E(f387(x15273,x15274,x15271),f387(x15273,x15274,x15272))
% 15.02/14.81 [1528]~E(x15281,x15282)+E(f531(x15281,x15283,x15284,x15285,x15286),f531(x15282,x15283,x15284,x15285,x15286))
% 15.02/14.81 [1529]~E(x15291,x15292)+E(f531(x15293,x15291,x15294,x15295,x15296),f531(x15293,x15292,x15294,x15295,x15296))
% 15.02/14.81 [1530]~E(x15301,x15302)+E(f531(x15303,x15304,x15301,x15305,x15306),f531(x15303,x15304,x15302,x15305,x15306))
% 15.02/14.81 [1531]~E(x15311,x15312)+E(f531(x15313,x15314,x15315,x15311,x15316),f531(x15313,x15314,x15315,x15312,x15316))
% 15.02/14.81 [1532]~E(x15321,x15322)+E(f531(x15323,x15324,x15325,x15326,x15321),f531(x15323,x15324,x15325,x15326,x15322))
% 15.02/14.81 [1533]~E(x15331,x15332)+E(f495(x15331,x15333,x15334,x15335),f495(x15332,x15333,x15334,x15335))
% 15.02/14.81 [1534]~E(x15341,x15342)+E(f495(x15343,x15341,x15344,x15345),f495(x15343,x15342,x15344,x15345))
% 15.02/14.81 [1535]~E(x15351,x15352)+E(f495(x15353,x15354,x15351,x15355),f495(x15353,x15354,x15352,x15355))
% 15.02/14.81 [1536]~E(x15361,x15362)+E(f495(x15363,x15364,x15365,x15361),f495(x15363,x15364,x15365,x15362))
% 15.02/14.81 [1537]~E(x15371,x15372)+E(f540(x15371,x15373,x15374,x15375),f540(x15372,x15373,x15374,x15375))
% 15.02/14.81 [1538]~E(x15381,x15382)+E(f540(x15383,x15381,x15384,x15385),f540(x15383,x15382,x15384,x15385))
% 15.02/14.81 [1539]~E(x15391,x15392)+E(f540(x15393,x15394,x15391,x15395),f540(x15393,x15394,x15392,x15395))
% 15.02/14.81 [1540]~E(x15401,x15402)+E(f540(x15403,x15404,x15405,x15401),f540(x15403,x15404,x15405,x15402))
% 15.02/14.81 [1541]~E(x15411,x15412)+E(f666(x15411,x15413,x15414,x15415),f666(x15412,x15413,x15414,x15415))
% 15.02/14.81 [1542]~E(x15421,x15422)+E(f666(x15423,x15421,x15424,x15425),f666(x15423,x15422,x15424,x15425))
% 15.02/14.81 [1543]~E(x15431,x15432)+E(f666(x15433,x15434,x15431,x15435),f666(x15433,x15434,x15432,x15435))
% 15.02/14.81 [1544]~E(x15441,x15442)+E(f666(x15443,x15444,x15445,x15441),f666(x15443,x15444,x15445,x15442))
% 15.02/14.81 [1545]~E(x15451,x15452)+E(f199(x15451,x15453,x15454,x15455),f199(x15452,x15453,x15454,x15455))
% 15.02/14.81 [1546]~E(x15461,x15462)+E(f199(x15463,x15461,x15464,x15465),f199(x15463,x15462,x15464,x15465))
% 15.02/14.81 [1547]~E(x15471,x15472)+E(f199(x15473,x15474,x15471,x15475),f199(x15473,x15474,x15472,x15475))
% 15.02/14.81 [1548]~E(x15481,x15482)+E(f199(x15483,x15484,x15485,x15481),f199(x15483,x15484,x15485,x15482))
% 15.02/14.81 [1549]~E(x15491,x15492)+E(f210(x15491,x15493,x15494,x15495),f210(x15492,x15493,x15494,x15495))
% 15.02/14.81 [1550]~E(x15501,x15502)+E(f210(x15503,x15501,x15504,x15505),f210(x15503,x15502,x15504,x15505))
% 15.02/14.81 [1551]~E(x15511,x15512)+E(f210(x15513,x15514,x15511,x15515),f210(x15513,x15514,x15512,x15515))
% 15.02/14.81 [1552]~E(x15521,x15522)+E(f210(x15523,x15524,x15525,x15521),f210(x15523,x15524,x15525,x15522))
% 15.02/14.81 [1553]~E(x15531,x15532)+E(f525(x15531,x15533,x15534),f525(x15532,x15533,x15534))
% 15.02/14.81 [1554]~E(x15541,x15542)+E(f525(x15543,x15541,x15544),f525(x15543,x15542,x15544))
% 15.02/14.81 [1555]~E(x15551,x15552)+E(f525(x15553,x15554,x15551),f525(x15553,x15554,x15552))
% 15.02/14.81 [1556]~E(x15561,x15562)+E(f625(x15561,x15563,x15564,x15565,x15566),f625(x15562,x15563,x15564,x15565,x15566))
% 15.02/14.81 [1557]~E(x15571,x15572)+E(f625(x15573,x15571,x15574,x15575,x15576),f625(x15573,x15572,x15574,x15575,x15576))
% 15.02/14.81 [1558]~E(x15581,x15582)+E(f625(x15583,x15584,x15581,x15585,x15586),f625(x15583,x15584,x15582,x15585,x15586))
% 15.02/14.81 [1559]~E(x15591,x15592)+E(f625(x15593,x15594,x15595,x15591,x15596),f625(x15593,x15594,x15595,x15592,x15596))
% 15.02/14.81 [1560]~E(x15601,x15602)+E(f625(x15603,x15604,x15605,x15606,x15601),f625(x15603,x15604,x15605,x15606,x15602))
% 15.02/14.81 [1561]~E(x15611,x15612)+E(f753(x15611,x15613,x15614,x15615),f753(x15612,x15613,x15614,x15615))
% 15.02/14.81 [1562]~E(x15621,x15622)+E(f753(x15623,x15621,x15624,x15625),f753(x15623,x15622,x15624,x15625))
% 15.02/14.81 [1563]~E(x15631,x15632)+E(f753(x15633,x15634,x15631,x15635),f753(x15633,x15634,x15632,x15635))
% 15.02/14.81 [1564]~E(x15641,x15642)+E(f753(x15643,x15644,x15645,x15641),f753(x15643,x15644,x15645,x15642))
% 15.02/14.81 [1565]~E(x15651,x15652)+E(f569(x15651,x15653,x15654,x15655),f569(x15652,x15653,x15654,x15655))
% 15.02/14.81 [1566]~E(x15661,x15662)+E(f569(x15663,x15661,x15664,x15665),f569(x15663,x15662,x15664,x15665))
% 15.02/14.81 [1567]~E(x15671,x15672)+E(f569(x15673,x15674,x15671,x15675),f569(x15673,x15674,x15672,x15675))
% 15.02/14.81 [1568]~E(x15681,x15682)+E(f569(x15683,x15684,x15685,x15681),f569(x15683,x15684,x15685,x15682))
% 15.02/14.81 [1569]~E(x15691,x15692)+E(f878(x15691,x15693,x15694,x15695,x15696,x15697,x15698),f878(x15692,x15693,x15694,x15695,x15696,x15697,x15698))
% 15.02/14.81 [1570]~E(x15701,x15702)+E(f878(x15703,x15701,x15704,x15705,x15706,x15707,x15708),f878(x15703,x15702,x15704,x15705,x15706,x15707,x15708))
% 15.02/14.81 [1571]~E(x15711,x15712)+E(f878(x15713,x15714,x15711,x15715,x15716,x15717,x15718),f878(x15713,x15714,x15712,x15715,x15716,x15717,x15718))
% 15.02/14.81 [1572]~E(x15721,x15722)+E(f878(x15723,x15724,x15725,x15721,x15726,x15727,x15728),f878(x15723,x15724,x15725,x15722,x15726,x15727,x15728))
% 15.02/14.81 [1573]~E(x15731,x15732)+E(f878(x15733,x15734,x15735,x15736,x15731,x15737,x15738),f878(x15733,x15734,x15735,x15736,x15732,x15737,x15738))
% 15.02/14.81 [1574]~E(x15741,x15742)+E(f878(x15743,x15744,x15745,x15746,x15747,x15741,x15748),f878(x15743,x15744,x15745,x15746,x15747,x15742,x15748))
% 15.02/14.81 [1575]~E(x15751,x15752)+E(f878(x15753,x15754,x15755,x15756,x15757,x15758,x15751),f878(x15753,x15754,x15755,x15756,x15757,x15758,x15752))
% 15.02/14.81 [1576]~E(x15761,x15762)+E(f710(x15761,x15763),f710(x15762,x15763))
% 15.02/14.81 [1577]~E(x15771,x15772)+E(f710(x15773,x15771),f710(x15773,x15772))
% 15.02/14.81 [1578]~E(x15781,x15782)+E(f909(x15781,x15783,x15784,x15785,x15786),f909(x15782,x15783,x15784,x15785,x15786))
% 15.02/14.81 [1579]~E(x15791,x15792)+E(f909(x15793,x15791,x15794,x15795,x15796),f909(x15793,x15792,x15794,x15795,x15796))
% 15.02/14.81 [1580]~E(x15801,x15802)+E(f909(x15803,x15804,x15801,x15805,x15806),f909(x15803,x15804,x15802,x15805,x15806))
% 15.02/14.81 [1581]~E(x15811,x15812)+E(f909(x15813,x15814,x15815,x15811,x15816),f909(x15813,x15814,x15815,x15812,x15816))
% 15.02/14.81 [1582]~E(x15821,x15822)+E(f909(x15823,x15824,x15825,x15826,x15821),f909(x15823,x15824,x15825,x15826,x15822))
% 15.02/14.81 [1583]~E(x15831,x15832)+E(f409(x15831,x15833),f409(x15832,x15833))
% 15.02/14.81 [1584]~E(x15841,x15842)+E(f409(x15843,x15841),f409(x15843,x15842))
% 15.02/14.81 [1585]~E(x15851,x15852)+E(f422(x15851,x15853,x15854,x15855),f422(x15852,x15853,x15854,x15855))
% 15.02/14.81 [1586]~E(x15861,x15862)+E(f422(x15863,x15861,x15864,x15865),f422(x15863,x15862,x15864,x15865))
% 15.02/14.81 [1587]~E(x15871,x15872)+E(f422(x15873,x15874,x15871,x15875),f422(x15873,x15874,x15872,x15875))
% 15.02/14.81 [1588]~E(x15881,x15882)+E(f422(x15883,x15884,x15885,x15881),f422(x15883,x15884,x15885,x15882))
% 15.02/14.81 [1589]~E(x15891,x15892)+E(f504(x15891,x15893,x15894,x15895),f504(x15892,x15893,x15894,x15895))
% 15.02/14.81 [1590]~E(x15901,x15902)+E(f504(x15903,x15901,x15904,x15905),f504(x15903,x15902,x15904,x15905))
% 15.02/14.81 [1591]~E(x15911,x15912)+E(f504(x15913,x15914,x15911,x15915),f504(x15913,x15914,x15912,x15915))
% 15.02/14.81 [1592]~E(x15921,x15922)+E(f504(x15923,x15924,x15925,x15921),f504(x15923,x15924,x15925,x15922))
% 15.02/14.81 [1593]~E(x15931,x15932)+E(f53(x15931,x15933),f53(x15932,x15933))
% 15.02/14.81 [1594]~E(x15941,x15942)+E(f53(x15943,x15941),f53(x15943,x15942))
% 15.02/14.81 [1595]~E(x15951,x15952)+E(f349(x15951),f349(x15952))
% 15.02/14.81 [1596]~E(x15961,x15962)+E(f497(x15961,x15963,x15964,x15965),f497(x15962,x15963,x15964,x15965))
% 15.02/14.81 [1597]~E(x15971,x15972)+E(f497(x15973,x15971,x15974,x15975),f497(x15973,x15972,x15974,x15975))
% 15.02/14.81 [1598]~E(x15981,x15982)+E(f497(x15983,x15984,x15981,x15985),f497(x15983,x15984,x15982,x15985))
% 15.02/14.81 [1599]~E(x15991,x15992)+E(f497(x15993,x15994,x15995,x15991),f497(x15993,x15994,x15995,x15992))
% 15.02/14.81 [1600]~E(x16001,x16002)+E(f849(x16001,x16003,x16004,x16005,x16006,x16007,x16008,x16009),f849(x16002,x16003,x16004,x16005,x16006,x16007,x16008,x16009))
% 15.02/14.81 [1601]~E(x16011,x16012)+E(f849(x16013,x16011,x16014,x16015,x16016,x16017,x16018,x16019),f849(x16013,x16012,x16014,x16015,x16016,x16017,x16018,x16019))
% 15.02/14.81 [1602]~E(x16021,x16022)+E(f849(x16023,x16024,x16021,x16025,x16026,x16027,x16028,x16029),f849(x16023,x16024,x16022,x16025,x16026,x16027,x16028,x16029))
% 15.02/14.81 [1603]~E(x16031,x16032)+E(f849(x16033,x16034,x16035,x16031,x16036,x16037,x16038,x16039),f849(x16033,x16034,x16035,x16032,x16036,x16037,x16038,x16039))
% 15.02/14.81 [1604]~E(x16041,x16042)+E(f849(x16043,x16044,x16045,x16046,x16041,x16047,x16048,x16049),f849(x16043,x16044,x16045,x16046,x16042,x16047,x16048,x16049))
% 15.02/14.81 [1605]~E(x16051,x16052)+E(f849(x16053,x16054,x16055,x16056,x16057,x16051,x16058,x16059),f849(x16053,x16054,x16055,x16056,x16057,x16052,x16058,x16059))
% 15.02/14.81 [1606]~E(x16061,x16062)+E(f849(x16063,x16064,x16065,x16066,x16067,x16068,x16061,x16069),f849(x16063,x16064,x16065,x16066,x16067,x16068,x16062,x16069))
% 15.02/14.81 [1607]~E(x16071,x16072)+E(f849(x16073,x16074,x16075,x16076,x16077,x16078,x16079,x16071),f849(x16073,x16074,x16075,x16076,x16077,x16078,x16079,x16072))
% 15.02/14.81 [1608]~E(x16081,x16082)+E(f821(x16081,x16083),f821(x16082,x16083))
% 15.02/14.81 [1609]~E(x16091,x16092)+E(f821(x16093,x16091),f821(x16093,x16092))
% 15.02/14.81 [1610]~E(x16101,x16102)+E(f402(x16101,x16103,x16104),f402(x16102,x16103,x16104))
% 15.02/14.81 [1611]~E(x16111,x16112)+E(f402(x16113,x16111,x16114),f402(x16113,x16112,x16114))
% 15.02/14.81 [1612]~E(x16121,x16122)+E(f402(x16123,x16124,x16121),f402(x16123,x16124,x16122))
% 15.02/14.81 [1613]~E(x16131,x16132)+E(f527(x16131,x16133,x16134,x16135,x16136),f527(x16132,x16133,x16134,x16135,x16136))
% 15.02/14.81 [1614]~E(x16141,x16142)+E(f527(x16143,x16141,x16144,x16145,x16146),f527(x16143,x16142,x16144,x16145,x16146))
% 15.02/14.81 [1615]~E(x16151,x16152)+E(f527(x16153,x16154,x16151,x16155,x16156),f527(x16153,x16154,x16152,x16155,x16156))
% 15.02/14.81 [1616]~E(x16161,x16162)+E(f527(x16163,x16164,x16165,x16161,x16166),f527(x16163,x16164,x16165,x16162,x16166))
% 15.02/14.81 [1617]~E(x16171,x16172)+E(f527(x16173,x16174,x16175,x16176,x16171),f527(x16173,x16174,x16175,x16176,x16172))
% 15.02/14.81 [1618]~E(x16181,x16182)+E(f406(x16181),f406(x16182))
% 15.02/14.81 [1619]~E(x16191,x16192)+E(f624(x16191,x16193,x16194,x16195,x16196),f624(x16192,x16193,x16194,x16195,x16196))
% 15.02/14.81 [1620]~E(x16201,x16202)+E(f624(x16203,x16201,x16204,x16205,x16206),f624(x16203,x16202,x16204,x16205,x16206))
% 15.02/14.81 [1621]~E(x16211,x16212)+E(f624(x16213,x16214,x16211,x16215,x16216),f624(x16213,x16214,x16212,x16215,x16216))
% 15.02/14.81 [1622]~E(x16221,x16222)+E(f624(x16223,x16224,x16225,x16221,x16226),f624(x16223,x16224,x16225,x16222,x16226))
% 15.02/14.81 [1623]~E(x16231,x16232)+E(f624(x16233,x16234,x16235,x16236,x16231),f624(x16233,x16234,x16235,x16236,x16232))
% 15.02/14.81 [1624]~E(x16241,x16242)+E(f330(x16241,x16243,x16244,x16245),f330(x16242,x16243,x16244,x16245))
% 15.02/14.81 [1625]~E(x16251,x16252)+E(f330(x16253,x16251,x16254,x16255),f330(x16253,x16252,x16254,x16255))
% 15.02/14.81 [1626]~E(x16261,x16262)+E(f330(x16263,x16264,x16261,x16265),f330(x16263,x16264,x16262,x16265))
% 15.02/14.81 [1627]~E(x16271,x16272)+E(f330(x16273,x16274,x16275,x16271),f330(x16273,x16274,x16275,x16272))
% 15.02/14.81 [1628]~E(x16281,x16282)+E(f772(x16281,x16283,x16284),f772(x16282,x16283,x16284))
% 15.02/14.81 [1629]~E(x16291,x16292)+E(f772(x16293,x16291,x16294),f772(x16293,x16292,x16294))
% 15.02/14.81 [1630]~E(x16301,x16302)+E(f772(x16303,x16304,x16301),f772(x16303,x16304,x16302))
% 15.02/14.81 [1631]~E(x16311,x16312)+E(f715(x16311,x16313,x16314),f715(x16312,x16313,x16314))
% 15.02/14.81 [1632]~E(x16321,x16322)+E(f715(x16323,x16321,x16324),f715(x16323,x16322,x16324))
% 15.02/14.81 [1633]~E(x16331,x16332)+E(f715(x16333,x16334,x16331),f715(x16333,x16334,x16332))
% 15.02/14.81 [1634]~E(x16341,x16342)+E(f404(x16341,x16343,x16344),f404(x16342,x16343,x16344))
% 15.02/14.81 [1635]~E(x16351,x16352)+E(f404(x16353,x16351,x16354),f404(x16353,x16352,x16354))
% 15.02/14.81 [1636]~E(x16361,x16362)+E(f404(x16363,x16364,x16361),f404(x16363,x16364,x16362))
% 15.02/14.81 [1637]~E(x16371,x16372)+E(f617(x16371,x16373),f617(x16372,x16373))
% 15.02/14.81 [1638]~E(x16381,x16382)+E(f617(x16383,x16381),f617(x16383,x16382))
% 15.02/14.81 [1639]~E(x16391,x16392)+E(f400(x16391,x16393,x16394,x16395),f400(x16392,x16393,x16394,x16395))
% 15.02/14.81 [1640]~E(x16401,x16402)+E(f400(x16403,x16401,x16404,x16405),f400(x16403,x16402,x16404,x16405))
% 15.02/14.81 [1641]~E(x16411,x16412)+E(f400(x16413,x16414,x16411,x16415),f400(x16413,x16414,x16412,x16415))
% 15.02/14.81 [1642]~E(x16421,x16422)+E(f400(x16423,x16424,x16425,x16421),f400(x16423,x16424,x16425,x16422))
% 15.02/14.81 [1643]~E(x16431,x16432)+E(f291(x16431,x16433),f291(x16432,x16433))
% 15.02/14.81 [1644]~E(x16441,x16442)+E(f291(x16443,x16441),f291(x16443,x16442))
% 15.02/14.81 [1645]~E(x16451,x16452)+E(f681(x16451,x16453,x16454,x16455,x16456),f681(x16452,x16453,x16454,x16455,x16456))
% 15.02/14.81 [1646]~E(x16461,x16462)+E(f681(x16463,x16461,x16464,x16465,x16466),f681(x16463,x16462,x16464,x16465,x16466))
% 15.02/14.81 [1647]~E(x16471,x16472)+E(f681(x16473,x16474,x16471,x16475,x16476),f681(x16473,x16474,x16472,x16475,x16476))
% 15.02/14.81 [1648]~E(x16481,x16482)+E(f681(x16483,x16484,x16485,x16481,x16486),f681(x16483,x16484,x16485,x16482,x16486))
% 15.02/14.81 [1649]~E(x16491,x16492)+E(f681(x16493,x16494,x16495,x16496,x16491),f681(x16493,x16494,x16495,x16496,x16492))
% 15.02/14.81 [1650]~E(x16501,x16502)+E(f742(x16501,x16503,x16504,x16505),f742(x16502,x16503,x16504,x16505))
% 15.02/14.81 [1651]~E(x16511,x16512)+E(f742(x16513,x16511,x16514,x16515),f742(x16513,x16512,x16514,x16515))
% 15.02/14.81 [1652]~E(x16521,x16522)+E(f742(x16523,x16524,x16521,x16525),f742(x16523,x16524,x16522,x16525))
% 15.02/14.81 [1653]~E(x16531,x16532)+E(f742(x16533,x16534,x16535,x16531),f742(x16533,x16534,x16535,x16532))
% 15.02/14.81 [1654]~E(x16541,x16542)+E(f744(x16541,x16543,x16544,x16545,x16546),f744(x16542,x16543,x16544,x16545,x16546))
% 15.02/14.81 [1655]~E(x16551,x16552)+E(f744(x16553,x16551,x16554,x16555,x16556),f744(x16553,x16552,x16554,x16555,x16556))
% 15.02/14.81 [1656]~E(x16561,x16562)+E(f744(x16563,x16564,x16561,x16565,x16566),f744(x16563,x16564,x16562,x16565,x16566))
% 15.02/14.81 [1657]~E(x16571,x16572)+E(f744(x16573,x16574,x16575,x16571,x16576),f744(x16573,x16574,x16575,x16572,x16576))
% 15.02/14.81 [1658]~E(x16581,x16582)+E(f744(x16583,x16584,x16585,x16586,x16581),f744(x16583,x16584,x16585,x16586,x16582))
% 15.02/14.81 [1659]~E(x16591,x16592)+E(f277(x16591),f277(x16592))
% 15.02/14.81 [1660]~E(x16601,x16602)+E(f645(x16601,x16603,x16604,x16605,x16606),f645(x16602,x16603,x16604,x16605,x16606))
% 15.02/14.81 [1661]~E(x16611,x16612)+E(f645(x16613,x16611,x16614,x16615,x16616),f645(x16613,x16612,x16614,x16615,x16616))
% 15.02/14.81 [1662]~E(x16621,x16622)+E(f645(x16623,x16624,x16621,x16625,x16626),f645(x16623,x16624,x16622,x16625,x16626))
% 15.02/14.81 [1663]~E(x16631,x16632)+E(f645(x16633,x16634,x16635,x16631,x16636),f645(x16633,x16634,x16635,x16632,x16636))
% 15.02/14.81 [1664]~E(x16641,x16642)+E(f645(x16643,x16644,x16645,x16646,x16641),f645(x16643,x16644,x16645,x16646,x16642))
% 15.02/14.81 [1665]~E(x16651,x16652)+E(f501(x16651,x16653,x16654),f501(x16652,x16653,x16654))
% 15.02/14.81 [1666]~E(x16661,x16662)+E(f501(x16663,x16661,x16664),f501(x16663,x16662,x16664))
% 15.02/14.81 [1667]~E(x16671,x16672)+E(f501(x16673,x16674,x16671),f501(x16673,x16674,x16672))
% 15.02/14.81 [1668]~E(x16681,x16682)+E(f231(x16681,x16683,x16684),f231(x16682,x16683,x16684))
% 15.02/14.81 [1669]~E(x16691,x16692)+E(f231(x16693,x16691,x16694),f231(x16693,x16692,x16694))
% 15.02/14.81 [1670]~E(x16701,x16702)+E(f231(x16703,x16704,x16701),f231(x16703,x16704,x16702))
% 15.02/14.81 [1671]~E(x16711,x16712)+E(f627(x16711,x16713,x16714,x16715,x16716),f627(x16712,x16713,x16714,x16715,x16716))
% 15.02/14.81 [1672]~E(x16721,x16722)+E(f627(x16723,x16721,x16724,x16725,x16726),f627(x16723,x16722,x16724,x16725,x16726))
% 15.02/14.81 [1673]~E(x16731,x16732)+E(f627(x16733,x16734,x16731,x16735,x16736),f627(x16733,x16734,x16732,x16735,x16736))
% 15.02/14.81 [1674]~E(x16741,x16742)+E(f627(x16743,x16744,x16745,x16741,x16746),f627(x16743,x16744,x16745,x16742,x16746))
% 15.02/14.81 [1675]~E(x16751,x16752)+E(f627(x16753,x16754,x16755,x16756,x16751),f627(x16753,x16754,x16755,x16756,x16752))
% 15.02/14.81 [1676]~E(x16761,x16762)+E(f537(x16761,x16763,x16764,x16765),f537(x16762,x16763,x16764,x16765))
% 15.02/14.81 [1677]~E(x16771,x16772)+E(f537(x16773,x16771,x16774,x16775),f537(x16773,x16772,x16774,x16775))
% 15.02/14.81 [1678]~E(x16781,x16782)+E(f537(x16783,x16784,x16781,x16785),f537(x16783,x16784,x16782,x16785))
% 15.02/14.81 [1679]~E(x16791,x16792)+E(f537(x16793,x16794,x16795,x16791),f537(x16793,x16794,x16795,x16792))
% 15.02/14.81 [1680]~E(x16801,x16802)+E(f521(x16801,x16803,x16804),f521(x16802,x16803,x16804))
% 15.02/14.81 [1681]~E(x16811,x16812)+E(f521(x16813,x16811,x16814),f521(x16813,x16812,x16814))
% 15.02/14.81 [1682]~E(x16821,x16822)+E(f521(x16823,x16824,x16821),f521(x16823,x16824,x16822))
% 15.02/14.81 [1683]~E(x16831,x16832)+E(f517(x16831,x16833,x16834),f517(x16832,x16833,x16834))
% 15.02/14.81 [1684]~E(x16841,x16842)+E(f517(x16843,x16841,x16844),f517(x16843,x16842,x16844))
% 15.02/14.81 [1685]~E(x16851,x16852)+E(f517(x16853,x16854,x16851),f517(x16853,x16854,x16852))
% 15.02/14.81 [1686]~E(x16861,x16862)+E(f196(x16861,x16863,x16864,x16865),f196(x16862,x16863,x16864,x16865))
% 15.02/14.81 [1687]~E(x16871,x16872)+E(f196(x16873,x16871,x16874,x16875),f196(x16873,x16872,x16874,x16875))
% 15.02/14.81 [1688]~E(x16881,x16882)+E(f196(x16883,x16884,x16881,x16885),f196(x16883,x16884,x16882,x16885))
% 15.02/14.81 [1689]~E(x16891,x16892)+E(f196(x16893,x16894,x16895,x16891),f196(x16893,x16894,x16895,x16892))
% 15.02/14.81 [1690]~E(x16901,x16902)+E(f538(x16901,x16903,x16904,x16905,x16906,x16907),f538(x16902,x16903,x16904,x16905,x16906,x16907))
% 15.02/14.81 [1691]~E(x16911,x16912)+E(f538(x16913,x16911,x16914,x16915,x16916,x16917),f538(x16913,x16912,x16914,x16915,x16916,x16917))
% 15.02/14.81 [1692]~E(x16921,x16922)+E(f538(x16923,x16924,x16921,x16925,x16926,x16927),f538(x16923,x16924,x16922,x16925,x16926,x16927))
% 15.02/14.81 [1693]~E(x16931,x16932)+E(f538(x16933,x16934,x16935,x16931,x16936,x16937),f538(x16933,x16934,x16935,x16932,x16936,x16937))
% 15.02/14.81 [1694]~E(x16941,x16942)+E(f538(x16943,x16944,x16945,x16946,x16941,x16947),f538(x16943,x16944,x16945,x16946,x16942,x16947))
% 15.02/14.81 [1695]~E(x16951,x16952)+E(f538(x16953,x16954,x16955,x16956,x16957,x16951),f538(x16953,x16954,x16955,x16956,x16957,x16952))
% 15.02/14.81 [1696]~E(x16961,x16962)+E(f379(x16961,x16963,x16964),f379(x16962,x16963,x16964))
% 15.02/14.81 [1697]~E(x16971,x16972)+E(f379(x16973,x16971,x16974),f379(x16973,x16972,x16974))
% 15.02/14.81 [1698]~E(x16981,x16982)+E(f379(x16983,x16984,x16981),f379(x16983,x16984,x16982))
% 15.02/14.81 [1699]~E(x16991,x16992)+E(f848(x16991,x16993,x16994,x16995,x16996,x16997,x16998),f848(x16992,x16993,x16994,x16995,x16996,x16997,x16998))
% 15.02/14.81 [1700]~E(x17001,x17002)+E(f848(x17003,x17001,x17004,x17005,x17006,x17007,x17008),f848(x17003,x17002,x17004,x17005,x17006,x17007,x17008))
% 15.02/14.81 [1701]~E(x17011,x17012)+E(f848(x17013,x17014,x17011,x17015,x17016,x17017,x17018),f848(x17013,x17014,x17012,x17015,x17016,x17017,x17018))
% 15.02/14.81 [1702]~E(x17021,x17022)+E(f848(x17023,x17024,x17025,x17021,x17026,x17027,x17028),f848(x17023,x17024,x17025,x17022,x17026,x17027,x17028))
% 15.02/14.81 [1703]~E(x17031,x17032)+E(f848(x17033,x17034,x17035,x17036,x17031,x17037,x17038),f848(x17033,x17034,x17035,x17036,x17032,x17037,x17038))
% 15.02/14.81 [1704]~E(x17041,x17042)+E(f848(x17043,x17044,x17045,x17046,x17047,x17041,x17048),f848(x17043,x17044,x17045,x17046,x17047,x17042,x17048))
% 15.02/14.81 [1705]~E(x17051,x17052)+E(f848(x17053,x17054,x17055,x17056,x17057,x17058,x17051),f848(x17053,x17054,x17055,x17056,x17057,x17058,x17052))
% 15.02/14.81 [1706]~E(x17061,x17062)+E(f438(x17061,x17063),f438(x17062,x17063))
% 15.02/14.81 [1707]~E(x17071,x17072)+E(f438(x17073,x17071),f438(x17073,x17072))
% 15.02/14.81 [1708]~E(x17081,x17082)+E(f352(x17081,x17083),f352(x17082,x17083))
% 15.02/14.81 [1709]~E(x17091,x17092)+E(f352(x17093,x17091),f352(x17093,x17092))
% 15.02/14.81 [1710]~E(x17101,x17102)+E(f887(x17101,x17103,x17104,x17105,x17106,x17107,x17108),f887(x17102,x17103,x17104,x17105,x17106,x17107,x17108))
% 15.02/14.81 [1711]~E(x17111,x17112)+E(f887(x17113,x17111,x17114,x17115,x17116,x17117,x17118),f887(x17113,x17112,x17114,x17115,x17116,x17117,x17118))
% 15.02/14.81 [1712]~E(x17121,x17122)+E(f887(x17123,x17124,x17121,x17125,x17126,x17127,x17128),f887(x17123,x17124,x17122,x17125,x17126,x17127,x17128))
% 15.02/14.81 [1713]~E(x17131,x17132)+E(f887(x17133,x17134,x17135,x17131,x17136,x17137,x17138),f887(x17133,x17134,x17135,x17132,x17136,x17137,x17138))
% 15.02/14.81 [1714]~E(x17141,x17142)+E(f887(x17143,x17144,x17145,x17146,x17141,x17147,x17148),f887(x17143,x17144,x17145,x17146,x17142,x17147,x17148))
% 15.02/14.81 [1715]~E(x17151,x17152)+E(f887(x17153,x17154,x17155,x17156,x17157,x17151,x17158),f887(x17153,x17154,x17155,x17156,x17157,x17152,x17158))
% 15.02/14.81 [1716]~E(x17161,x17162)+E(f887(x17163,x17164,x17165,x17166,x17167,x17168,x17161),f887(x17163,x17164,x17165,x17166,x17167,x17168,x17162))
% 15.02/14.81 [1717]~E(x17171,x17172)+E(f812(x17171,x17173),f812(x17172,x17173))
% 15.02/14.81 [1718]~E(x17181,x17182)+E(f812(x17183,x17181),f812(x17183,x17182))
% 15.02/14.81 [1719]~E(x17191,x17192)+E(f893(x17191,x17193,x17194),f893(x17192,x17193,x17194))
% 15.02/14.81 [1720]~E(x17201,x17202)+E(f893(x17203,x17201,x17204),f893(x17203,x17202,x17204))
% 15.02/14.81 [1721]~E(x17211,x17212)+E(f893(x17213,x17214,x17211),f893(x17213,x17214,x17212))
% 15.02/14.81 [1722]~E(x17221,x17222)+E(f687(x17221,x17223,x17224,x17225),f687(x17222,x17223,x17224,x17225))
% 15.02/14.81 [1723]~E(x17231,x17232)+E(f687(x17233,x17231,x17234,x17235),f687(x17233,x17232,x17234,x17235))
% 15.02/14.81 [1724]~E(x17241,x17242)+E(f687(x17243,x17244,x17241,x17245),f687(x17243,x17244,x17242,x17245))
% 15.02/14.81 [1725]~E(x17251,x17252)+E(f687(x17253,x17254,x17255,x17251),f687(x17253,x17254,x17255,x17252))
% 15.02/14.81 [1726]~E(x17261,x17262)+E(f738(x17261,x17263),f738(x17262,x17263))
% 15.02/14.81 [1727]~E(x17271,x17272)+E(f738(x17273,x17271),f738(x17273,x17272))
% 15.02/14.81 [1728]~E(x17281,x17282)+E(f486(x17281,x17283,x17284,x17285,x17286,x17287,x17288),f486(x17282,x17283,x17284,x17285,x17286,x17287,x17288))
% 15.02/14.81 [1729]~E(x17291,x17292)+E(f486(x17293,x17291,x17294,x17295,x17296,x17297,x17298),f486(x17293,x17292,x17294,x17295,x17296,x17297,x17298))
% 15.02/14.81 [1730]~E(x17301,x17302)+E(f486(x17303,x17304,x17301,x17305,x17306,x17307,x17308),f486(x17303,x17304,x17302,x17305,x17306,x17307,x17308))
% 15.02/14.81 [1731]~E(x17311,x17312)+E(f486(x17313,x17314,x17315,x17311,x17316,x17317,x17318),f486(x17313,x17314,x17315,x17312,x17316,x17317,x17318))
% 15.02/14.81 [1732]~E(x17321,x17322)+E(f486(x17323,x17324,x17325,x17326,x17321,x17327,x17328),f486(x17323,x17324,x17325,x17326,x17322,x17327,x17328))
% 15.02/14.81 [1733]~E(x17331,x17332)+E(f486(x17333,x17334,x17335,x17336,x17337,x17331,x17338),f486(x17333,x17334,x17335,x17336,x17337,x17332,x17338))
% 15.02/14.81 [1734]~E(x17341,x17342)+E(f486(x17343,x17344,x17345,x17346,x17347,x17348,x17341),f486(x17343,x17344,x17345,x17346,x17347,x17348,x17342))
% 15.02/14.81 [1735]~E(x17351,x17352)+E(f577(x17351,x17353,x17354,x17355,x17356),f577(x17352,x17353,x17354,x17355,x17356))
% 15.02/14.81 [1736]~E(x17361,x17362)+E(f577(x17363,x17361,x17364,x17365,x17366),f577(x17363,x17362,x17364,x17365,x17366))
% 15.02/14.81 [1737]~E(x17371,x17372)+E(f577(x17373,x17374,x17371,x17375,x17376),f577(x17373,x17374,x17372,x17375,x17376))
% 15.02/14.81 [1738]~E(x17381,x17382)+E(f577(x17383,x17384,x17385,x17381,x17386),f577(x17383,x17384,x17385,x17382,x17386))
% 15.02/14.81 [1739]~E(x17391,x17392)+E(f577(x17393,x17394,x17395,x17396,x17391),f577(x17393,x17394,x17395,x17396,x17392))
% 15.02/14.81 [1740]~E(x17401,x17402)+E(f690(x17401,x17403,x17404),f690(x17402,x17403,x17404))
% 15.02/14.81 [1741]~E(x17411,x17412)+E(f690(x17413,x17411,x17414),f690(x17413,x17412,x17414))
% 15.02/14.81 [1742]~E(x17421,x17422)+E(f690(x17423,x17424,x17421),f690(x17423,x17424,x17422))
% 15.02/14.81 [1743]~E(x17431,x17432)+E(f835(x17431,x17433,x17434),f835(x17432,x17433,x17434))
% 15.02/14.81 [1744]~E(x17441,x17442)+E(f835(x17443,x17441,x17444),f835(x17443,x17442,x17444))
% 15.02/14.81 [1745]~E(x17451,x17452)+E(f835(x17453,x17454,x17451),f835(x17453,x17454,x17452))
% 15.02/14.81 [1746]~E(x17461,x17462)+E(f21(x17461,x17463,x17464,x17465),f21(x17462,x17463,x17464,x17465))
% 15.02/14.81 [1747]~E(x17471,x17472)+E(f21(x17473,x17471,x17474,x17475),f21(x17473,x17472,x17474,x17475))
% 15.02/14.81 [1748]~E(x17481,x17482)+E(f21(x17483,x17484,x17481,x17485),f21(x17483,x17484,x17482,x17485))
% 15.02/14.81 [1749]~E(x17491,x17492)+E(f21(x17493,x17494,x17495,x17491),f21(x17493,x17494,x17495,x17492))
% 15.02/14.81 [1750]~E(x17501,x17502)+E(f268(x17501,x17503),f268(x17502,x17503))
% 15.02/14.81 [1751]~E(x17511,x17512)+E(f268(x17513,x17511),f268(x17513,x17512))
% 15.02/14.81 [1752]~E(x17521,x17522)+E(f643(x17521,x17523,x17524,x17525),f643(x17522,x17523,x17524,x17525))
% 15.02/14.81 [1753]~E(x17531,x17532)+E(f643(x17533,x17531,x17534,x17535),f643(x17533,x17532,x17534,x17535))
% 15.02/14.81 [1754]~E(x17541,x17542)+E(f643(x17543,x17544,x17541,x17545),f643(x17543,x17544,x17542,x17545))
% 15.02/14.81 [1755]~E(x17551,x17552)+E(f643(x17553,x17554,x17555,x17551),f643(x17553,x17554,x17555,x17552))
% 15.02/14.81 [1756]~E(x17561,x17562)+E(f739(x17561,x17563,x17564),f739(x17562,x17563,x17564))
% 15.02/14.81 [1757]~E(x17571,x17572)+E(f739(x17573,x17571,x17574),f739(x17573,x17572,x17574))
% 15.02/14.81 [1758]~E(x17581,x17582)+E(f739(x17583,x17584,x17581),f739(x17583,x17584,x17582))
% 15.02/14.81 [1759]~E(x17591,x17592)+E(f667(x17591,x17593),f667(x17592,x17593))
% 15.02/14.81 [1760]~E(x17601,x17602)+E(f667(x17603,x17601),f667(x17603,x17602))
% 15.02/14.81 [1761]~E(x17611,x17612)+E(f356(x17611,x17613,x17614),f356(x17612,x17613,x17614))
% 15.02/14.81 [1762]~E(x17621,x17622)+E(f356(x17623,x17621,x17624),f356(x17623,x17622,x17624))
% 15.02/14.81 [1763]~E(x17631,x17632)+E(f356(x17633,x17634,x17631),f356(x17633,x17634,x17632))
% 15.02/14.81 [1764]~E(x17641,x17642)+E(f828(x17641,x17643,x17644,x17645),f828(x17642,x17643,x17644,x17645))
% 15.02/14.81 [1765]~E(x17651,x17652)+E(f828(x17653,x17651,x17654,x17655),f828(x17653,x17652,x17654,x17655))
% 15.02/14.81 [1766]~E(x17661,x17662)+E(f828(x17663,x17664,x17661,x17665),f828(x17663,x17664,x17662,x17665))
% 15.02/14.81 [1767]~E(x17671,x17672)+E(f828(x17673,x17674,x17675,x17671),f828(x17673,x17674,x17675,x17672))
% 15.02/14.81 [1768]~E(x17681,x17682)+E(f419(x17681,x17683,x17684,x17685,x17686,x17687),f419(x17682,x17683,x17684,x17685,x17686,x17687))
% 15.02/14.81 [1769]~E(x17691,x17692)+E(f419(x17693,x17691,x17694,x17695,x17696,x17697),f419(x17693,x17692,x17694,x17695,x17696,x17697))
% 15.02/14.81 [1770]~E(x17701,x17702)+E(f419(x17703,x17704,x17701,x17705,x17706,x17707),f419(x17703,x17704,x17702,x17705,x17706,x17707))
% 15.02/14.81 [1771]~E(x17711,x17712)+E(f419(x17713,x17714,x17715,x17711,x17716,x17717),f419(x17713,x17714,x17715,x17712,x17716,x17717))
% 15.02/14.81 [1772]~E(x17721,x17722)+E(f419(x17723,x17724,x17725,x17726,x17721,x17727),f419(x17723,x17724,x17725,x17726,x17722,x17727))
% 15.02/14.81 [1773]~E(x17731,x17732)+E(f419(x17733,x17734,x17735,x17736,x17737,x17731),f419(x17733,x17734,x17735,x17736,x17737,x17732))
% 15.02/14.81 [1774]~E(x17741,x17742)+E(f895(x17741,x17743,x17744,x17745),f895(x17742,x17743,x17744,x17745))
% 15.02/14.81 [1775]~E(x17751,x17752)+E(f895(x17753,x17751,x17754,x17755),f895(x17753,x17752,x17754,x17755))
% 15.02/14.81 [1776]~E(x17761,x17762)+E(f895(x17763,x17764,x17761,x17765),f895(x17763,x17764,x17762,x17765))
% 15.02/14.81 [1777]~E(x17771,x17772)+E(f895(x17773,x17774,x17775,x17771),f895(x17773,x17774,x17775,x17772))
% 15.02/14.81 [1778]~E(x17781,x17782)+E(f800(x17781,x17783,x17784,x17785,x17786),f800(x17782,x17783,x17784,x17785,x17786))
% 15.02/14.81 [1779]~E(x17791,x17792)+E(f800(x17793,x17791,x17794,x17795,x17796),f800(x17793,x17792,x17794,x17795,x17796))
% 15.02/14.81 [1780]~E(x17801,x17802)+E(f800(x17803,x17804,x17801,x17805,x17806),f800(x17803,x17804,x17802,x17805,x17806))
% 15.02/14.81 [1781]~E(x17811,x17812)+E(f800(x17813,x17814,x17815,x17811,x17816),f800(x17813,x17814,x17815,x17812,x17816))
% 15.02/14.81 [1782]~E(x17821,x17822)+E(f800(x17823,x17824,x17825,x17826,x17821),f800(x17823,x17824,x17825,x17826,x17822))
% 15.02/14.81 [1783]~E(x17831,x17832)+E(f388(x17831,x17833,x17834,x17835),f388(x17832,x17833,x17834,x17835))
% 15.02/14.81 [1784]~E(x17841,x17842)+E(f388(x17843,x17841,x17844,x17845),f388(x17843,x17842,x17844,x17845))
% 15.02/14.81 [1785]~E(x17851,x17852)+E(f388(x17853,x17854,x17851,x17855),f388(x17853,x17854,x17852,x17855))
% 15.02/14.81 [1786]~E(x17861,x17862)+E(f388(x17863,x17864,x17865,x17861),f388(x17863,x17864,x17865,x17862))
% 15.02/14.81 [1787]~E(x17871,x17872)+E(f764(x17871,x17873,x17874),f764(x17872,x17873,x17874))
% 15.02/14.81 [1788]~E(x17881,x17882)+E(f764(x17883,x17881,x17884),f764(x17883,x17882,x17884))
% 15.02/14.81 [1789]~E(x17891,x17892)+E(f764(x17893,x17894,x17891),f764(x17893,x17894,x17892))
% 15.02/14.81 [1790]~E(x17901,x17902)+E(f123(x17901),f123(x17902))
% 15.02/14.81 [1791]~E(x17911,x17912)+E(f198(x17911,x17913,x17914,x17915),f198(x17912,x17913,x17914,x17915))
% 15.02/14.81 [1792]~E(x17921,x17922)+E(f198(x17923,x17921,x17924,x17925),f198(x17923,x17922,x17924,x17925))
% 15.02/14.81 [1793]~E(x17931,x17932)+E(f198(x17933,x17934,x17931,x17935),f198(x17933,x17934,x17932,x17935))
% 15.02/14.81 [1794]~E(x17941,x17942)+E(f198(x17943,x17944,x17945,x17941),f198(x17943,x17944,x17945,x17942))
% 15.02/14.81 [1795]~E(x17951,x17952)+E(f767(x17951,x17953,x17954),f767(x17952,x17953,x17954))
% 15.02/14.81 [1796]~E(x17961,x17962)+E(f767(x17963,x17961,x17964),f767(x17963,x17962,x17964))
% 15.02/14.81 [1797]~E(x17971,x17972)+E(f767(x17973,x17974,x17971),f767(x17973,x17974,x17972))
% 15.02/14.81 [1798]~E(x17981,x17982)+E(f728(x17981,x17983),f728(x17982,x17983))
% 15.02/14.81 [1799]~E(x17991,x17992)+E(f728(x17993,x17991),f728(x17993,x17992))
% 15.02/14.81 [1800]~E(x18001,x18002)+E(f829(x18001,x18003,x18004,x18005),f829(x18002,x18003,x18004,x18005))
% 15.02/14.81 [1801]~E(x18011,x18012)+E(f829(x18013,x18011,x18014,x18015),f829(x18013,x18012,x18014,x18015))
% 15.02/14.81 [1802]~E(x18021,x18022)+E(f829(x18023,x18024,x18021,x18025),f829(x18023,x18024,x18022,x18025))
% 15.02/14.81 [1803]~E(x18031,x18032)+E(f829(x18033,x18034,x18035,x18031),f829(x18033,x18034,x18035,x18032))
% 15.02/14.81 [1804]~E(x18041,x18042)+E(f695(x18041,x18043,x18044,x18045,x18046),f695(x18042,x18043,x18044,x18045,x18046))
% 15.02/14.81 [1805]~E(x18051,x18052)+E(f695(x18053,x18051,x18054,x18055,x18056),f695(x18053,x18052,x18054,x18055,x18056))
% 15.02/14.81 [1806]~E(x18061,x18062)+E(f695(x18063,x18064,x18061,x18065,x18066),f695(x18063,x18064,x18062,x18065,x18066))
% 15.02/14.81 [1807]~E(x18071,x18072)+E(f695(x18073,x18074,x18075,x18071,x18076),f695(x18073,x18074,x18075,x18072,x18076))
% 15.02/14.81 [1808]~E(x18081,x18082)+E(f695(x18083,x18084,x18085,x18086,x18081),f695(x18083,x18084,x18085,x18086,x18082))
% 15.02/14.81 [1809]~E(x18091,x18092)+E(f629(x18091,x18093,x18094,x18095,x18096),f629(x18092,x18093,x18094,x18095,x18096))
% 15.02/14.81 [1810]~E(x18101,x18102)+E(f629(x18103,x18101,x18104,x18105,x18106),f629(x18103,x18102,x18104,x18105,x18106))
% 15.02/14.81 [1811]~E(x18111,x18112)+E(f629(x18113,x18114,x18111,x18115,x18116),f629(x18113,x18114,x18112,x18115,x18116))
% 15.02/14.81 [1812]~E(x18121,x18122)+E(f629(x18123,x18124,x18125,x18121,x18126),f629(x18123,x18124,x18125,x18122,x18126))
% 15.02/14.81 [1813]~E(x18131,x18132)+E(f629(x18133,x18134,x18135,x18136,x18131),f629(x18133,x18134,x18135,x18136,x18132))
% 15.02/14.81 [1814]~E(x18141,x18142)+E(f358(x18141,x18143,x18144,x18145),f358(x18142,x18143,x18144,x18145))
% 15.02/14.81 [1815]~E(x18151,x18152)+E(f358(x18153,x18151,x18154,x18155),f358(x18153,x18152,x18154,x18155))
% 15.02/14.81 [1816]~E(x18161,x18162)+E(f358(x18163,x18164,x18161,x18165),f358(x18163,x18164,x18162,x18165))
% 15.02/14.81 [1817]~E(x18171,x18172)+E(f358(x18173,x18174,x18175,x18171),f358(x18173,x18174,x18175,x18172))
% 15.02/14.81 [1818]~E(x18181,x18182)+E(f711(x18181,x18183,x18184),f711(x18182,x18183,x18184))
% 15.02/14.81 [1819]~E(x18191,x18192)+E(f711(x18193,x18191,x18194),f711(x18193,x18192,x18194))
% 15.02/14.81 [1820]~E(x18201,x18202)+E(f711(x18203,x18204,x18201),f711(x18203,x18204,x18202))
% 15.02/14.81 [1821]~E(x18211,x18212)+E(f901(x18211,x18213,x18214,x18215,x18216),f901(x18212,x18213,x18214,x18215,x18216))
% 15.02/14.81 [1822]~E(x18221,x18222)+E(f901(x18223,x18221,x18224,x18225,x18226),f901(x18223,x18222,x18224,x18225,x18226))
% 15.02/14.81 [1823]~E(x18231,x18232)+E(f901(x18233,x18234,x18231,x18235,x18236),f901(x18233,x18234,x18232,x18235,x18236))
% 15.02/14.81 [1824]~E(x18241,x18242)+E(f901(x18243,x18244,x18245,x18241,x18246),f901(x18243,x18244,x18245,x18242,x18246))
% 15.02/14.81 [1825]~E(x18251,x18252)+E(f901(x18253,x18254,x18255,x18256,x18251),f901(x18253,x18254,x18255,x18256,x18252))
% 15.02/14.81 [1826]~E(x18261,x18262)+E(f719(x18261,x18263,x18264),f719(x18262,x18263,x18264))
% 15.02/14.81 [1827]~E(x18271,x18272)+E(f719(x18273,x18271,x18274),f719(x18273,x18272,x18274))
% 15.02/14.81 [1828]~E(x18281,x18282)+E(f719(x18283,x18284,x18281),f719(x18283,x18284,x18282))
% 15.02/14.81 [1829]~E(x18291,x18292)+E(f184(x18291,x18293,x18294),f184(x18292,x18293,x18294))
% 15.02/14.81 [1830]~E(x18301,x18302)+E(f184(x18303,x18301,x18304),f184(x18303,x18302,x18304))
% 15.02/14.81 [1831]~E(x18311,x18312)+E(f184(x18313,x18314,x18311),f184(x18313,x18314,x18312))
% 15.02/14.81 [1832]~E(x18321,x18322)+E(f396(x18321,x18323,x18324),f396(x18322,x18323,x18324))
% 15.02/14.81 [1833]~E(x18331,x18332)+E(f396(x18333,x18331,x18334),f396(x18333,x18332,x18334))
% 15.02/14.81 [1834]~E(x18341,x18342)+E(f396(x18343,x18344,x18341),f396(x18343,x18344,x18342))
% 15.02/14.81 [1835]~E(x18351,x18352)+E(f809(x18351),f809(x18352))
% 15.02/14.81 [1836]~E(x18361,x18362)+E(f634(x18361,x18363,x18364,x18365,x18366),f634(x18362,x18363,x18364,x18365,x18366))
% 15.02/14.81 [1837]~E(x18371,x18372)+E(f634(x18373,x18371,x18374,x18375,x18376),f634(x18373,x18372,x18374,x18375,x18376))
% 15.02/14.81 [1838]~E(x18381,x18382)+E(f634(x18383,x18384,x18381,x18385,x18386),f634(x18383,x18384,x18382,x18385,x18386))
% 15.02/14.81 [1839]~E(x18391,x18392)+E(f634(x18393,x18394,x18395,x18391,x18396),f634(x18393,x18394,x18395,x18392,x18396))
% 15.02/14.81 [1840]~E(x18401,x18402)+E(f634(x18403,x18404,x18405,x18406,x18401),f634(x18403,x18404,x18405,x18406,x18402))
% 15.02/14.81 [1841]~E(x18411,x18412)+E(f369(x18411),f369(x18412))
% 15.02/14.81 [1842]~E(x18421,x18422)+E(f670(x18421,x18423,x18424,x18425),f670(x18422,x18423,x18424,x18425))
% 15.02/14.81 [1843]~E(x18431,x18432)+E(f670(x18433,x18431,x18434,x18435),f670(x18433,x18432,x18434,x18435))
% 15.02/14.81 [1844]~E(x18441,x18442)+E(f670(x18443,x18444,x18441,x18445),f670(x18443,x18444,x18442,x18445))
% 15.02/14.81 [1845]~E(x18451,x18452)+E(f670(x18453,x18454,x18455,x18451),f670(x18453,x18454,x18455,x18452))
% 15.02/14.81 [1846]~E(x18461,x18462)+E(f790(x18461,x18463,x18464,x18465,x18466,x18467,x18468),f790(x18462,x18463,x18464,x18465,x18466,x18467,x18468))
% 15.02/14.81 [1847]~E(x18471,x18472)+E(f790(x18473,x18471,x18474,x18475,x18476,x18477,x18478),f790(x18473,x18472,x18474,x18475,x18476,x18477,x18478))
% 15.02/14.81 [1848]~E(x18481,x18482)+E(f790(x18483,x18484,x18481,x18485,x18486,x18487,x18488),f790(x18483,x18484,x18482,x18485,x18486,x18487,x18488))
% 15.02/14.81 [1849]~E(x18491,x18492)+E(f790(x18493,x18494,x18495,x18491,x18496,x18497,x18498),f790(x18493,x18494,x18495,x18492,x18496,x18497,x18498))
% 15.02/14.81 [1850]~E(x18501,x18502)+E(f790(x18503,x18504,x18505,x18506,x18501,x18507,x18508),f790(x18503,x18504,x18505,x18506,x18502,x18507,x18508))
% 15.02/14.81 [1851]~E(x18511,x18512)+E(f790(x18513,x18514,x18515,x18516,x18517,x18511,x18518),f790(x18513,x18514,x18515,x18516,x18517,x18512,x18518))
% 15.02/14.81 [1852]~E(x18521,x18522)+E(f790(x18523,x18524,x18525,x18526,x18527,x18528,x18521),f790(x18523,x18524,x18525,x18526,x18527,x18528,x18522))
% 15.02/14.81 [1853]~E(x18531,x18532)+E(f265(x18531,x18533),f265(x18532,x18533))
% 15.02/14.81 [1854]~E(x18541,x18542)+E(f265(x18543,x18541),f265(x18543,x18542))
% 15.02/14.81 [1855]~E(x18551,x18552)+E(f390(x18551,x18553,x18554),f390(x18552,x18553,x18554))
% 15.02/14.81 [1856]~E(x18561,x18562)+E(f390(x18563,x18561,x18564),f390(x18563,x18562,x18564))
% 15.02/14.81 [1857]~E(x18571,x18572)+E(f390(x18573,x18574,x18571),f390(x18573,x18574,x18572))
% 15.02/14.81 [1858]~E(x18581,x18582)+E(f851(x18581,x18583,x18584,x18585,x18586,x18587),f851(x18582,x18583,x18584,x18585,x18586,x18587))
% 15.02/14.81 [1859]~E(x18591,x18592)+E(f851(x18593,x18591,x18594,x18595,x18596,x18597),f851(x18593,x18592,x18594,x18595,x18596,x18597))
% 15.02/14.81 [1860]~E(x18601,x18602)+E(f851(x18603,x18604,x18601,x18605,x18606,x18607),f851(x18603,x18604,x18602,x18605,x18606,x18607))
% 15.02/14.81 [1861]~E(x18611,x18612)+E(f851(x18613,x18614,x18615,x18611,x18616,x18617),f851(x18613,x18614,x18615,x18612,x18616,x18617))
% 15.02/14.81 [1862]~E(x18621,x18622)+E(f851(x18623,x18624,x18625,x18626,x18621,x18627),f851(x18623,x18624,x18625,x18626,x18622,x18627))
% 15.02/14.81 [1863]~E(x18631,x18632)+E(f851(x18633,x18634,x18635,x18636,x18637,x18631),f851(x18633,x18634,x18635,x18636,x18637,x18632))
% 15.02/14.81 [1864]~E(x18641,x18642)+E(f505(x18641,x18643,x18644,x18645),f505(x18642,x18643,x18644,x18645))
% 15.02/14.81 [1865]~E(x18651,x18652)+E(f505(x18653,x18651,x18654,x18655),f505(x18653,x18652,x18654,x18655))
% 15.02/14.81 [1866]~E(x18661,x18662)+E(f505(x18663,x18664,x18661,x18665),f505(x18663,x18664,x18662,x18665))
% 15.02/14.81 [1867]~E(x18671,x18672)+E(f505(x18673,x18674,x18675,x18671),f505(x18673,x18674,x18675,x18672))
% 15.02/14.81 [1868]~E(x18681,x18682)+E(f889(x18681,x18683,x18684),f889(x18682,x18683,x18684))
% 15.02/14.81 [1869]~E(x18691,x18692)+E(f889(x18693,x18691,x18694),f889(x18693,x18692,x18694))
% 15.02/14.81 [1870]~E(x18701,x18702)+E(f889(x18703,x18704,x18701),f889(x18703,x18704,x18702))
% 15.02/14.81 [1871]~E(x18711,x18712)+E(f393(x18711,x18713,x18714),f393(x18712,x18713,x18714))
% 15.02/14.81 [1872]~E(x18721,x18722)+E(f393(x18723,x18721,x18724),f393(x18723,x18722,x18724))
% 15.02/14.81 [1873]~E(x18731,x18732)+E(f393(x18733,x18734,x18731),f393(x18733,x18734,x18732))
% 15.02/14.81 [1874]~E(x18741,x18742)+E(f494(x18741,x18743,x18744,x18745),f494(x18742,x18743,x18744,x18745))
% 15.02/14.81 [1875]~E(x18751,x18752)+E(f494(x18753,x18751,x18754,x18755),f494(x18753,x18752,x18754,x18755))
% 15.02/14.81 [1876]~E(x18761,x18762)+E(f494(x18763,x18764,x18761,x18765),f494(x18763,x18764,x18762,x18765))
% 15.02/14.81 [1877]~E(x18771,x18772)+E(f494(x18773,x18774,x18775,x18771),f494(x18773,x18774,x18775,x18772))
% 15.02/14.81 [1878]~E(x18781,x18782)+E(f631(x18781,x18783,x18784,x18785,x18786),f631(x18782,x18783,x18784,x18785,x18786))
% 15.02/14.81 [1879]~E(x18791,x18792)+E(f631(x18793,x18791,x18794,x18795,x18796),f631(x18793,x18792,x18794,x18795,x18796))
% 15.02/14.81 [1880]~E(x18801,x18802)+E(f631(x18803,x18804,x18801,x18805,x18806),f631(x18803,x18804,x18802,x18805,x18806))
% 15.02/14.81 [1881]~E(x18811,x18812)+E(f631(x18813,x18814,x18815,x18811,x18816),f631(x18813,x18814,x18815,x18812,x18816))
% 15.02/14.81 [1882]~E(x18821,x18822)+E(f631(x18823,x18824,x18825,x18826,x18821),f631(x18823,x18824,x18825,x18826,x18822))
% 15.02/14.81 [1883]~E(x18831,x18832)+E(f502(x18831,x18833,x18834,x18835),f502(x18832,x18833,x18834,x18835))
% 15.02/14.81 [1884]~E(x18841,x18842)+E(f502(x18843,x18841,x18844,x18845),f502(x18843,x18842,x18844,x18845))
% 15.02/14.81 [1885]~E(x18851,x18852)+E(f502(x18853,x18854,x18851,x18855),f502(x18853,x18854,x18852,x18855))
% 15.02/14.81 [1886]~E(x18861,x18862)+E(f502(x18863,x18864,x18865,x18861),f502(x18863,x18864,x18865,x18862))
% 15.02/14.81 [1887]~E(x18871,x18872)+E(f389(x18871,x18873,x18874),f389(x18872,x18873,x18874))
% 15.02/14.81 [1888]~E(x18881,x18882)+E(f389(x18883,x18881,x18884),f389(x18883,x18882,x18884))
% 15.02/14.81 [1889]~E(x18891,x18892)+E(f389(x18893,x18894,x18891),f389(x18893,x18894,x18892))
% 15.02/14.81 [1890]~E(x18901,x18902)+E(f820(x18901,x18903,x18904),f820(x18902,x18903,x18904))
% 15.02/14.81 [1891]~E(x18911,x18912)+E(f820(x18913,x18911,x18914),f820(x18913,x18912,x18914))
% 15.02/14.81 [1892]~E(x18921,x18922)+E(f820(x18923,x18924,x18921),f820(x18923,x18924,x18922))
% 15.02/14.81 [1893]~E(x18931,x18932)+E(f448(x18931,x18933,x18934,x18935),f448(x18932,x18933,x18934,x18935))
% 15.02/14.81 [1894]~E(x18941,x18942)+E(f448(x18943,x18941,x18944,x18945),f448(x18943,x18942,x18944,x18945))
% 15.02/14.81 [1895]~E(x18951,x18952)+E(f448(x18953,x18954,x18951,x18955),f448(x18953,x18954,x18952,x18955))
% 15.02/14.81 [1896]~E(x18961,x18962)+E(f448(x18963,x18964,x18965,x18961),f448(x18963,x18964,x18965,x18962))
% 15.02/14.81 [1897]~E(x18971,x18972)+E(f616(x18971,x18973),f616(x18972,x18973))
% 15.02/14.81 [1898]~E(x18981,x18982)+E(f616(x18983,x18981),f616(x18983,x18982))
% 15.02/14.81 [1899]~E(x18991,x18992)+E(f272(x18991,x18993,x18994,x18995),f272(x18992,x18993,x18994,x18995))
% 15.02/14.81 [1900]~E(x19001,x19002)+E(f272(x19003,x19001,x19004,x19005),f272(x19003,x19002,x19004,x19005))
% 15.02/14.81 [1901]~E(x19011,x19012)+E(f272(x19013,x19014,x19011,x19015),f272(x19013,x19014,x19012,x19015))
% 15.02/14.81 [1902]~E(x19021,x19022)+E(f272(x19023,x19024,x19025,x19021),f272(x19023,x19024,x19025,x19022))
% 15.02/14.81 [1903]~E(x19031,x19032)+E(f583(x19031,x19033),f583(x19032,x19033))
% 15.02/14.81 [1904]~E(x19041,x19042)+E(f583(x19043,x19041),f583(x19043,x19042))
% 15.02/14.81 [1905]~E(x19051,x19052)+E(f725(x19051,x19053,x19054,x19055),f725(x19052,x19053,x19054,x19055))
% 15.02/14.81 [1906]~E(x19061,x19062)+E(f725(x19063,x19061,x19064,x19065),f725(x19063,x19062,x19064,x19065))
% 15.02/14.81 [1907]~E(x19071,x19072)+E(f725(x19073,x19074,x19071,x19075),f725(x19073,x19074,x19072,x19075))
% 15.02/14.81 [1908]~E(x19081,x19082)+E(f725(x19083,x19084,x19085,x19081),f725(x19083,x19084,x19085,x19082))
% 15.02/14.81 [1909]~E(x19091,x19092)+E(f377(x19091,x19093,x19094,x19095),f377(x19092,x19093,x19094,x19095))
% 15.02/14.81 [1910]~E(x19101,x19102)+E(f377(x19103,x19101,x19104,x19105),f377(x19103,x19102,x19104,x19105))
% 15.02/14.81 [1911]~E(x19111,x19112)+E(f377(x19113,x19114,x19111,x19115),f377(x19113,x19114,x19112,x19115))
% 15.02/14.81 [1912]~E(x19121,x19122)+E(f377(x19123,x19124,x19125,x19121),f377(x19123,x19124,x19125,x19122))
% 15.02/14.81 [1913]~E(x19131,x19132)+E(f638(x19131,x19133,x19134),f638(x19132,x19133,x19134))
% 15.02/14.81 [1914]~E(x19141,x19142)+E(f638(x19143,x19141,x19144),f638(x19143,x19142,x19144))
% 15.02/14.81 [1915]~E(x19151,x19152)+E(f638(x19153,x19154,x19151),f638(x19153,x19154,x19152))
% 15.02/14.81 [1916]~E(x19161,x19162)+E(f515(x19161,x19163,x19164),f515(x19162,x19163,x19164))
% 15.02/14.81 [1917]~E(x19171,x19172)+E(f515(x19173,x19171,x19174),f515(x19173,x19172,x19174))
% 15.02/14.81 [1918]~E(x19181,x19182)+E(f515(x19183,x19184,x19181),f515(x19183,x19184,x19182))
% 15.02/14.81 [1919]~E(x19191,x19192)+E(f227(x19191,x19193,x19194,x19195,x19196),f227(x19192,x19193,x19194,x19195,x19196))
% 15.02/14.81 [1920]~E(x19201,x19202)+E(f227(x19203,x19201,x19204,x19205,x19206),f227(x19203,x19202,x19204,x19205,x19206))
% 15.02/14.81 [1921]~E(x19211,x19212)+E(f227(x19213,x19214,x19211,x19215,x19216),f227(x19213,x19214,x19212,x19215,x19216))
% 15.02/14.81 [1922]~E(x19221,x19222)+E(f227(x19223,x19224,x19225,x19221,x19226),f227(x19223,x19224,x19225,x19222,x19226))
% 15.02/14.81 [1923]~E(x19231,x19232)+E(f227(x19233,x19234,x19235,x19236,x19231),f227(x19233,x19234,x19235,x19236,x19232))
% 15.02/14.81 [1924]~E(x19241,x19242)+E(f202(x19241),f202(x19242))
% 15.02/14.81 [1925]~E(x19251,x19252)+E(f530(x19251,x19253,x19254,x19255,x19256),f530(x19252,x19253,x19254,x19255,x19256))
% 15.02/14.81 [1926]~E(x19261,x19262)+E(f530(x19263,x19261,x19264,x19265,x19266),f530(x19263,x19262,x19264,x19265,x19266))
% 15.02/14.81 [1927]~E(x19271,x19272)+E(f530(x19273,x19274,x19271,x19275,x19276),f530(x19273,x19274,x19272,x19275,x19276))
% 15.02/14.81 [1928]~E(x19281,x19282)+E(f530(x19283,x19284,x19285,x19281,x19286),f530(x19283,x19284,x19285,x19282,x19286))
% 15.02/14.81 [1929]~E(x19291,x19292)+E(f530(x19293,x19294,x19295,x19296,x19291),f530(x19293,x19294,x19295,x19296,x19292))
% 15.02/14.81 [1930]~E(x19301,x19302)+E(f665(x19301,x19303,x19304),f665(x19302,x19303,x19304))
% 15.02/14.81 [1931]~E(x19311,x19312)+E(f665(x19313,x19311,x19314),f665(x19313,x19312,x19314))
% 15.02/14.81 [1932]~E(x19321,x19322)+E(f665(x19323,x19324,x19321),f665(x19323,x19324,x19322))
% 15.02/14.81 [1933]~E(x19331,x19332)+E(f428(x19331,x19333,x19334,x19335,x19336),f428(x19332,x19333,x19334,x19335,x19336))
% 15.02/14.81 [1934]~E(x19341,x19342)+E(f428(x19343,x19341,x19344,x19345,x19346),f428(x19343,x19342,x19344,x19345,x19346))
% 15.02/14.81 [1935]~E(x19351,x19352)+E(f428(x19353,x19354,x19351,x19355,x19356),f428(x19353,x19354,x19352,x19355,x19356))
% 15.02/14.81 [1936]~E(x19361,x19362)+E(f428(x19363,x19364,x19365,x19361,x19366),f428(x19363,x19364,x19365,x19362,x19366))
% 15.02/14.81 [1937]~E(x19371,x19372)+E(f428(x19373,x19374,x19375,x19376,x19371),f428(x19373,x19374,x19375,x19376,x19372))
% 15.02/14.81 [1938]~E(x19381,x19382)+E(f677(x19381,x19383,x19384,x19385),f677(x19382,x19383,x19384,x19385))
% 15.02/14.81 [1939]~E(x19391,x19392)+E(f677(x19393,x19391,x19394,x19395),f677(x19393,x19392,x19394,x19395))
% 15.02/14.81 [1940]~E(x19401,x19402)+E(f677(x19403,x19404,x19401,x19405),f677(x19403,x19404,x19402,x19405))
% 15.02/14.81 [1941]~E(x19411,x19412)+E(f677(x19413,x19414,x19415,x19411),f677(x19413,x19414,x19415,x19412))
% 15.02/14.81 [1942]~E(x19421,x19422)+E(f620(x19421,x19423,x19424),f620(x19422,x19423,x19424))
% 15.02/14.81 [1943]~E(x19431,x19432)+E(f620(x19433,x19431,x19434),f620(x19433,x19432,x19434))
% 15.02/14.81 [1944]~E(x19441,x19442)+E(f620(x19443,x19444,x19441),f620(x19443,x19444,x19442))
% 15.02/14.81 [1945]~E(x19451,x19452)+E(f581(x19451,x19453),f581(x19452,x19453))
% 15.02/14.81 [1946]~E(x19461,x19462)+E(f581(x19463,x19461),f581(x19463,x19462))
% 15.02/14.81 [1947]~E(x19471,x19472)+E(f131(x19471,x19473,x19474,x19475),f131(x19472,x19473,x19474,x19475))
% 15.02/14.81 [1948]~E(x19481,x19482)+E(f131(x19483,x19481,x19484,x19485),f131(x19483,x19482,x19484,x19485))
% 15.02/14.81 [1949]~E(x19491,x19492)+E(f131(x19493,x19494,x19491,x19495),f131(x19493,x19494,x19492,x19495))
% 15.02/14.81 [1950]~E(x19501,x19502)+E(f131(x19503,x19504,x19505,x19501),f131(x19503,x19504,x19505,x19502))
% 15.02/14.81 [1951]~E(x19511,x19512)+E(f347(x19511,x19513,x19514,x19515),f347(x19512,x19513,x19514,x19515))
% 15.02/14.81 [1952]~E(x19521,x19522)+E(f347(x19523,x19521,x19524,x19525),f347(x19523,x19522,x19524,x19525))
% 15.02/14.81 [1953]~E(x19531,x19532)+E(f347(x19533,x19534,x19531,x19535),f347(x19533,x19534,x19532,x19535))
% 15.02/14.81 [1954]~E(x19541,x19542)+E(f347(x19543,x19544,x19545,x19541),f347(x19543,x19544,x19545,x19542))
% 15.02/14.81 [1955]~E(x19551,x19552)+E(f557(x19551,x19553),f557(x19552,x19553))
% 15.02/14.81 [1956]~E(x19561,x19562)+E(f557(x19563,x19561),f557(x19563,x19562))
% 15.02/14.81 [1957]~E(x19571,x19572)+E(f337(x19571),f337(x19572))
% 15.02/14.81 [1958]~E(x19581,x19582)+E(f375(x19581,x19583,x19584),f375(x19582,x19583,x19584))
% 15.02/14.81 [1959]~E(x19591,x19592)+E(f375(x19593,x19591,x19594),f375(x19593,x19592,x19594))
% 15.02/14.81 [1960]~E(x19601,x19602)+E(f375(x19603,x19604,x19601),f375(x19603,x19604,x19602))
% 15.02/14.81 [1961]~E(x19611,x19612)+E(f860(x19611,x19613),f860(x19612,x19613))
% 15.02/14.81 [1962]~E(x19621,x19622)+E(f860(x19623,x19621),f860(x19623,x19622))
% 15.02/14.81 [1963]~E(x19631,x19632)+E(f338(x19631),f338(x19632))
% 15.02/14.81 [1964]~E(x19641,x19642)+E(f410(x19641,x19643),f410(x19642,x19643))
% 15.02/14.81 [1965]~E(x19651,x19652)+E(f410(x19653,x19651),f410(x19653,x19652))
% 15.02/14.81 [1966]~E(x19661,x19662)+E(f596(x19661,x19663),f596(x19662,x19663))
% 15.02/14.81 [1967]~E(x19671,x19672)+E(f596(x19673,x19671),f596(x19673,x19672))
% 15.02/14.81 [1968]~E(x19681,x19682)+E(f364(x19681,x19683,x19684),f364(x19682,x19683,x19684))
% 15.02/14.81 [1969]~E(x19691,x19692)+E(f364(x19693,x19691,x19694),f364(x19693,x19692,x19694))
% 15.02/14.81 [1970]~E(x19701,x19702)+E(f364(x19703,x19704,x19701),f364(x19703,x19704,x19702))
% 15.02/14.81 [1971]~E(x19711,x19712)+E(f587(x19711,x19713,x19714,x19715,x19716),f587(x19712,x19713,x19714,x19715,x19716))
% 15.02/14.81 [1972]~E(x19721,x19722)+E(f587(x19723,x19721,x19724,x19725,x19726),f587(x19723,x19722,x19724,x19725,x19726))
% 15.02/14.81 [1973]~E(x19731,x19732)+E(f587(x19733,x19734,x19731,x19735,x19736),f587(x19733,x19734,x19732,x19735,x19736))
% 15.02/14.81 [1974]~E(x19741,x19742)+E(f587(x19743,x19744,x19745,x19741,x19746),f587(x19743,x19744,x19745,x19742,x19746))
% 15.02/14.81 [1975]~E(x19751,x19752)+E(f587(x19753,x19754,x19755,x19756,x19751),f587(x19753,x19754,x19755,x19756,x19752))
% 15.02/14.81 [1976]~E(x19761,x19762)+E(f785(x19761,x19763),f785(x19762,x19763))
% 15.02/14.81 [1977]~E(x19771,x19772)+E(f785(x19773,x19771),f785(x19773,x19772))
% 15.02/14.81 [1978]~E(x19781,x19782)+E(f736(x19781,x19783,x19784,x19785),f736(x19782,x19783,x19784,x19785))
% 15.02/14.81 [1979]~E(x19791,x19792)+E(f736(x19793,x19791,x19794,x19795),f736(x19793,x19792,x19794,x19795))
% 15.02/14.81 [1980]~E(x19801,x19802)+E(f736(x19803,x19804,x19801,x19805),f736(x19803,x19804,x19802,x19805))
% 15.02/14.81 [1981]~E(x19811,x19812)+E(f736(x19813,x19814,x19815,x19811),f736(x19813,x19814,x19815,x19812))
% 15.02/14.81 [1982]~E(x19821,x19822)+E(f297(x19821,x19823,x19824),f297(x19822,x19823,x19824))
% 15.02/14.81 [1983]~E(x19831,x19832)+E(f297(x19833,x19831,x19834),f297(x19833,x19832,x19834))
% 15.02/14.81 [1984]~E(x19841,x19842)+E(f297(x19843,x19844,x19841),f297(x19843,x19844,x19842))
% 15.02/14.81 [1985]~E(x19851,x19852)+E(f588(x19851,x19853,x19854),f588(x19852,x19853,x19854))
% 15.02/14.81 [1986]~E(x19861,x19862)+E(f588(x19863,x19861,x19864),f588(x19863,x19862,x19864))
% 15.02/14.81 [1987]~E(x19871,x19872)+E(f588(x19873,x19874,x19871),f588(x19873,x19874,x19872))
% 15.02/14.81 [1988]~E(x19881,x19882)+E(f117(x19881,x19883,x19884),f117(x19882,x19883,x19884))
% 15.02/14.81 [1989]~E(x19891,x19892)+E(f117(x19893,x19891,x19894),f117(x19893,x19892,x19894))
% 15.02/14.81 [1990]~E(x19901,x19902)+E(f117(x19903,x19904,x19901),f117(x19903,x19904,x19902))
% 15.02/14.81 [1991]~E(x19911,x19912)+E(f366(x19911,x19913,x19914,x19915),f366(x19912,x19913,x19914,x19915))
% 15.02/14.81 [1992]~E(x19921,x19922)+E(f366(x19923,x19921,x19924,x19925),f366(x19923,x19922,x19924,x19925))
% 15.02/14.81 [1993]~E(x19931,x19932)+E(f366(x19933,x19934,x19931,x19935),f366(x19933,x19934,x19932,x19935))
% 15.02/14.81 [1994]~E(x19941,x19942)+E(f366(x19943,x19944,x19945,x19941),f366(x19943,x19944,x19945,x19942))
% 15.02/14.81 [1995]~E(x19951,x19952)+E(f794(x19951,x19953,x19954,x19955),f794(x19952,x19953,x19954,x19955))
% 15.02/14.81 [1996]~E(x19961,x19962)+E(f794(x19963,x19961,x19964,x19965),f794(x19963,x19962,x19964,x19965))
% 15.02/14.81 [1997]~E(x19971,x19972)+E(f794(x19973,x19974,x19971,x19975),f794(x19973,x19974,x19972,x19975))
% 15.02/14.81 [1998]~E(x19981,x19982)+E(f794(x19983,x19984,x19985,x19981),f794(x19983,x19984,x19985,x19982))
% 15.02/14.81 [1999]~E(x19991,x19992)+E(f905(x19991,x19993),f905(x19992,x19993))
% 15.02/14.81 [2000]~E(x20001,x20002)+E(f905(x20003,x20001),f905(x20003,x20002))
% 15.02/14.81 [2001]~E(x20011,x20012)+E(f716(x20011,x20013,x20014),f716(x20012,x20013,x20014))
% 15.02/14.81 [2002]~E(x20021,x20022)+E(f716(x20023,x20021,x20024),f716(x20023,x20022,x20024))
% 15.02/14.81 [2003]~E(x20031,x20032)+E(f716(x20033,x20034,x20031),f716(x20033,x20034,x20032))
% 15.02/14.81 [2004]~E(x20041,x20042)+E(f510(x20041,x20043,x20044,x20045),f510(x20042,x20043,x20044,x20045))
% 15.02/14.81 [2005]~E(x20051,x20052)+E(f510(x20053,x20051,x20054,x20055),f510(x20053,x20052,x20054,x20055))
% 15.02/14.81 [2006]~E(x20061,x20062)+E(f510(x20063,x20064,x20061,x20065),f510(x20063,x20064,x20062,x20065))
% 15.02/14.81 [2007]~E(x20071,x20072)+E(f510(x20073,x20074,x20075,x20071),f510(x20073,x20074,x20075,x20072))
% 15.02/14.81 [2008]~E(x20081,x20082)+E(f664(x20081,x20083,x20084,x20085,x20086,x20087),f664(x20082,x20083,x20084,x20085,x20086,x20087))
% 15.02/14.81 [2009]~E(x20091,x20092)+E(f664(x20093,x20091,x20094,x20095,x20096,x20097),f664(x20093,x20092,x20094,x20095,x20096,x20097))
% 15.02/14.81 [2010]~E(x20101,x20102)+E(f664(x20103,x20104,x20101,x20105,x20106,x20107),f664(x20103,x20104,x20102,x20105,x20106,x20107))
% 15.02/14.81 [2011]~E(x20111,x20112)+E(f664(x20113,x20114,x20115,x20111,x20116,x20117),f664(x20113,x20114,x20115,x20112,x20116,x20117))
% 15.02/14.81 [2012]~E(x20121,x20122)+E(f664(x20123,x20124,x20125,x20126,x20121,x20127),f664(x20123,x20124,x20125,x20126,x20122,x20127))
% 15.02/14.81 [2013]~E(x20131,x20132)+E(f664(x20133,x20134,x20135,x20136,x20137,x20131),f664(x20133,x20134,x20135,x20136,x20137,x20132))
% 15.02/14.81 [2014]~E(x20141,x20142)+E(f823(x20141,x20143),f823(x20142,x20143))
% 15.02/14.81 [2015]~E(x20151,x20152)+E(f823(x20153,x20151),f823(x20153,x20152))
% 15.02/14.81 [2016]~E(x20161,x20162)+E(f94(x20161,x20163,x20164,x20165),f94(x20162,x20163,x20164,x20165))
% 15.02/14.81 [2017]~E(x20171,x20172)+E(f94(x20173,x20171,x20174,x20175),f94(x20173,x20172,x20174,x20175))
% 15.02/14.81 [2018]~E(x20181,x20182)+E(f94(x20183,x20184,x20181,x20185),f94(x20183,x20184,x20182,x20185))
% 15.02/14.81 [2019]~E(x20191,x20192)+E(f94(x20193,x20194,x20195,x20191),f94(x20193,x20194,x20195,x20192))
% 15.02/14.81 [2020]~E(x20201,x20202)+E(f641(x20201,x20203,x20204),f641(x20202,x20203,x20204))
% 15.02/14.81 [2021]~E(x20211,x20212)+E(f641(x20213,x20211,x20214),f641(x20213,x20212,x20214))
% 15.02/14.81 [2022]~E(x20221,x20222)+E(f641(x20223,x20224,x20221),f641(x20223,x20224,x20222))
% 15.02/14.81 [2023]~E(x20231,x20232)+E(f518(x20231,x20233,x20234),f518(x20232,x20233,x20234))
% 15.02/14.81 [2024]~E(x20241,x20242)+E(f518(x20243,x20241,x20244),f518(x20243,x20242,x20244))
% 15.02/14.81 [2025]~E(x20251,x20252)+E(f518(x20253,x20254,x20251),f518(x20253,x20254,x20252))
% 15.02/14.81 [2026]~E(x20261,x20262)+E(f547(x20261,x20263,x20264,x20265,x20266,x20267,x20268,x20269),f547(x20262,x20263,x20264,x20265,x20266,x20267,x20268,x20269))
% 15.02/14.81 [2027]~E(x20271,x20272)+E(f547(x20273,x20271,x20274,x20275,x20276,x20277,x20278,x20279),f547(x20273,x20272,x20274,x20275,x20276,x20277,x20278,x20279))
% 15.02/14.81 [2028]~E(x20281,x20282)+E(f547(x20283,x20284,x20281,x20285,x20286,x20287,x20288,x20289),f547(x20283,x20284,x20282,x20285,x20286,x20287,x20288,x20289))
% 15.02/14.81 [2029]~E(x20291,x20292)+E(f547(x20293,x20294,x20295,x20291,x20296,x20297,x20298,x20299),f547(x20293,x20294,x20295,x20292,x20296,x20297,x20298,x20299))
% 15.02/14.81 [2030]~E(x20301,x20302)+E(f547(x20303,x20304,x20305,x20306,x20301,x20307,x20308,x20309),f547(x20303,x20304,x20305,x20306,x20302,x20307,x20308,x20309))
% 15.02/14.81 [2031]~E(x20311,x20312)+E(f547(x20313,x20314,x20315,x20316,x20317,x20311,x20318,x20319),f547(x20313,x20314,x20315,x20316,x20317,x20312,x20318,x20319))
% 15.02/14.81 [2032]~E(x20321,x20322)+E(f547(x20323,x20324,x20325,x20326,x20327,x20328,x20321,x20329),f547(x20323,x20324,x20325,x20326,x20327,x20328,x20322,x20329))
% 15.02/14.81 [2033]~E(x20331,x20332)+E(f547(x20333,x20334,x20335,x20336,x20337,x20338,x20339,x20331),f547(x20333,x20334,x20335,x20336,x20337,x20338,x20339,x20332))
% 15.02/14.81 [2034]~E(x20341,x20342)+E(f226(x20341,x20343,x20344,x20345,x20346),f226(x20342,x20343,x20344,x20345,x20346))
% 15.02/14.81 [2035]~E(x20351,x20352)+E(f226(x20353,x20351,x20354,x20355,x20356),f226(x20353,x20352,x20354,x20355,x20356))
% 15.02/14.81 [2036]~E(x20361,x20362)+E(f226(x20363,x20364,x20361,x20365,x20366),f226(x20363,x20364,x20362,x20365,x20366))
% 15.02/14.81 [2037]~E(x20371,x20372)+E(f226(x20373,x20374,x20375,x20371,x20376),f226(x20373,x20374,x20375,x20372,x20376))
% 15.02/14.81 [2038]~E(x20381,x20382)+E(f226(x20383,x20384,x20385,x20386,x20381),f226(x20383,x20384,x20385,x20386,x20382))
% 15.02/14.81 [2039]~E(x20391,x20392)+E(f633(x20391,x20393,x20394,x20395,x20396),f633(x20392,x20393,x20394,x20395,x20396))
% 15.02/14.81 [2040]~E(x20401,x20402)+E(f633(x20403,x20401,x20404,x20405,x20406),f633(x20403,x20402,x20404,x20405,x20406))
% 15.02/14.81 [2041]~E(x20411,x20412)+E(f633(x20413,x20414,x20411,x20415,x20416),f633(x20413,x20414,x20412,x20415,x20416))
% 15.02/14.81 [2042]~E(x20421,x20422)+E(f633(x20423,x20424,x20425,x20421,x20426),f633(x20423,x20424,x20425,x20422,x20426))
% 15.02/14.81 [2043]~E(x20431,x20432)+E(f633(x20433,x20434,x20435,x20436,x20431),f633(x20433,x20434,x20435,x20436,x20432))
% 15.02/14.81 [2044]~E(x20441,x20442)+E(f734(x20441,x20443,x20444,x20445,x20446,x20447,x20448,x20449),f734(x20442,x20443,x20444,x20445,x20446,x20447,x20448,x20449))
% 15.02/14.81 [2045]~E(x20451,x20452)+E(f734(x20453,x20451,x20454,x20455,x20456,x20457,x20458,x20459),f734(x20453,x20452,x20454,x20455,x20456,x20457,x20458,x20459))
% 15.02/14.81 [2046]~E(x20461,x20462)+E(f734(x20463,x20464,x20461,x20465,x20466,x20467,x20468,x20469),f734(x20463,x20464,x20462,x20465,x20466,x20467,x20468,x20469))
% 15.02/14.81 [2047]~E(x20471,x20472)+E(f734(x20473,x20474,x20475,x20471,x20476,x20477,x20478,x20479),f734(x20473,x20474,x20475,x20472,x20476,x20477,x20478,x20479))
% 15.02/14.81 [2048]~E(x20481,x20482)+E(f734(x20483,x20484,x20485,x20486,x20481,x20487,x20488,x20489),f734(x20483,x20484,x20485,x20486,x20482,x20487,x20488,x20489))
% 15.02/14.81 [2049]~E(x20491,x20492)+E(f734(x20493,x20494,x20495,x20496,x20497,x20491,x20498,x20499),f734(x20493,x20494,x20495,x20496,x20497,x20492,x20498,x20499))
% 15.02/14.81 [2050]~E(x20501,x20502)+E(f734(x20503,x20504,x20505,x20506,x20507,x20508,x20501,x20509),f734(x20503,x20504,x20505,x20506,x20507,x20508,x20502,x20509))
% 15.02/14.81 [2051]~E(x20511,x20512)+E(f734(x20513,x20514,x20515,x20516,x20517,x20518,x20519,x20511),f734(x20513,x20514,x20515,x20516,x20517,x20518,x20519,x20512))
% 15.02/14.81 [2052]~E(x20521,x20522)+E(f382(x20521,x20523,x20524),f382(x20522,x20523,x20524))
% 15.02/14.81 [2053]~E(x20531,x20532)+E(f382(x20533,x20531,x20534),f382(x20533,x20532,x20534))
% 15.02/14.81 [2054]~E(x20541,x20542)+E(f382(x20543,x20544,x20541),f382(x20543,x20544,x20542))
% 15.02/14.81 [2055]~E(x20551,x20552)+E(f483(x20551,x20553),f483(x20552,x20553))
% 15.02/14.81 [2056]~E(x20561,x20562)+E(f483(x20563,x20561),f483(x20563,x20562))
% 15.02/14.81 [2057]~E(x20571,x20572)+E(f118(x20571,x20573,x20574),f118(x20572,x20573,x20574))
% 15.02/14.81 [2058]~E(x20581,x20582)+E(f118(x20583,x20581,x20584),f118(x20583,x20582,x20584))
% 15.02/14.81 [2059]~E(x20591,x20592)+E(f118(x20593,x20594,x20591),f118(x20593,x20594,x20592))
% 15.02/14.81 [2060]~E(x20601,x20602)+E(f747(x20601,x20603,x20604,x20605,x20606),f747(x20602,x20603,x20604,x20605,x20606))
% 15.02/14.81 [2061]~E(x20611,x20612)+E(f747(x20613,x20611,x20614,x20615,x20616),f747(x20613,x20612,x20614,x20615,x20616))
% 15.02/14.81 [2062]~E(x20621,x20622)+E(f747(x20623,x20624,x20621,x20625,x20626),f747(x20623,x20624,x20622,x20625,x20626))
% 15.02/14.81 [2063]~E(x20631,x20632)+E(f747(x20633,x20634,x20635,x20631,x20636),f747(x20633,x20634,x20635,x20632,x20636))
% 15.02/14.81 [2064]~E(x20641,x20642)+E(f747(x20643,x20644,x20645,x20646,x20641),f747(x20643,x20644,x20645,x20646,x20642))
% 15.02/14.81 [2065]~E(x20651,x20652)+E(f575(x20651,x20653,x20654),f575(x20652,x20653,x20654))
% 15.02/14.81 [2066]~E(x20661,x20662)+E(f575(x20663,x20661,x20664),f575(x20663,x20662,x20664))
% 15.02/14.81 [2067]~E(x20671,x20672)+E(f575(x20673,x20674,x20671),f575(x20673,x20674,x20672))
% 15.02/14.81 [2068]~E(x20681,x20682)+E(f520(x20681,x20683,x20684,x20685),f520(x20682,x20683,x20684,x20685))
% 15.02/14.81 [2069]~E(x20691,x20692)+E(f520(x20693,x20691,x20694,x20695),f520(x20693,x20692,x20694,x20695))
% 15.02/14.81 [2070]~E(x20701,x20702)+E(f520(x20703,x20704,x20701,x20705),f520(x20703,x20704,x20702,x20705))
% 15.02/14.81 [2071]~E(x20711,x20712)+E(f520(x20713,x20714,x20715,x20711),f520(x20713,x20714,x20715,x20712))
% 15.02/14.81 [2072]~E(x20721,x20722)+E(f798(x20721,x20723,x20724,x20725),f798(x20722,x20723,x20724,x20725))
% 15.02/14.81 [2073]~E(x20731,x20732)+E(f798(x20733,x20731,x20734,x20735),f798(x20733,x20732,x20734,x20735))
% 15.02/14.81 [2074]~E(x20741,x20742)+E(f798(x20743,x20744,x20741,x20745),f798(x20743,x20744,x20742,x20745))
% 15.02/14.81 [2075]~E(x20751,x20752)+E(f798(x20753,x20754,x20755,x20751),f798(x20753,x20754,x20755,x20752))
% 15.02/14.81 [2076]~E(x20761,x20762)+E(f713(x20761,x20763,x20764),f713(x20762,x20763,x20764))
% 15.02/14.81 [2077]~E(x20771,x20772)+E(f713(x20773,x20771,x20774),f713(x20773,x20772,x20774))
% 15.02/14.81 [2078]~E(x20781,x20782)+E(f713(x20783,x20784,x20781),f713(x20783,x20784,x20782))
% 15.02/14.81 [2079]~E(x20791,x20792)+E(f477(x20791,x20793,x20794,x20795),f477(x20792,x20793,x20794,x20795))
% 15.02/14.81 [2080]~E(x20801,x20802)+E(f477(x20803,x20801,x20804,x20805),f477(x20803,x20802,x20804,x20805))
% 15.02/14.81 [2081]~E(x20811,x20812)+E(f477(x20813,x20814,x20811,x20815),f477(x20813,x20814,x20812,x20815))
% 15.02/14.81 [2082]~E(x20821,x20822)+E(f477(x20823,x20824,x20825,x20821),f477(x20823,x20824,x20825,x20822))
% 15.02/14.81 [2083]~E(x20831,x20832)+E(f459(x20831,x20833,x20834,x20835),f459(x20832,x20833,x20834,x20835))
% 15.02/14.81 [2084]~E(x20841,x20842)+E(f459(x20843,x20841,x20844,x20845),f459(x20843,x20842,x20844,x20845))
% 15.02/14.81 [2085]~E(x20851,x20852)+E(f459(x20853,x20854,x20851,x20855),f459(x20853,x20854,x20852,x20855))
% 15.02/14.81 [2086]~E(x20861,x20862)+E(f459(x20863,x20864,x20865,x20861),f459(x20863,x20864,x20865,x20862))
% 15.02/14.81 [2087]~E(x20871,x20872)+E(f435(x20871,x20873,x20874,x20875,x20876),f435(x20872,x20873,x20874,x20875,x20876))
% 15.02/14.81 [2088]~E(x20881,x20882)+E(f435(x20883,x20881,x20884,x20885,x20886),f435(x20883,x20882,x20884,x20885,x20886))
% 15.02/14.81 [2089]~E(x20891,x20892)+E(f435(x20893,x20894,x20891,x20895,x20896),f435(x20893,x20894,x20892,x20895,x20896))
% 15.02/14.81 [2090]~E(x20901,x20902)+E(f435(x20903,x20904,x20905,x20901,x20906),f435(x20903,x20904,x20905,x20902,x20906))
% 15.02/14.81 [2091]~E(x20911,x20912)+E(f435(x20913,x20914,x20915,x20916,x20911),f435(x20913,x20914,x20915,x20916,x20912))
% 15.02/14.81 [2092]~E(x20921,x20922)+E(f684(x20921,x20923,x20924,x20925,x20926),f684(x20922,x20923,x20924,x20925,x20926))
% 15.02/14.81 [2093]~E(x20931,x20932)+E(f684(x20933,x20931,x20934,x20935,x20936),f684(x20933,x20932,x20934,x20935,x20936))
% 15.02/14.81 [2094]~E(x20941,x20942)+E(f684(x20943,x20944,x20941,x20945,x20946),f684(x20943,x20944,x20942,x20945,x20946))
% 15.02/14.81 [2095]~E(x20951,x20952)+E(f684(x20953,x20954,x20955,x20951,x20956),f684(x20953,x20954,x20955,x20952,x20956))
% 15.02/14.81 [2096]~E(x20961,x20962)+E(f684(x20963,x20964,x20965,x20966,x20961),f684(x20963,x20964,x20965,x20966,x20962))
% 15.02/14.81 [2097]~E(x20971,x20972)+E(f647(x20971,x20973,x20974,x20975,x20976,x20977),f647(x20972,x20973,x20974,x20975,x20976,x20977))
% 15.02/14.81 [2098]~E(x20981,x20982)+E(f647(x20983,x20981,x20984,x20985,x20986,x20987),f647(x20983,x20982,x20984,x20985,x20986,x20987))
% 15.02/14.81 [2099]~E(x20991,x20992)+E(f647(x20993,x20994,x20991,x20995,x20996,x20997),f647(x20993,x20994,x20992,x20995,x20996,x20997))
% 15.02/14.81 [2100]~E(x21001,x21002)+E(f647(x21003,x21004,x21005,x21001,x21006,x21007),f647(x21003,x21004,x21005,x21002,x21006,x21007))
% 15.02/14.81 [2101]~E(x21011,x21012)+E(f647(x21013,x21014,x21015,x21016,x21011,x21017),f647(x21013,x21014,x21015,x21016,x21012,x21017))
% 15.02/14.81 [2102]~E(x21021,x21022)+E(f647(x21023,x21024,x21025,x21026,x21027,x21021),f647(x21023,x21024,x21025,x21026,x21027,x21022))
% 15.02/14.81 [2103]~E(x21031,x21032)+E(f245(x21031,x21033,x21034,x21035,x21036,x21037),f245(x21032,x21033,x21034,x21035,x21036,x21037))
% 15.02/14.81 [2104]~E(x21041,x21042)+E(f245(x21043,x21041,x21044,x21045,x21046,x21047),f245(x21043,x21042,x21044,x21045,x21046,x21047))
% 15.02/14.81 [2105]~E(x21051,x21052)+E(f245(x21053,x21054,x21051,x21055,x21056,x21057),f245(x21053,x21054,x21052,x21055,x21056,x21057))
% 15.02/14.81 [2106]~E(x21061,x21062)+E(f245(x21063,x21064,x21065,x21061,x21066,x21067),f245(x21063,x21064,x21065,x21062,x21066,x21067))
% 15.02/14.81 [2107]~E(x21071,x21072)+E(f245(x21073,x21074,x21075,x21076,x21071,x21077),f245(x21073,x21074,x21075,x21076,x21072,x21077))
% 15.02/14.81 [2108]~E(x21081,x21082)+E(f245(x21083,x21084,x21085,x21086,x21087,x21081),f245(x21083,x21084,x21085,x21086,x21087,x21082))
% 15.02/14.81 [2109]~E(x21091,x21092)+E(f451(x21091,x21093,x21094,x21095,x21096),f451(x21092,x21093,x21094,x21095,x21096))
% 15.02/14.81 [2110]~E(x21101,x21102)+E(f451(x21103,x21101,x21104,x21105,x21106),f451(x21103,x21102,x21104,x21105,x21106))
% 15.02/14.81 [2111]~E(x21111,x21112)+E(f451(x21113,x21114,x21111,x21115,x21116),f451(x21113,x21114,x21112,x21115,x21116))
% 15.02/14.81 [2112]~E(x21121,x21122)+E(f451(x21123,x21124,x21125,x21121,x21126),f451(x21123,x21124,x21125,x21122,x21126))
% 15.02/14.81 [2113]~E(x21131,x21132)+E(f451(x21133,x21134,x21135,x21136,x21131),f451(x21133,x21134,x21135,x21136,x21132))
% 15.02/14.81 [2114]~E(x21141,x21142)+E(f827(x21141,x21143,x21144),f827(x21142,x21143,x21144))
% 15.02/14.81 [2115]~E(x21151,x21152)+E(f827(x21153,x21151,x21154),f827(x21153,x21152,x21154))
% 15.02/14.81 [2116]~E(x21161,x21162)+E(f827(x21163,x21164,x21161),f827(x21163,x21164,x21162))
% 15.02/14.81 [2117]~E(x21171,x21172)+E(f811(x21171,x21173,x21174),f811(x21172,x21173,x21174))
% 15.02/14.81 [2118]~E(x21181,x21182)+E(f811(x21183,x21181,x21184),f811(x21183,x21182,x21184))
% 15.02/14.81 [2119]~E(x21191,x21192)+E(f811(x21193,x21194,x21191),f811(x21193,x21194,x21192))
% 15.02/14.81 [2120]~E(x21201,x21202)+E(f427(x21201,x21203,x21204,x21205,x21206),f427(x21202,x21203,x21204,x21205,x21206))
% 15.02/14.81 [2121]~E(x21211,x21212)+E(f427(x21213,x21211,x21214,x21215,x21216),f427(x21213,x21212,x21214,x21215,x21216))
% 15.02/14.81 [2122]~E(x21221,x21222)+E(f427(x21223,x21224,x21221,x21225,x21226),f427(x21223,x21224,x21222,x21225,x21226))
% 15.02/14.81 [2123]~E(x21231,x21232)+E(f427(x21233,x21234,x21235,x21231,x21236),f427(x21233,x21234,x21235,x21232,x21236))
% 15.02/14.81 [2124]~E(x21241,x21242)+E(f427(x21243,x21244,x21245,x21246,x21241),f427(x21243,x21244,x21245,x21246,x21242))
% 15.02/14.81 [2125]~E(x21251,x21252)+E(f279(x21251,x21253,x21254,x21255),f279(x21252,x21253,x21254,x21255))
% 15.02/14.81 [2126]~E(x21261,x21262)+E(f279(x21263,x21261,x21264,x21265),f279(x21263,x21262,x21264,x21265))
% 15.02/14.81 [2127]~E(x21271,x21272)+E(f279(x21273,x21274,x21271,x21275),f279(x21273,x21274,x21272,x21275))
% 15.02/14.81 [2128]~E(x21281,x21282)+E(f279(x21283,x21284,x21285,x21281),f279(x21283,x21284,x21285,x21282))
% 15.02/14.81 [2129]~E(x21291,x21292)+E(f381(x21291,x21293,x21294),f381(x21292,x21293,x21294))
% 15.02/14.81 [2130]~E(x21301,x21302)+E(f381(x21303,x21301,x21304),f381(x21303,x21302,x21304))
% 15.02/14.81 [2131]~E(x21311,x21312)+E(f381(x21313,x21314,x21311),f381(x21313,x21314,x21312))
% 15.02/14.81 [2132]~E(x21321,x21322)+E(f529(x21321,x21323,x21324,x21325,x21326),f529(x21322,x21323,x21324,x21325,x21326))
% 15.02/14.81 [2133]~E(x21331,x21332)+E(f529(x21333,x21331,x21334,x21335,x21336),f529(x21333,x21332,x21334,x21335,x21336))
% 15.02/14.81 [2134]~E(x21341,x21342)+E(f529(x21343,x21344,x21341,x21345,x21346),f529(x21343,x21344,x21342,x21345,x21346))
% 15.02/14.81 [2135]~E(x21351,x21352)+E(f529(x21353,x21354,x21355,x21351,x21356),f529(x21353,x21354,x21355,x21352,x21356))
% 15.02/14.81 [2136]~E(x21361,x21362)+E(f529(x21363,x21364,x21365,x21366,x21361),f529(x21363,x21364,x21365,x21366,x21362))
% 15.02/14.81 [2137]~E(x21371,x21372)+E(f784(x21371,x21373,x21374),f784(x21372,x21373,x21374))
% 15.02/14.81 [2138]~E(x21381,x21382)+E(f784(x21383,x21381,x21384),f784(x21383,x21382,x21384))
% 15.02/14.81 [2139]~E(x21391,x21392)+E(f784(x21393,x21394,x21391),f784(x21393,x21394,x21392))
% 15.02/14.81 [2140]~E(x21401,x21402)+E(f481(x21401,x21403,x21404,x21405,x21406),f481(x21402,x21403,x21404,x21405,x21406))
% 15.02/14.81 [2141]~E(x21411,x21412)+E(f481(x21413,x21411,x21414,x21415,x21416),f481(x21413,x21412,x21414,x21415,x21416))
% 15.02/14.81 [2142]~E(x21421,x21422)+E(f481(x21423,x21424,x21421,x21425,x21426),f481(x21423,x21424,x21422,x21425,x21426))
% 15.02/14.81 [2143]~E(x21431,x21432)+E(f481(x21433,x21434,x21435,x21431,x21436),f481(x21433,x21434,x21435,x21432,x21436))
% 15.02/14.81 [2144]~E(x21441,x21442)+E(f481(x21443,x21444,x21445,x21446,x21441),f481(x21443,x21444,x21445,x21446,x21442))
% 15.02/14.81 [2145]~E(x21451,x21452)+E(f441(x21451,x21453,x21454,x21455,x21456,x21457,x21458),f441(x21452,x21453,x21454,x21455,x21456,x21457,x21458))
% 15.02/14.81 [2146]~E(x21461,x21462)+E(f441(x21463,x21461,x21464,x21465,x21466,x21467,x21468),f441(x21463,x21462,x21464,x21465,x21466,x21467,x21468))
% 15.02/14.81 [2147]~E(x21471,x21472)+E(f441(x21473,x21474,x21471,x21475,x21476,x21477,x21478),f441(x21473,x21474,x21472,x21475,x21476,x21477,x21478))
% 15.02/14.81 [2148]~E(x21481,x21482)+E(f441(x21483,x21484,x21485,x21481,x21486,x21487,x21488),f441(x21483,x21484,x21485,x21482,x21486,x21487,x21488))
% 15.02/14.81 [2149]~E(x21491,x21492)+E(f441(x21493,x21494,x21495,x21496,x21491,x21497,x21498),f441(x21493,x21494,x21495,x21496,x21492,x21497,x21498))
% 15.02/14.81 [2150]~E(x21501,x21502)+E(f441(x21503,x21504,x21505,x21506,x21507,x21501,x21508),f441(x21503,x21504,x21505,x21506,x21507,x21502,x21508))
% 15.02/14.81 [2151]~E(x21511,x21512)+E(f441(x21513,x21514,x21515,x21516,x21517,x21518,x21511),f441(x21513,x21514,x21515,x21516,x21517,x21518,x21512))
% 15.02/14.81 [2152]~E(x21521,x21522)+E(f528(x21521,x21523,x21524,x21525,x21526),f528(x21522,x21523,x21524,x21525,x21526))
% 15.02/14.81 [2153]~E(x21531,x21532)+E(f528(x21533,x21531,x21534,x21535,x21536),f528(x21533,x21532,x21534,x21535,x21536))
% 15.02/14.81 [2154]~E(x21541,x21542)+E(f528(x21543,x21544,x21541,x21545,x21546),f528(x21543,x21544,x21542,x21545,x21546))
% 15.02/14.81 [2155]~E(x21551,x21552)+E(f528(x21553,x21554,x21555,x21551,x21556),f528(x21553,x21554,x21555,x21552,x21556))
% 15.02/14.81 [2156]~E(x21561,x21562)+E(f528(x21563,x21564,x21565,x21566,x21561),f528(x21563,x21564,x21565,x21566,x21562))
% 15.02/14.81 [2157]~E(x21571,x21572)+E(f751(x21571,x21573,x21574),f751(x21572,x21573,x21574))
% 15.02/14.81 [2158]~E(x21581,x21582)+E(f751(x21583,x21581,x21584),f751(x21583,x21582,x21584))
% 15.02/14.81 [2159]~E(x21591,x21592)+E(f751(x21593,x21594,x21591),f751(x21593,x21594,x21592))
% 15.02/14.81 [2160]~E(x21601,x21602)+E(f556(x21601,x21603),f556(x21602,x21603))
% 15.02/14.81 [2161]~E(x21611,x21612)+E(f556(x21613,x21611),f556(x21613,x21612))
% 15.02/14.81 [2162]~E(x21621,x21622)+E(f763(x21621,x21623,x21624),f763(x21622,x21623,x21624))
% 15.02/14.81 [2163]~E(x21631,x21632)+E(f763(x21633,x21631,x21634),f763(x21633,x21632,x21634))
% 15.02/14.81 [2164]~E(x21641,x21642)+E(f763(x21643,x21644,x21641),f763(x21643,x21644,x21642))
% 15.02/14.81 [2165]~E(x21651,x21652)+E(f786(x21651,x21653,x21654,x21655,x21656,x21657,x21658),f786(x21652,x21653,x21654,x21655,x21656,x21657,x21658))
% 15.02/14.81 [2166]~E(x21661,x21662)+E(f786(x21663,x21661,x21664,x21665,x21666,x21667,x21668),f786(x21663,x21662,x21664,x21665,x21666,x21667,x21668))
% 15.02/14.81 [2167]~E(x21671,x21672)+E(f786(x21673,x21674,x21671,x21675,x21676,x21677,x21678),f786(x21673,x21674,x21672,x21675,x21676,x21677,x21678))
% 15.02/14.81 [2168]~E(x21681,x21682)+E(f786(x21683,x21684,x21685,x21681,x21686,x21687,x21688),f786(x21683,x21684,x21685,x21682,x21686,x21687,x21688))
% 15.02/14.81 [2169]~E(x21691,x21692)+E(f786(x21693,x21694,x21695,x21696,x21691,x21697,x21698),f786(x21693,x21694,x21695,x21696,x21692,x21697,x21698))
% 15.02/14.81 [2170]~E(x21701,x21702)+E(f786(x21703,x21704,x21705,x21706,x21707,x21701,x21708),f786(x21703,x21704,x21705,x21706,x21707,x21702,x21708))
% 15.02/14.81 [2171]~E(x21711,x21712)+E(f786(x21713,x21714,x21715,x21716,x21717,x21718,x21711),f786(x21713,x21714,x21715,x21716,x21717,x21718,x21712))
% 15.02/14.81 [2172]~E(x21721,x21722)+E(f163(x21721,x21723,x21724,x21725),f163(x21722,x21723,x21724,x21725))
% 15.02/14.81 [2173]~E(x21731,x21732)+E(f163(x21733,x21731,x21734,x21735),f163(x21733,x21732,x21734,x21735))
% 15.02/14.81 [2174]~E(x21741,x21742)+E(f163(x21743,x21744,x21741,x21745),f163(x21743,x21744,x21742,x21745))
% 15.02/14.81 [2175]~E(x21751,x21752)+E(f163(x21753,x21754,x21755,x21751),f163(x21753,x21754,x21755,x21752))
% 15.02/14.81 [2176]~E(x21761,x21762)+E(f572(x21761,x21763,x21764,x21765),f572(x21762,x21763,x21764,x21765))
% 15.02/14.81 [2177]~E(x21771,x21772)+E(f572(x21773,x21771,x21774,x21775),f572(x21773,x21772,x21774,x21775))
% 15.02/14.81 [2178]~E(x21781,x21782)+E(f572(x21783,x21784,x21781,x21785),f572(x21783,x21784,x21782,x21785))
% 15.02/14.81 [2179]~E(x21791,x21792)+E(f572(x21793,x21794,x21795,x21791),f572(x21793,x21794,x21795,x21792))
% 15.02/14.81 [2180]~E(x21801,x21802)+E(f726(x21801,x21803),f726(x21802,x21803))
% 15.02/14.81 [2181]~E(x21811,x21812)+E(f726(x21813,x21811),f726(x21813,x21812))
% 15.02/14.81 [2182]~E(x21821,x21822)+E(f894(x21821,x21823,x21824,x21825,x21826,x21827,x21828),f894(x21822,x21823,x21824,x21825,x21826,x21827,x21828))
% 15.02/14.81 [2183]~E(x21831,x21832)+E(f894(x21833,x21831,x21834,x21835,x21836,x21837,x21838),f894(x21833,x21832,x21834,x21835,x21836,x21837,x21838))
% 15.02/14.81 [2184]~E(x21841,x21842)+E(f894(x21843,x21844,x21841,x21845,x21846,x21847,x21848),f894(x21843,x21844,x21842,x21845,x21846,x21847,x21848))
% 15.02/14.81 [2185]~E(x21851,x21852)+E(f894(x21853,x21854,x21855,x21851,x21856,x21857,x21858),f894(x21853,x21854,x21855,x21852,x21856,x21857,x21858))
% 15.02/14.81 [2186]~E(x21861,x21862)+E(f894(x21863,x21864,x21865,x21866,x21861,x21867,x21868),f894(x21863,x21864,x21865,x21866,x21862,x21867,x21868))
% 15.02/14.81 [2187]~E(x21871,x21872)+E(f894(x21873,x21874,x21875,x21876,x21877,x21871,x21878),f894(x21873,x21874,x21875,x21876,x21877,x21872,x21878))
% 15.02/14.81 [2188]~E(x21881,x21882)+E(f894(x21883,x21884,x21885,x21886,x21887,x21888,x21881),f894(x21883,x21884,x21885,x21886,x21887,x21888,x21882))
% 15.02/14.81 [2189]~E(x21891,x21892)+E(f453(x21891,x21893,x21894,x21895,x21896),f453(x21892,x21893,x21894,x21895,x21896))
% 15.02/14.81 [2190]~E(x21901,x21902)+E(f453(x21903,x21901,x21904,x21905,x21906),f453(x21903,x21902,x21904,x21905,x21906))
% 15.02/14.81 [2191]~E(x21911,x21912)+E(f453(x21913,x21914,x21911,x21915,x21916),f453(x21913,x21914,x21912,x21915,x21916))
% 15.02/14.81 [2192]~E(x21921,x21922)+E(f453(x21923,x21924,x21925,x21921,x21926),f453(x21923,x21924,x21925,x21922,x21926))
% 15.02/14.81 [2193]~E(x21931,x21932)+E(f453(x21933,x21934,x21935,x21936,x21931),f453(x21933,x21934,x21935,x21936,x21932))
% 15.02/14.81 [2194]~E(x21941,x21942)+E(f19(x21941,x21943,x21944,x21945),f19(x21942,x21943,x21944,x21945))
% 15.02/14.81 [2195]~E(x21951,x21952)+E(f19(x21953,x21951,x21954,x21955),f19(x21953,x21952,x21954,x21955))
% 15.02/14.81 [2196]~E(x21961,x21962)+E(f19(x21963,x21964,x21961,x21965),f19(x21963,x21964,x21962,x21965))
% 15.02/14.81 [2197]~E(x21971,x21972)+E(f19(x21973,x21974,x21975,x21971),f19(x21973,x21974,x21975,x21972))
% 15.02/14.81 [2198]~E(x21981,x21982)+E(f797(x21981,x21983,x21984),f797(x21982,x21983,x21984))
% 15.02/14.81 [2199]~E(x21991,x21992)+E(f797(x21993,x21991,x21994),f797(x21993,x21992,x21994))
% 15.02/14.81 [2200]~E(x22001,x22002)+E(f797(x22003,x22004,x22001),f797(x22003,x22004,x22002))
% 15.02/14.81 [2201]~E(x22011,x22012)+E(f343(x22011,x22013,x22014,x22015,x22016,x22017),f343(x22012,x22013,x22014,x22015,x22016,x22017))
% 15.02/14.81 [2202]~E(x22021,x22022)+E(f343(x22023,x22021,x22024,x22025,x22026,x22027),f343(x22023,x22022,x22024,x22025,x22026,x22027))
% 15.02/14.81 [2203]~E(x22031,x22032)+E(f343(x22033,x22034,x22031,x22035,x22036,x22037),f343(x22033,x22034,x22032,x22035,x22036,x22037))
% 15.02/14.81 [2204]~E(x22041,x22042)+E(f343(x22043,x22044,x22045,x22041,x22046,x22047),f343(x22043,x22044,x22045,x22042,x22046,x22047))
% 15.02/14.81 [2205]~E(x22051,x22052)+E(f343(x22053,x22054,x22055,x22056,x22051,x22057),f343(x22053,x22054,x22055,x22056,x22052,x22057))
% 15.02/14.81 [2206]~E(x22061,x22062)+E(f343(x22063,x22064,x22065,x22066,x22067,x22061),f343(x22063,x22064,x22065,x22066,x22067,x22062))
% 15.02/14.81 [2207]~E(x22071,x22072)+E(f576(x22071,x22073,x22074,x22075),f576(x22072,x22073,x22074,x22075))
% 15.02/14.81 [2208]~E(x22081,x22082)+E(f576(x22083,x22081,x22084,x22085),f576(x22083,x22082,x22084,x22085))
% 15.02/14.81 [2209]~E(x22091,x22092)+E(f576(x22093,x22094,x22091,x22095),f576(x22093,x22094,x22092,x22095))
% 15.02/14.81 [2210]~E(x22101,x22102)+E(f576(x22103,x22104,x22105,x22101),f576(x22103,x22104,x22105,x22102))
% 15.02/14.81 [2211]~E(x22111,x22112)+E(f485(x22111,x22113,x22114,x22115,x22116,x22117,x22118),f485(x22112,x22113,x22114,x22115,x22116,x22117,x22118))
% 15.02/14.81 [2212]~E(x22121,x22122)+E(f485(x22123,x22121,x22124,x22125,x22126,x22127,x22128),f485(x22123,x22122,x22124,x22125,x22126,x22127,x22128))
% 15.02/14.81 [2213]~E(x22131,x22132)+E(f485(x22133,x22134,x22131,x22135,x22136,x22137,x22138),f485(x22133,x22134,x22132,x22135,x22136,x22137,x22138))
% 15.02/14.81 [2214]~E(x22141,x22142)+E(f485(x22143,x22144,x22145,x22141,x22146,x22147,x22148),f485(x22143,x22144,x22145,x22142,x22146,x22147,x22148))
% 15.02/14.81 [2215]~E(x22151,x22152)+E(f485(x22153,x22154,x22155,x22156,x22151,x22157,x22158),f485(x22153,x22154,x22155,x22156,x22152,x22157,x22158))
% 15.02/14.81 [2216]~E(x22161,x22162)+E(f485(x22163,x22164,x22165,x22166,x22167,x22161,x22168),f485(x22163,x22164,x22165,x22166,x22167,x22162,x22168))
% 15.02/14.81 [2217]~E(x22171,x22172)+E(f485(x22173,x22174,x22175,x22176,x22177,x22178,x22171),f485(x22173,x22174,x22175,x22176,x22177,x22178,x22172))
% 15.02/14.81 [2218]~E(x22181,x22182)+E(f595(x22181,x22183,x22184,x22185,x22186,x22187,x22188,x22189),f595(x22182,x22183,x22184,x22185,x22186,x22187,x22188,x22189))
% 15.02/14.81 [2219]~E(x22191,x22192)+E(f595(x22193,x22191,x22194,x22195,x22196,x22197,x22198,x22199),f595(x22193,x22192,x22194,x22195,x22196,x22197,x22198,x22199))
% 15.02/14.81 [2220]~E(x22201,x22202)+E(f595(x22203,x22204,x22201,x22205,x22206,x22207,x22208,x22209),f595(x22203,x22204,x22202,x22205,x22206,x22207,x22208,x22209))
% 15.02/14.81 [2221]~E(x22211,x22212)+E(f595(x22213,x22214,x22215,x22211,x22216,x22217,x22218,x22219),f595(x22213,x22214,x22215,x22212,x22216,x22217,x22218,x22219))
% 15.02/14.81 [2222]~E(x22221,x22222)+E(f595(x22223,x22224,x22225,x22226,x22221,x22227,x22228,x22229),f595(x22223,x22224,x22225,x22226,x22222,x22227,x22228,x22229))
% 15.02/14.81 [2223]~E(x22231,x22232)+E(f595(x22233,x22234,x22235,x22236,x22237,x22231,x22238,x22239),f595(x22233,x22234,x22235,x22236,x22237,x22232,x22238,x22239))
% 15.02/14.81 [2224]~E(x22241,x22242)+E(f595(x22243,x22244,x22245,x22246,x22247,x22248,x22241,x22249),f595(x22243,x22244,x22245,x22246,x22247,x22248,x22242,x22249))
% 15.02/14.81 [2225]~E(x22251,x22252)+E(f595(x22253,x22254,x22255,x22256,x22257,x22258,x22259,x22251),f595(x22253,x22254,x22255,x22256,x22257,x22258,x22259,x22252))
% 15.02/14.81 [2226]~E(x22261,x22262)+E(f606(x22261,x22263,x22264,x22265),f606(x22262,x22263,x22264,x22265))
% 15.02/14.81 [2227]~E(x22271,x22272)+E(f606(x22273,x22271,x22274,x22275),f606(x22273,x22272,x22274,x22275))
% 15.02/14.81 [2228]~E(x22281,x22282)+E(f606(x22283,x22284,x22281,x22285),f606(x22283,x22284,x22282,x22285))
% 15.02/14.81 [2229]~E(x22291,x22292)+E(f606(x22293,x22294,x22295,x22291),f606(x22293,x22294,x22295,x22292))
% 15.02/14.81 [2230]~E(x22301,x22302)+E(f850(x22301,x22303,x22304,x22305,x22306,x22307,x22308,x22309),f850(x22302,x22303,x22304,x22305,x22306,x22307,x22308,x22309))
% 15.02/14.81 [2231]~E(x22311,x22312)+E(f850(x22313,x22311,x22314,x22315,x22316,x22317,x22318,x22319),f850(x22313,x22312,x22314,x22315,x22316,x22317,x22318,x22319))
% 15.02/14.81 [2232]~E(x22321,x22322)+E(f850(x22323,x22324,x22321,x22325,x22326,x22327,x22328,x22329),f850(x22323,x22324,x22322,x22325,x22326,x22327,x22328,x22329))
% 15.02/14.81 [2233]~E(x22331,x22332)+E(f850(x22333,x22334,x22335,x22331,x22336,x22337,x22338,x22339),f850(x22333,x22334,x22335,x22332,x22336,x22337,x22338,x22339))
% 15.02/14.81 [2234]~E(x22341,x22342)+E(f850(x22343,x22344,x22345,x22346,x22341,x22347,x22348,x22349),f850(x22343,x22344,x22345,x22346,x22342,x22347,x22348,x22349))
% 15.02/14.81 [2235]~E(x22351,x22352)+E(f850(x22353,x22354,x22355,x22356,x22357,x22351,x22358,x22359),f850(x22353,x22354,x22355,x22356,x22357,x22352,x22358,x22359))
% 15.02/14.81 [2236]~E(x22361,x22362)+E(f850(x22363,x22364,x22365,x22366,x22367,x22368,x22361,x22369),f850(x22363,x22364,x22365,x22366,x22367,x22368,x22362,x22369))
% 15.02/14.81 [2237]~E(x22371,x22372)+E(f850(x22373,x22374,x22375,x22376,x22377,x22378,x22379,x22371),f850(x22373,x22374,x22375,x22376,x22377,x22378,x22379,x22372))
% 15.02/14.81 [2238]~E(x22381,x22382)+E(f589(x22381,x22383,x22384,x22385,x22386,x22387),f589(x22382,x22383,x22384,x22385,x22386,x22387))
% 15.02/14.81 [2239]~E(x22391,x22392)+E(f589(x22393,x22391,x22394,x22395,x22396,x22397),f589(x22393,x22392,x22394,x22395,x22396,x22397))
% 15.02/14.81 [2240]~E(x22401,x22402)+E(f589(x22403,x22404,x22401,x22405,x22406,x22407),f589(x22403,x22404,x22402,x22405,x22406,x22407))
% 15.02/14.81 [2241]~E(x22411,x22412)+E(f589(x22413,x22414,x22415,x22411,x22416,x22417),f589(x22413,x22414,x22415,x22412,x22416,x22417))
% 15.02/14.81 [2242]~E(x22421,x22422)+E(f589(x22423,x22424,x22425,x22426,x22421,x22427),f589(x22423,x22424,x22425,x22426,x22422,x22427))
% 15.02/14.81 [2243]~E(x22431,x22432)+E(f589(x22433,x22434,x22435,x22436,x22437,x22431),f589(x22433,x22434,x22435,x22436,x22437,x22432))
% 15.02/14.81 [2244]~E(x22441,x22442)+E(f841(x22441,x22443,x22444,x22445,x22446,x22447,x22448,x22449),f841(x22442,x22443,x22444,x22445,x22446,x22447,x22448,x22449))
% 15.02/14.81 [2245]~E(x22451,x22452)+E(f841(x22453,x22451,x22454,x22455,x22456,x22457,x22458,x22459),f841(x22453,x22452,x22454,x22455,x22456,x22457,x22458,x22459))
% 15.02/14.81 [2246]~E(x22461,x22462)+E(f841(x22463,x22464,x22461,x22465,x22466,x22467,x22468,x22469),f841(x22463,x22464,x22462,x22465,x22466,x22467,x22468,x22469))
% 15.02/14.81 [2247]~E(x22471,x22472)+E(f841(x22473,x22474,x22475,x22471,x22476,x22477,x22478,x22479),f841(x22473,x22474,x22475,x22472,x22476,x22477,x22478,x22479))
% 15.02/14.81 [2248]~E(x22481,x22482)+E(f841(x22483,x22484,x22485,x22486,x22481,x22487,x22488,x22489),f841(x22483,x22484,x22485,x22486,x22482,x22487,x22488,x22489))
% 15.02/14.81 [2249]~E(x22491,x22492)+E(f841(x22493,x22494,x22495,x22496,x22497,x22491,x22498,x22499),f841(x22493,x22494,x22495,x22496,x22497,x22492,x22498,x22499))
% 15.02/14.81 [2250]~E(x22501,x22502)+E(f841(x22503,x22504,x22505,x22506,x22507,x22508,x22501,x22509),f841(x22503,x22504,x22505,x22506,x22507,x22508,x22502,x22509))
% 15.02/14.81 [2251]~E(x22511,x22512)+E(f841(x22513,x22514,x22515,x22516,x22517,x22518,x22519,x22511),f841(x22513,x22514,x22515,x22516,x22517,x22518,x22519,x22512))
% 15.02/14.81 [2252]~E(x22521,x22522)+E(f437(x22521,x22523),f437(x22522,x22523))
% 15.02/14.81 [2253]~E(x22531,x22532)+E(f437(x22533,x22531),f437(x22533,x22532))
% 15.02/14.81 [2254]~E(x22541,x22542)+E(f254(x22541,x22543,x22544,x22545),f254(x22542,x22543,x22544,x22545))
% 15.02/14.81 [2255]~E(x22551,x22552)+E(f254(x22553,x22551,x22554,x22555),f254(x22553,x22552,x22554,x22555))
% 15.02/14.81 [2256]~E(x22561,x22562)+E(f254(x22563,x22564,x22561,x22565),f254(x22563,x22564,x22562,x22565))
% 15.02/14.81 [2257]~E(x22571,x22572)+E(f254(x22573,x22574,x22575,x22571),f254(x22573,x22574,x22575,x22572))
% 15.02/14.81 [2258]~E(x22581,x22582)+E(f756(x22581,x22583,x22584),f756(x22582,x22583,x22584))
% 15.02/14.81 [2259]~E(x22591,x22592)+E(f756(x22593,x22591,x22594),f756(x22593,x22592,x22594))
% 15.02/14.81 [2260]~E(x22601,x22602)+E(f756(x22603,x22604,x22601),f756(x22603,x22604,x22602))
% 15.02/14.81 [2261]~E(x22611,x22612)+E(f705(x22611,x22613,x22614),f705(x22612,x22613,x22614))
% 15.02/14.81 [2262]~E(x22621,x22622)+E(f705(x22623,x22621,x22624),f705(x22623,x22622,x22624))
% 15.02/14.81 [2263]~E(x22631,x22632)+E(f705(x22633,x22634,x22631),f705(x22633,x22634,x22632))
% 15.02/14.81 [2264]~E(x22641,x22642)+E(f792(x22641,x22643),f792(x22642,x22643))
% 15.02/14.81 [2265]~E(x22651,x22652)+E(f792(x22653,x22651),f792(x22653,x22652))
% 15.02/14.81 [2266]~E(x22661,x22662)+E(f737(x22661,x22663,x22664,x22665,x22666),f737(x22662,x22663,x22664,x22665,x22666))
% 15.02/14.81 [2267]~E(x22671,x22672)+E(f737(x22673,x22671,x22674,x22675,x22676),f737(x22673,x22672,x22674,x22675,x22676))
% 15.02/14.81 [2268]~E(x22681,x22682)+E(f737(x22683,x22684,x22681,x22685,x22686),f737(x22683,x22684,x22682,x22685,x22686))
% 15.02/14.81 [2269]~E(x22691,x22692)+E(f737(x22693,x22694,x22695,x22691,x22696),f737(x22693,x22694,x22695,x22692,x22696))
% 15.02/14.81 [2270]~E(x22701,x22702)+E(f737(x22703,x22704,x22705,x22706,x22701),f737(x22703,x22704,x22705,x22706,x22702))
% 15.02/14.81 [2271]~E(x22711,x22712)+E(f788(x22711,x22713),f788(x22712,x22713))
% 15.02/14.81 [2272]~E(x22721,x22722)+E(f788(x22723,x22721),f788(x22723,x22722))
% 15.02/14.81 [2273]~E(x22731,x22732)+E(f191(x22731,x22733,x22734,x22735),f191(x22732,x22733,x22734,x22735))
% 15.02/14.81 [2274]~E(x22741,x22742)+E(f191(x22743,x22741,x22744,x22745),f191(x22743,x22742,x22744,x22745))
% 15.02/14.81 [2275]~E(x22751,x22752)+E(f191(x22753,x22754,x22751,x22755),f191(x22753,x22754,x22752,x22755))
% 15.02/14.81 [2276]~E(x22761,x22762)+E(f191(x22763,x22764,x22765,x22761),f191(x22763,x22764,x22765,x22762))
% 15.02/14.81 [2277]~E(x22771,x22772)+E(f597(x22771,x22773,x22774),f597(x22772,x22773,x22774))
% 15.02/14.81 [2278]~E(x22781,x22782)+E(f597(x22783,x22781,x22784),f597(x22783,x22782,x22784))
% 15.02/14.81 [2279]~E(x22791,x22792)+E(f597(x22793,x22794,x22791),f597(x22793,x22794,x22792))
% 15.02/14.81 [2280]~E(x22801,x22802)+E(f825(x22801,x22803,x22804,x22805,x22806,x22807),f825(x22802,x22803,x22804,x22805,x22806,x22807))
% 15.02/14.81 [2281]~E(x22811,x22812)+E(f825(x22813,x22811,x22814,x22815,x22816,x22817),f825(x22813,x22812,x22814,x22815,x22816,x22817))
% 15.02/14.81 [2282]~E(x22821,x22822)+E(f825(x22823,x22824,x22821,x22825,x22826,x22827),f825(x22823,x22824,x22822,x22825,x22826,x22827))
% 15.02/14.81 [2283]~E(x22831,x22832)+E(f825(x22833,x22834,x22835,x22831,x22836,x22837),f825(x22833,x22834,x22835,x22832,x22836,x22837))
% 15.02/14.81 [2284]~E(x22841,x22842)+E(f825(x22843,x22844,x22845,x22846,x22841,x22847),f825(x22843,x22844,x22845,x22846,x22842,x22847))
% 15.02/14.81 [2285]~E(x22851,x22852)+E(f825(x22853,x22854,x22855,x22856,x22857,x22851),f825(x22853,x22854,x22855,x22856,x22857,x22852))
% 15.02/14.81 [2286]~E(x22861,x22862)+E(f858(x22861,x22863,x22864),f858(x22862,x22863,x22864))
% 15.02/14.81 [2287]~E(x22871,x22872)+E(f858(x22873,x22871,x22874),f858(x22873,x22872,x22874))
% 15.02/14.81 [2288]~E(x22881,x22882)+E(f858(x22883,x22884,x22881),f858(x22883,x22884,x22882))
% 15.02/14.81 [2289]~E(x22891,x22892)+E(f467(x22891,x22893,x22894,x22895),f467(x22892,x22893,x22894,x22895))
% 15.02/14.81 [2290]~E(x22901,x22902)+E(f467(x22903,x22901,x22904,x22905),f467(x22903,x22902,x22904,x22905))
% 15.02/14.81 [2291]~E(x22911,x22912)+E(f467(x22913,x22914,x22911,x22915),f467(x22913,x22914,x22912,x22915))
% 15.02/14.81 [2292]~E(x22921,x22922)+E(f467(x22923,x22924,x22925,x22921),f467(x22923,x22924,x22925,x22922))
% 15.02/14.81 [2293]~E(x22931,x22932)+E(f844(x22931,x22933,x22934,x22935,x22936,x22937),f844(x22932,x22933,x22934,x22935,x22936,x22937))
% 15.02/14.81 [2294]~E(x22941,x22942)+E(f844(x22943,x22941,x22944,x22945,x22946,x22947),f844(x22943,x22942,x22944,x22945,x22946,x22947))
% 15.02/14.81 [2295]~E(x22951,x22952)+E(f844(x22953,x22954,x22951,x22955,x22956,x22957),f844(x22953,x22954,x22952,x22955,x22956,x22957))
% 15.02/14.81 [2296]~E(x22961,x22962)+E(f844(x22963,x22964,x22965,x22961,x22966,x22967),f844(x22963,x22964,x22965,x22962,x22966,x22967))
% 15.02/14.81 [2297]~E(x22971,x22972)+E(f844(x22973,x22974,x22975,x22976,x22971,x22977),f844(x22973,x22974,x22975,x22976,x22972,x22977))
% 15.02/14.81 [2298]~E(x22981,x22982)+E(f844(x22983,x22984,x22985,x22986,x22987,x22981),f844(x22983,x22984,x22985,x22986,x22987,x22982))
% 15.02/14.81 [2299]~E(x22991,x22992)+E(f207(x22991,x22993,x22994,x22995),f207(x22992,x22993,x22994,x22995))
% 15.02/14.81 [2300]~E(x23001,x23002)+E(f207(x23003,x23001,x23004,x23005),f207(x23003,x23002,x23004,x23005))
% 15.02/14.81 [2301]~E(x23011,x23012)+E(f207(x23013,x23014,x23011,x23015),f207(x23013,x23014,x23012,x23015))
% 15.02/14.81 [2302]~E(x23021,x23022)+E(f207(x23023,x23024,x23025,x23021),f207(x23023,x23024,x23025,x23022))
% 15.02/14.81 [2303]~E(x23031,x23032)+E(f565(x23031,x23033,x23034,x23035),f565(x23032,x23033,x23034,x23035))
% 15.02/14.81 [2304]~E(x23041,x23042)+E(f565(x23043,x23041,x23044,x23045),f565(x23043,x23042,x23044,x23045))
% 15.02/14.81 [2305]~E(x23051,x23052)+E(f565(x23053,x23054,x23051,x23055),f565(x23053,x23054,x23052,x23055))
% 15.02/14.81 [2306]~E(x23061,x23062)+E(f565(x23063,x23064,x23065,x23061),f565(x23063,x23064,x23065,x23062))
% 15.02/14.81 [2307]~E(x23071,x23072)+E(f637(x23071,x23073,x23074,x23075),f637(x23072,x23073,x23074,x23075))
% 15.02/14.81 [2308]~E(x23081,x23082)+E(f637(x23083,x23081,x23084,x23085),f637(x23083,x23082,x23084,x23085))
% 15.02/14.81 [2309]~E(x23091,x23092)+E(f637(x23093,x23094,x23091,x23095),f637(x23093,x23094,x23092,x23095))
% 15.02/14.81 [2310]~E(x23101,x23102)+E(f637(x23103,x23104,x23105,x23101),f637(x23103,x23104,x23105,x23102))
% 15.02/14.81 [2311]~E(x23111,x23112)+E(f808(x23111,x23113,x23114,x23115,x23116,x23117,x23118),f808(x23112,x23113,x23114,x23115,x23116,x23117,x23118))
% 15.02/14.81 [2312]~E(x23121,x23122)+E(f808(x23123,x23121,x23124,x23125,x23126,x23127,x23128),f808(x23123,x23122,x23124,x23125,x23126,x23127,x23128))
% 15.02/14.81 [2313]~E(x23131,x23132)+E(f808(x23133,x23134,x23131,x23135,x23136,x23137,x23138),f808(x23133,x23134,x23132,x23135,x23136,x23137,x23138))
% 15.02/14.81 [2314]~E(x23141,x23142)+E(f808(x23143,x23144,x23145,x23141,x23146,x23147,x23148),f808(x23143,x23144,x23145,x23142,x23146,x23147,x23148))
% 15.02/14.81 [2315]~E(x23151,x23152)+E(f808(x23153,x23154,x23155,x23156,x23151,x23157,x23158),f808(x23153,x23154,x23155,x23156,x23152,x23157,x23158))
% 15.02/14.81 [2316]~E(x23161,x23162)+E(f808(x23163,x23164,x23165,x23166,x23167,x23161,x23168),f808(x23163,x23164,x23165,x23166,x23167,x23162,x23168))
% 15.02/14.81 [2317]~E(x23171,x23172)+E(f808(x23173,x23174,x23175,x23176,x23177,x23178,x23171),f808(x23173,x23174,x23175,x23176,x23177,x23178,x23172))
% 15.02/14.81 [2318]~E(x23181,x23182)+E(f621(x23181,x23183),f621(x23182,x23183))
% 15.02/14.81 [2319]~E(x23191,x23192)+E(f621(x23193,x23191),f621(x23193,x23192))
% 15.02/14.81 [2320]~E(x23201,x23202)+E(f93(x23201,x23203,x23204),f93(x23202,x23203,x23204))
% 15.02/14.81 [2321]~E(x23211,x23212)+E(f93(x23213,x23211,x23214),f93(x23213,x23212,x23214))
% 15.02/14.81 [2322]~E(x23221,x23222)+E(f93(x23223,x23224,x23221),f93(x23223,x23224,x23222))
% 15.02/14.81 [2323]~E(x23231,x23232)+E(f360(x23231,x23233,x23234),f360(x23232,x23233,x23234))
% 15.02/14.81 [2324]~E(x23241,x23242)+E(f360(x23243,x23241,x23244),f360(x23243,x23242,x23244))
% 15.02/14.81 [2325]~E(x23251,x23252)+E(f360(x23253,x23254,x23251),f360(x23253,x23254,x23252))
% 15.02/14.81 [2326]~E(x23261,x23262)+E(f418(x23261,x23263,x23264,x23265,x23266),f418(x23262,x23263,x23264,x23265,x23266))
% 15.02/14.81 [2327]~E(x23271,x23272)+E(f418(x23273,x23271,x23274,x23275,x23276),f418(x23273,x23272,x23274,x23275,x23276))
% 15.02/14.81 [2328]~E(x23281,x23282)+E(f418(x23283,x23284,x23281,x23285,x23286),f418(x23283,x23284,x23282,x23285,x23286))
% 15.02/14.81 [2329]~E(x23291,x23292)+E(f418(x23293,x23294,x23295,x23291,x23296),f418(x23293,x23294,x23295,x23292,x23296))
% 15.02/14.81 [2330]~E(x23301,x23302)+E(f418(x23303,x23304,x23305,x23306,x23301),f418(x23303,x23304,x23305,x23306,x23302))
% 15.02/14.81 [2331]~E(x23311,x23312)+E(f674(x23311,x23313,x23314),f674(x23312,x23313,x23314))
% 15.02/14.81 [2332]~E(x23321,x23322)+E(f674(x23323,x23321,x23324),f674(x23323,x23322,x23324))
% 15.02/14.81 [2333]~E(x23331,x23332)+E(f674(x23333,x23334,x23331),f674(x23333,x23334,x23332))
% 15.02/14.81 [2334]~E(x23341,x23342)+E(f333(x23341),f333(x23342))
% 15.02/14.81 [2335]~E(x23351,x23352)+E(f209(x23351),f209(x23352))
% 15.02/14.81 [2336]~E(x23361,x23362)+E(f826(x23361,x23363,x23364,x23365,x23366),f826(x23362,x23363,x23364,x23365,x23366))
% 15.02/14.81 [2337]~E(x23371,x23372)+E(f826(x23373,x23371,x23374,x23375,x23376),f826(x23373,x23372,x23374,x23375,x23376))
% 15.02/14.81 [2338]~E(x23381,x23382)+E(f826(x23383,x23384,x23381,x23385,x23386),f826(x23383,x23384,x23382,x23385,x23386))
% 15.02/14.81 [2339]~E(x23391,x23392)+E(f826(x23393,x23394,x23395,x23391,x23396),f826(x23393,x23394,x23395,x23392,x23396))
% 15.02/14.81 [2340]~E(x23401,x23402)+E(f826(x23403,x23404,x23405,x23406,x23401),f826(x23403,x23404,x23405,x23406,x23402))
% 15.02/14.81 [2341]~E(x23411,x23412)+E(f712(x23411,x23413,x23414),f712(x23412,x23413,x23414))
% 15.02/14.81 [2342]~E(x23421,x23422)+E(f712(x23423,x23421,x23424),f712(x23423,x23422,x23424))
% 15.02/14.81 [2343]~E(x23431,x23432)+E(f712(x23433,x23434,x23431),f712(x23433,x23434,x23432))
% 15.02/14.81 [2344]~E(x23441,x23442)+E(f496(x23441,x23443,x23444,x23445),f496(x23442,x23443,x23444,x23445))
% 15.02/14.81 [2345]~E(x23451,x23452)+E(f496(x23453,x23451,x23454,x23455),f496(x23453,x23452,x23454,x23455))
% 15.02/14.81 [2346]~E(x23461,x23462)+E(f496(x23463,x23464,x23461,x23465),f496(x23463,x23464,x23462,x23465))
% 15.02/14.81 [2347]~E(x23471,x23472)+E(f496(x23473,x23474,x23475,x23471),f496(x23473,x23474,x23475,x23472))
% 15.02/14.81 [2348]~E(x23481,x23482)+E(f523(x23481,x23483,x23484),f523(x23482,x23483,x23484))
% 15.02/14.81 [2349]~E(x23491,x23492)+E(f523(x23493,x23491,x23494),f523(x23493,x23492,x23494))
% 15.02/14.81 [2350]~E(x23501,x23502)+E(f523(x23503,x23504,x23501),f523(x23503,x23504,x23502))
% 15.02/14.81 [2351]~E(x23511,x23512)+E(f491(x23511,x23513),f491(x23512,x23513))
% 15.02/14.81 [2352]~E(x23521,x23522)+E(f491(x23523,x23521),f491(x23523,x23522))
% 15.02/14.81 [2353]~E(x23531,x23532)+E(f660(x23531,x23533,x23534),f660(x23532,x23533,x23534))
% 15.02/14.81 [2354]~E(x23541,x23542)+E(f660(x23543,x23541,x23544),f660(x23543,x23542,x23544))
% 15.02/14.81 [2355]~E(x23551,x23552)+E(f660(x23553,x23554,x23551),f660(x23553,x23554,x23552))
% 15.02/14.81 [2356]~E(x23561,x23562)+E(f604(x23561,x23563,x23564),f604(x23562,x23563,x23564))
% 15.02/14.81 [2357]~E(x23571,x23572)+E(f604(x23573,x23571,x23574),f604(x23573,x23572,x23574))
% 15.02/14.81 [2358]~E(x23581,x23582)+E(f604(x23583,x23584,x23581),f604(x23583,x23584,x23582))
% 15.02/14.81 [2359]~E(x23591,x23592)+E(f852(x23591,x23593,x23594,x23595,x23596,x23597),f852(x23592,x23593,x23594,x23595,x23596,x23597))
% 15.02/14.81 [2360]~E(x23601,x23602)+E(f852(x23603,x23601,x23604,x23605,x23606,x23607),f852(x23603,x23602,x23604,x23605,x23606,x23607))
% 15.02/14.81 [2361]~E(x23611,x23612)+E(f852(x23613,x23614,x23611,x23615,x23616,x23617),f852(x23613,x23614,x23612,x23615,x23616,x23617))
% 15.02/14.81 [2362]~E(x23621,x23622)+E(f852(x23623,x23624,x23625,x23621,x23626,x23627),f852(x23623,x23624,x23625,x23622,x23626,x23627))
% 15.02/14.81 [2363]~E(x23631,x23632)+E(f852(x23633,x23634,x23635,x23636,x23631,x23637),f852(x23633,x23634,x23635,x23636,x23632,x23637))
% 15.02/14.81 [2364]~E(x23641,x23642)+E(f852(x23643,x23644,x23645,x23646,x23647,x23641),f852(x23643,x23644,x23645,x23646,x23647,x23642))
% 15.02/14.81 [2365]~E(x23651,x23652)+E(f855(x23651,x23653,x23654),f855(x23652,x23653,x23654))
% 15.02/14.81 [2366]~E(x23661,x23662)+E(f855(x23663,x23661,x23664),f855(x23663,x23662,x23664))
% 15.02/14.81 [2367]~E(x23671,x23672)+E(f855(x23673,x23674,x23671),f855(x23673,x23674,x23672))
% 15.02/14.81 [2368]~E(x23681,x23682)+E(f601(x23681,x23683,x23684),f601(x23682,x23683,x23684))
% 15.02/14.81 [2369]~E(x23691,x23692)+E(f601(x23693,x23691,x23694),f601(x23693,x23692,x23694))
% 15.02/14.81 [2370]~E(x23701,x23702)+E(f601(x23703,x23704,x23701),f601(x23703,x23704,x23702))
% 15.02/14.81 [2371]~E(x23711,x23712)+E(f549(x23711,x23713,x23714),f549(x23712,x23713,x23714))
% 15.02/14.81 [2372]~E(x23721,x23722)+E(f549(x23723,x23721,x23724),f549(x23723,x23722,x23724))
% 15.02/14.81 [2373]~E(x23731,x23732)+E(f549(x23733,x23734,x23731),f549(x23733,x23734,x23732))
% 15.02/14.81 [2374]~E(x23741,x23742)+E(f706(x23741,x23743),f706(x23742,x23743))
% 15.02/14.81 [2375]~E(x23751,x23752)+E(f706(x23753,x23751),f706(x23753,x23752))
% 15.02/14.81 [2376]~E(x23761,x23762)+E(f762(x23761,x23763,x23764),f762(x23762,x23763,x23764))
% 15.02/14.81 [2377]~E(x23771,x23772)+E(f762(x23773,x23771,x23774),f762(x23773,x23772,x23774))
% 15.02/14.81 [2378]~E(x23781,x23782)+E(f762(x23783,x23784,x23781),f762(x23783,x23784,x23782))
% 15.02/14.81 [2379]~E(x23791,x23792)+E(f449(x23791,x23793,x23794,x23795),f449(x23792,x23793,x23794,x23795))
% 15.02/14.81 [2380]~E(x23801,x23802)+E(f449(x23803,x23801,x23804,x23805),f449(x23803,x23802,x23804,x23805))
% 15.02/14.81 [2381]~E(x23811,x23812)+E(f449(x23813,x23814,x23811,x23815),f449(x23813,x23814,x23812,x23815))
% 15.02/14.81 [2382]~E(x23821,x23822)+E(f449(x23823,x23824,x23825,x23821),f449(x23823,x23824,x23825,x23822))
% 15.02/14.81 [2383]~E(x23831,x23832)+E(f545(x23831,x23833,x23834,x23835,x23836),f545(x23832,x23833,x23834,x23835,x23836))
% 15.02/14.81 [2384]~E(x23841,x23842)+E(f545(x23843,x23841,x23844,x23845,x23846),f545(x23843,x23842,x23844,x23845,x23846))
% 15.02/14.81 [2385]~E(x23851,x23852)+E(f545(x23853,x23854,x23851,x23855,x23856),f545(x23853,x23854,x23852,x23855,x23856))
% 15.02/14.81 [2386]~E(x23861,x23862)+E(f545(x23863,x23864,x23865,x23861,x23866),f545(x23863,x23864,x23865,x23862,x23866))
% 15.02/14.81 [2387]~E(x23871,x23872)+E(f545(x23873,x23874,x23875,x23876,x23871),f545(x23873,x23874,x23875,x23876,x23872))
% 15.02/14.81 [2388]~E(x23881,x23882)+E(f431(x23881,x23883,x23884,x23885,x23886),f431(x23882,x23883,x23884,x23885,x23886))
% 15.02/14.81 [2389]~E(x23891,x23892)+E(f431(x23893,x23891,x23894,x23895,x23896),f431(x23893,x23892,x23894,x23895,x23896))
% 15.02/14.81 [2390]~E(x23901,x23902)+E(f431(x23903,x23904,x23901,x23905,x23906),f431(x23903,x23904,x23902,x23905,x23906))
% 15.02/14.81 [2391]~E(x23911,x23912)+E(f431(x23913,x23914,x23915,x23911,x23916),f431(x23913,x23914,x23915,x23912,x23916))
% 15.02/14.81 [2392]~E(x23921,x23922)+E(f431(x23923,x23924,x23925,x23926,x23921),f431(x23923,x23924,x23925,x23926,x23922))
% 15.02/14.81 [2393]~E(x23931,x23932)+E(f722(x23931,x23933),f722(x23932,x23933))
% 15.02/14.81 [2394]~E(x23941,x23942)+E(f722(x23943,x23941),f722(x23943,x23942))
% 15.02/14.81 [2395]~E(x23951,x23952)+E(f708(x23951,x23953),f708(x23952,x23953))
% 15.02/14.81 [2396]~E(x23961,x23962)+E(f708(x23963,x23961),f708(x23963,x23962))
% 15.02/14.81 [2397]~E(x23971,x23972)+E(f750(x23971,x23973),f750(x23972,x23973))
% 15.02/14.81 [2398]~E(x23981,x23982)+E(f750(x23983,x23981),f750(x23983,x23982))
% 15.02/14.81 [2399]~E(x23991,x23992)+E(f897(x23991,x23993,x23994,x23995),f897(x23992,x23993,x23994,x23995))
% 15.02/14.81 [2400]~E(x24001,x24002)+E(f897(x24003,x24001,x24004,x24005),f897(x24003,x24002,x24004,x24005))
% 15.02/14.81 [2401]~E(x24011,x24012)+E(f897(x24013,x24014,x24011,x24015),f897(x24013,x24014,x24012,x24015))
% 15.02/14.81 [2402]~E(x24021,x24022)+E(f897(x24023,x24024,x24025,x24021),f897(x24023,x24024,x24025,x24022))
% 15.02/14.81 [2403]~E(x24031,x24032)+E(f628(x24031,x24033,x24034,x24035),f628(x24032,x24033,x24034,x24035))
% 15.02/14.81 [2404]~E(x24041,x24042)+E(f628(x24043,x24041,x24044,x24045),f628(x24043,x24042,x24044,x24045))
% 15.02/14.81 [2405]~E(x24051,x24052)+E(f628(x24053,x24054,x24051,x24055),f628(x24053,x24054,x24052,x24055))
% 15.02/14.81 [2406]~E(x24061,x24062)+E(f628(x24063,x24064,x24065,x24061),f628(x24063,x24064,x24065,x24062))
% 15.02/14.81 [2407]~E(x24071,x24072)+E(f743(x24071,x24073,x24074,x24075,x24076),f743(x24072,x24073,x24074,x24075,x24076))
% 15.02/14.81 [2408]~E(x24081,x24082)+E(f743(x24083,x24081,x24084,x24085,x24086),f743(x24083,x24082,x24084,x24085,x24086))
% 15.02/14.81 [2409]~E(x24091,x24092)+E(f743(x24093,x24094,x24091,x24095,x24096),f743(x24093,x24094,x24092,x24095,x24096))
% 15.02/14.81 [2410]~E(x24101,x24102)+E(f743(x24103,x24104,x24105,x24101,x24106),f743(x24103,x24104,x24105,x24102,x24106))
% 15.02/14.81 [2411]~E(x24111,x24112)+E(f743(x24113,x24114,x24115,x24116,x24111),f743(x24113,x24114,x24115,x24116,x24112))
% 15.02/14.81 [2412]~E(x24121,x24122)+E(f881(x24121,x24123,x24124),f881(x24122,x24123,x24124))
% 15.02/14.81 [2413]~E(x24131,x24132)+E(f881(x24133,x24131,x24134),f881(x24133,x24132,x24134))
% 15.02/14.81 [2414]~E(x24141,x24142)+E(f881(x24143,x24144,x24141),f881(x24143,x24144,x24142))
% 15.02/14.81 [2415]~E(x24151,x24152)+E(f424(x24151,x24153,x24154,x24155),f424(x24152,x24153,x24154,x24155))
% 15.02/14.81 [2416]~E(x24161,x24162)+E(f424(x24163,x24161,x24164,x24165),f424(x24163,x24162,x24164,x24165))
% 15.02/14.81 [2417]~E(x24171,x24172)+E(f424(x24173,x24174,x24171,x24175),f424(x24173,x24174,x24172,x24175))
% 15.02/14.81 [2418]~E(x24181,x24182)+E(f424(x24183,x24184,x24185,x24181),f424(x24183,x24184,x24185,x24182))
% 15.02/14.81 [2419]~E(x24191,x24192)+E(f509(x24191,x24193,x24194),f509(x24192,x24193,x24194))
% 15.02/14.81 [2420]~E(x24201,x24202)+E(f509(x24203,x24201,x24204),f509(x24203,x24202,x24204))
% 15.02/14.81 [2421]~E(x24211,x24212)+E(f509(x24213,x24214,x24211),f509(x24213,x24214,x24212))
% 15.02/14.81 [2422]~E(x24221,x24222)+E(f834(x24221,x24223,x24224,x24225,x24226),f834(x24222,x24223,x24224,x24225,x24226))
% 15.02/14.81 [2423]~E(x24231,x24232)+E(f834(x24233,x24231,x24234,x24235,x24236),f834(x24233,x24232,x24234,x24235,x24236))
% 15.02/14.81 [2424]~E(x24241,x24242)+E(f834(x24243,x24244,x24241,x24245,x24246),f834(x24243,x24244,x24242,x24245,x24246))
% 15.02/14.81 [2425]~E(x24251,x24252)+E(f834(x24253,x24254,x24255,x24251,x24256),f834(x24253,x24254,x24255,x24252,x24256))
% 15.02/14.81 [2426]~E(x24261,x24262)+E(f834(x24263,x24264,x24265,x24266,x24261),f834(x24263,x24264,x24265,x24266,x24262))
% 15.02/14.81 [2427]~E(x24271,x24272)+E(f474(x24271,x24273),f474(x24272,x24273))
% 15.02/14.81 [2428]~E(x24281,x24282)+E(f474(x24283,x24281),f474(x24283,x24282))
% 15.02/14.81 [2429]~E(x24291,x24292)+E(f571(x24291,x24293,x24294,x24295),f571(x24292,x24293,x24294,x24295))
% 15.02/14.81 [2430]~E(x24301,x24302)+E(f571(x24303,x24301,x24304,x24305),f571(x24303,x24302,x24304,x24305))
% 15.02/14.81 [2431]~E(x24311,x24312)+E(f571(x24313,x24314,x24311,x24315),f571(x24313,x24314,x24312,x24315))
% 15.02/14.81 [2432]~E(x24321,x24322)+E(f571(x24323,x24324,x24325,x24321),f571(x24323,x24324,x24325,x24322))
% 15.02/14.81 [2433]~E(x24331,x24332)+E(f773(x24331,x24333,x24334),f773(x24332,x24333,x24334))
% 15.02/14.81 [2434]~E(x24341,x24342)+E(f773(x24343,x24341,x24344),f773(x24343,x24342,x24344))
% 15.02/14.81 [2435]~E(x24351,x24352)+E(f773(x24353,x24354,x24351),f773(x24353,x24354,x24352))
% 15.02/14.81 [2436]~E(x24361,x24362)+E(f433(x24361,x24363),f433(x24362,x24363))
% 15.02/14.81 [2437]~E(x24371,x24372)+E(f433(x24373,x24371),f433(x24373,x24372))
% 15.02/14.81 [2438]~E(x24381,x24382)+E(f519(x24381,x24383,x24384),f519(x24382,x24383,x24384))
% 15.02/14.81 [2439]~E(x24391,x24392)+E(f519(x24393,x24391,x24394),f519(x24393,x24392,x24394))
% 15.02/14.81 [2440]~E(x24401,x24402)+E(f519(x24403,x24404,x24401),f519(x24403,x24404,x24402))
% 15.02/14.81 [2441]~E(x24411,x24412)+E(f414(x24411,x24413),f414(x24412,x24413))
% 15.02/14.81 [2442]~E(x24421,x24422)+E(f414(x24423,x24421),f414(x24423,x24422))
% 15.02/14.81 [2443]~E(x24431,x24432)+E(f342(x24431,x24433,x24434,x24435),f342(x24432,x24433,x24434,x24435))
% 15.02/14.81 [2444]~E(x24441,x24442)+E(f342(x24443,x24441,x24444,x24445),f342(x24443,x24442,x24444,x24445))
% 15.02/14.81 [2445]~E(x24451,x24452)+E(f342(x24453,x24454,x24451,x24455),f342(x24453,x24454,x24452,x24455))
% 15.02/14.81 [2446]~E(x24461,x24462)+E(f342(x24463,x24464,x24465,x24461),f342(x24463,x24464,x24465,x24462))
% 15.02/14.81 [2447]~E(x24471,x24472)+E(f746(x24471,x24473,x24474,x24475,x24476),f746(x24472,x24473,x24474,x24475,x24476))
% 15.02/14.81 [2448]~E(x24481,x24482)+E(f746(x24483,x24481,x24484,x24485,x24486),f746(x24483,x24482,x24484,x24485,x24486))
% 15.02/14.81 [2449]~E(x24491,x24492)+E(f746(x24493,x24494,x24491,x24495,x24496),f746(x24493,x24494,x24492,x24495,x24496))
% 15.02/14.81 [2450]~E(x24501,x24502)+E(f746(x24503,x24504,x24505,x24501,x24506),f746(x24503,x24504,x24505,x24502,x24506))
% 15.02/14.81 [2451]~E(x24511,x24512)+E(f746(x24513,x24514,x24515,x24516,x24511),f746(x24513,x24514,x24515,x24516,x24512))
% 15.02/14.81 [2452]~E(x24521,x24522)+E(f599(x24521,x24523,x24524),f599(x24522,x24523,x24524))
% 15.02/14.81 [2453]~E(x24531,x24532)+E(f599(x24533,x24531,x24534),f599(x24533,x24532,x24534))
% 15.02/14.81 [2454]~E(x24541,x24542)+E(f599(x24543,x24544,x24541),f599(x24543,x24544,x24542))
% 15.02/14.81 [2455]~E(x24551,x24552)+E(f455(x24551,x24553,x24554),f455(x24552,x24553,x24554))
% 15.02/14.81 [2456]~E(x24561,x24562)+E(f455(x24563,x24561,x24564),f455(x24563,x24562,x24564))
% 15.02/14.81 [2457]~E(x24571,x24572)+E(f455(x24573,x24574,x24571),f455(x24573,x24574,x24572))
% 15.02/14.81 [2458]~E(x24581,x24582)+E(f95(x24581,x24583,x24584,x24585),f95(x24582,x24583,x24584,x24585))
% 15.02/14.81 [2459]~E(x24591,x24592)+E(f95(x24593,x24591,x24594,x24595),f95(x24593,x24592,x24594,x24595))
% 15.02/14.81 [2460]~E(x24601,x24602)+E(f95(x24603,x24604,x24601,x24605),f95(x24603,x24604,x24602,x24605))
% 15.02/14.81 [2461]~E(x24611,x24612)+E(f95(x24613,x24614,x24615,x24611),f95(x24613,x24614,x24615,x24612))
% 15.02/14.81 [2462]~E(x24621,x24622)+E(f900(x24621,x24623,x24624,x24625,x24626),f900(x24622,x24623,x24624,x24625,x24626))
% 15.02/14.81 [2463]~E(x24631,x24632)+E(f900(x24633,x24631,x24634,x24635,x24636),f900(x24633,x24632,x24634,x24635,x24636))
% 15.02/14.81 [2464]~E(x24641,x24642)+E(f900(x24643,x24644,x24641,x24645,x24646),f900(x24643,x24644,x24642,x24645,x24646))
% 15.02/14.81 [2465]~E(x24651,x24652)+E(f900(x24653,x24654,x24655,x24651,x24656),f900(x24653,x24654,x24655,x24652,x24656))
% 15.02/14.81 [2466]~E(x24661,x24662)+E(f900(x24663,x24664,x24665,x24666,x24661),f900(x24663,x24664,x24665,x24666,x24662))
% 15.02/14.81 [2467]~E(x24671,x24672)+E(f462(x24671,x24673,x24674,x24675),f462(x24672,x24673,x24674,x24675))
% 15.02/14.81 [2468]~E(x24681,x24682)+E(f462(x24683,x24681,x24684,x24685),f462(x24683,x24682,x24684,x24685))
% 15.02/14.81 [2469]~E(x24691,x24692)+E(f462(x24693,x24694,x24691,x24695),f462(x24693,x24694,x24692,x24695))
% 15.02/14.81 [2470]~E(x24701,x24702)+E(f462(x24703,x24704,x24705,x24701),f462(x24703,x24704,x24705,x24702))
% 15.02/14.81 [2471]~E(x24711,x24712)+E(f635(x24711,x24713,x24714,x24715,x24716),f635(x24712,x24713,x24714,x24715,x24716))
% 15.02/14.81 [2472]~E(x24721,x24722)+E(f635(x24723,x24721,x24724,x24725,x24726),f635(x24723,x24722,x24724,x24725,x24726))
% 15.02/14.81 [2473]~E(x24731,x24732)+E(f635(x24733,x24734,x24731,x24735,x24736),f635(x24733,x24734,x24732,x24735,x24736))
% 15.02/14.81 [2474]~E(x24741,x24742)+E(f635(x24743,x24744,x24745,x24741,x24746),f635(x24743,x24744,x24745,x24742,x24746))
% 15.02/14.81 [2475]~E(x24751,x24752)+E(f635(x24753,x24754,x24755,x24756,x24751),f635(x24753,x24754,x24755,x24756,x24752))
% 15.02/14.81 [2476]~E(x24761,x24762)+E(f651(x24761,x24763,x24764),f651(x24762,x24763,x24764))
% 15.02/14.81 [2477]~E(x24771,x24772)+E(f651(x24773,x24771,x24774),f651(x24773,x24772,x24774))
% 15.02/14.81 [2478]~E(x24781,x24782)+E(f651(x24783,x24784,x24781),f651(x24783,x24784,x24782))
% 15.02/14.81 [2479]~E(x24791,x24792)+E(f802(x24791,x24793),f802(x24792,x24793))
% 15.02/14.81 [2480]~E(x24801,x24802)+E(f802(x24803,x24801),f802(x24803,x24802))
% 15.02/14.81 [2481]~E(x24811,x24812)+E(f365(x24811,x24813,x24814),f365(x24812,x24813,x24814))
% 15.02/14.81 [2482]~E(x24821,x24822)+E(f365(x24823,x24821,x24824),f365(x24823,x24822,x24824))
% 15.02/14.81 [2483]~E(x24831,x24832)+E(f365(x24833,x24834,x24831),f365(x24833,x24834,x24832))
% 15.02/14.81 [2484]~E(x24841,x24842)+E(f673(x24841,x24843),f673(x24842,x24843))
% 15.02/14.81 [2485]~E(x24851,x24852)+E(f673(x24853,x24851),f673(x24853,x24852))
% 15.02/14.81 [2486]~E(x24861,x24862)+E(f475(x24861,x24863,x24864,x24865),f475(x24862,x24863,x24864,x24865))
% 15.02/14.81 [2487]~E(x24871,x24872)+E(f475(x24873,x24871,x24874,x24875),f475(x24873,x24872,x24874,x24875))
% 15.02/14.81 [2488]~E(x24881,x24882)+E(f475(x24883,x24884,x24881,x24885),f475(x24883,x24884,x24882,x24885))
% 15.02/14.81 [2489]~E(x24891,x24892)+E(f475(x24893,x24894,x24895,x24891),f475(x24893,x24894,x24895,x24892))
% 15.02/14.81 [2490]~E(x24901,x24902)+E(f295(x24901,x24903,x24904),f295(x24902,x24903,x24904))
% 15.02/14.81 [2491]~E(x24911,x24912)+E(f295(x24913,x24911,x24914),f295(x24913,x24912,x24914))
% 15.02/14.81 [2492]~E(x24921,x24922)+E(f295(x24923,x24924,x24921),f295(x24923,x24924,x24922))
% 15.02/14.81 [2493]~E(x24931,x24932)+E(f276(x24931,x24933,x24934,x24935),f276(x24932,x24933,x24934,x24935))
% 15.02/14.81 [2494]~E(x24941,x24942)+E(f276(x24943,x24941,x24944,x24945),f276(x24943,x24942,x24944,x24945))
% 15.02/14.81 [2495]~E(x24951,x24952)+E(f276(x24953,x24954,x24951,x24955),f276(x24953,x24954,x24952,x24955))
% 15.02/14.81 [2496]~E(x24961,x24962)+E(f276(x24963,x24964,x24965,x24961),f276(x24963,x24964,x24965,x24962))
% 15.02/14.81 [2497]~E(x24971,x24972)+E(f87(x24971),f87(x24972))
% 15.02/14.81 [2498]~E(x24981,x24982)+E(f740(x24981,x24983),f740(x24982,x24983))
% 15.02/14.81 [2499]~E(x24991,x24992)+E(f740(x24993,x24991),f740(x24993,x24992))
% 15.02/14.81 [2500]~E(x25001,x25002)+E(f546(x25001,x25003,x25004,x25005,x25006,x25007,x25008,x25009),f546(x25002,x25003,x25004,x25005,x25006,x25007,x25008,x25009))
% 15.02/14.81 [2501]~E(x25011,x25012)+E(f546(x25013,x25011,x25014,x25015,x25016,x25017,x25018,x25019),f546(x25013,x25012,x25014,x25015,x25016,x25017,x25018,x25019))
% 15.02/14.81 [2502]~E(x25021,x25022)+E(f546(x25023,x25024,x25021,x25025,x25026,x25027,x25028,x25029),f546(x25023,x25024,x25022,x25025,x25026,x25027,x25028,x25029))
% 15.02/14.81 [2503]~E(x25031,x25032)+E(f546(x25033,x25034,x25035,x25031,x25036,x25037,x25038,x25039),f546(x25033,x25034,x25035,x25032,x25036,x25037,x25038,x25039))
% 15.02/14.81 [2504]~E(x25041,x25042)+E(f546(x25043,x25044,x25045,x25046,x25041,x25047,x25048,x25049),f546(x25043,x25044,x25045,x25046,x25042,x25047,x25048,x25049))
% 15.02/14.81 [2505]~E(x25051,x25052)+E(f546(x25053,x25054,x25055,x25056,x25057,x25051,x25058,x25059),f546(x25053,x25054,x25055,x25056,x25057,x25052,x25058,x25059))
% 15.02/14.81 [2506]~E(x25061,x25062)+E(f546(x25063,x25064,x25065,x25066,x25067,x25068,x25061,x25069),f546(x25063,x25064,x25065,x25066,x25067,x25068,x25062,x25069))
% 15.02/14.81 [2507]~E(x25071,x25072)+E(f546(x25073,x25074,x25075,x25076,x25077,x25078,x25079,x25071),f546(x25073,x25074,x25075,x25076,x25077,x25078,x25079,x25072))
% 15.02/14.81 [2508]~E(x25081,x25082)+E(f686(x25081,x25083,x25084,x25085),f686(x25082,x25083,x25084,x25085))
% 15.02/14.81 [2509]~E(x25091,x25092)+E(f686(x25093,x25091,x25094,x25095),f686(x25093,x25092,x25094,x25095))
% 15.02/14.81 [2510]~E(x25101,x25102)+E(f686(x25103,x25104,x25101,x25105),f686(x25103,x25104,x25102,x25105))
% 15.02/14.81 [2511]~E(x25111,x25112)+E(f686(x25113,x25114,x25115,x25111),f686(x25113,x25114,x25115,x25112))
% 15.02/14.81 [2512]~E(x25121,x25122)+E(f787(x25121,x25123,x25124,x25125,x25126,x25127,x25128),f787(x25122,x25123,x25124,x25125,x25126,x25127,x25128))
% 15.02/14.81 [2513]~E(x25131,x25132)+E(f787(x25133,x25131,x25134,x25135,x25136,x25137,x25138),f787(x25133,x25132,x25134,x25135,x25136,x25137,x25138))
% 15.02/14.81 [2514]~E(x25141,x25142)+E(f787(x25143,x25144,x25141,x25145,x25146,x25147,x25148),f787(x25143,x25144,x25142,x25145,x25146,x25147,x25148))
% 15.02/14.81 [2515]~E(x25151,x25152)+E(f787(x25153,x25154,x25155,x25151,x25156,x25157,x25158),f787(x25153,x25154,x25155,x25152,x25156,x25157,x25158))
% 15.02/14.81 [2516]~E(x25161,x25162)+E(f787(x25163,x25164,x25165,x25166,x25161,x25167,x25168),f787(x25163,x25164,x25165,x25166,x25162,x25167,x25168))
% 15.02/14.81 [2517]~E(x25171,x25172)+E(f787(x25173,x25174,x25175,x25176,x25177,x25171,x25178),f787(x25173,x25174,x25175,x25176,x25177,x25172,x25178))
% 15.02/14.81 [2518]~E(x25181,x25182)+E(f787(x25183,x25184,x25185,x25186,x25187,x25188,x25181),f787(x25183,x25184,x25185,x25186,x25187,x25188,x25182))
% 15.02/14.81 [2519]~E(x25191,x25192)+E(f623(x25191,x25193,x25194,x25195,x25196),f623(x25192,x25193,x25194,x25195,x25196))
% 15.02/14.81 [2520]~E(x25201,x25202)+E(f623(x25203,x25201,x25204,x25205,x25206),f623(x25203,x25202,x25204,x25205,x25206))
% 15.02/14.81 [2521]~E(x25211,x25212)+E(f623(x25213,x25214,x25211,x25215,x25216),f623(x25213,x25214,x25212,x25215,x25216))
% 15.02/14.81 [2522]~E(x25221,x25222)+E(f623(x25223,x25224,x25225,x25221,x25226),f623(x25223,x25224,x25225,x25222,x25226))
% 15.02/14.81 [2523]~E(x25231,x25232)+E(f623(x25233,x25234,x25235,x25236,x25231),f623(x25233,x25234,x25235,x25236,x25232))
% 15.02/14.81 [2524]~E(x25241,x25242)+E(f461(x25241,x25243,x25244,x25245),f461(x25242,x25243,x25244,x25245))
% 15.02/14.81 [2525]~E(x25251,x25252)+E(f461(x25253,x25251,x25254,x25255),f461(x25253,x25252,x25254,x25255))
% 15.02/14.81 [2526]~E(x25261,x25262)+E(f461(x25263,x25264,x25261,x25265),f461(x25263,x25264,x25262,x25265))
% 15.02/14.81 [2527]~E(x25271,x25272)+E(f461(x25273,x25274,x25275,x25271),f461(x25273,x25274,x25275,x25272))
% 15.02/14.81 [2528]~E(x25281,x25282)+E(f873(x25281,x25283,x25284,x25285,x25286),f873(x25282,x25283,x25284,x25285,x25286))
% 15.02/14.81 [2529]~E(x25291,x25292)+E(f873(x25293,x25291,x25294,x25295,x25296),f873(x25293,x25292,x25294,x25295,x25296))
% 15.02/14.81 [2530]~E(x25301,x25302)+E(f873(x25303,x25304,x25301,x25305,x25306),f873(x25303,x25304,x25302,x25305,x25306))
% 15.02/14.81 [2531]~E(x25311,x25312)+E(f873(x25313,x25314,x25315,x25311,x25316),f873(x25313,x25314,x25315,x25312,x25316))
% 15.02/14.81 [2532]~E(x25321,x25322)+E(f873(x25323,x25324,x25325,x25326,x25321),f873(x25323,x25324,x25325,x25326,x25322))
% 15.02/14.81 [2533]~E(x25331,x25332)+E(f783(x25331),f783(x25332))
% 15.02/14.81 [2534]~E(x25341,x25342)+E(f879(x25341,x25343,x25344),f879(x25342,x25343,x25344))
% 15.02/14.81 [2535]~E(x25351,x25352)+E(f879(x25353,x25351,x25354),f879(x25353,x25352,x25354))
% 15.02/14.81 [2536]~E(x25361,x25362)+E(f879(x25363,x25364,x25361),f879(x25363,x25364,x25362))
% 15.02/14.81 [2537]~E(x25371,x25372)+E(f450(x25371,x25373,x25374,x25375),f450(x25372,x25373,x25374,x25375))
% 15.02/14.81 [2538]~E(x25381,x25382)+E(f450(x25383,x25381,x25384,x25385),f450(x25383,x25382,x25384,x25385))
% 15.02/14.81 [2539]~E(x25391,x25392)+E(f450(x25393,x25394,x25391,x25395),f450(x25393,x25394,x25392,x25395))
% 15.02/14.81 [2540]~E(x25401,x25402)+E(f450(x25403,x25404,x25405,x25401),f450(x25403,x25404,x25405,x25402))
% 15.02/14.81 [2541]~E(x25411,x25412)+E(f341(x25411,x25413,x25414),f341(x25412,x25413,x25414))
% 15.02/14.81 [2542]~E(x25421,x25422)+E(f341(x25423,x25421,x25424),f341(x25423,x25422,x25424))
% 15.02/14.81 [2543]~E(x25431,x25432)+E(f341(x25433,x25434,x25431),f341(x25433,x25434,x25432))
% 15.02/14.81 [2544]~E(x25441,x25442)+E(f691(x25441,x25443,x25444),f691(x25442,x25443,x25444))
% 15.02/14.81 [2545]~E(x25451,x25452)+E(f691(x25453,x25451,x25454),f691(x25453,x25452,x25454))
% 15.02/14.81 [2546]~E(x25461,x25462)+E(f691(x25463,x25464,x25461),f691(x25463,x25464,x25462))
% 15.02/14.81 [2547]~E(x25471,x25472)+E(f457(x25471,x25473,x25474),f457(x25472,x25473,x25474))
% 15.02/14.81 [2548]~E(x25481,x25482)+E(f457(x25483,x25481,x25484),f457(x25483,x25482,x25484))
% 15.02/14.81 [2549]~E(x25491,x25492)+E(f457(x25493,x25494,x25491),f457(x25493,x25494,x25492))
% 15.02/14.81 [2550]~E(x25501,x25502)+E(f244(x25501,x25503,x25504),f244(x25502,x25503,x25504))
% 15.02/14.81 [2551]~E(x25511,x25512)+E(f244(x25513,x25511,x25514),f244(x25513,x25512,x25514))
% 15.02/14.81 [2552]~E(x25521,x25522)+E(f244(x25523,x25524,x25521),f244(x25523,x25524,x25522))
% 15.02/14.81 [2553]~E(x25531,x25532)+E(f368(x25531),f368(x25532))
% 15.02/14.81 [2554]~E(x25541,x25542)+E(f507(x25541,x25543,x25544,x25545,x25546,x25547,x25548,x25549),f507(x25542,x25543,x25544,x25545,x25546,x25547,x25548,x25549))
% 15.02/14.81 [2555]~E(x25551,x25552)+E(f507(x25553,x25551,x25554,x25555,x25556,x25557,x25558,x25559),f507(x25553,x25552,x25554,x25555,x25556,x25557,x25558,x25559))
% 15.02/14.81 [2556]~E(x25561,x25562)+E(f507(x25563,x25564,x25561,x25565,x25566,x25567,x25568,x25569),f507(x25563,x25564,x25562,x25565,x25566,x25567,x25568,x25569))
% 15.02/14.81 [2557]~E(x25571,x25572)+E(f507(x25573,x25574,x25575,x25571,x25576,x25577,x25578,x25579),f507(x25573,x25574,x25575,x25572,x25576,x25577,x25578,x25579))
% 15.02/14.81 [2558]~E(x25581,x25582)+E(f507(x25583,x25584,x25585,x25586,x25581,x25587,x25588,x25589),f507(x25583,x25584,x25585,x25586,x25582,x25587,x25588,x25589))
% 15.02/14.81 [2559]~E(x25591,x25592)+E(f507(x25593,x25594,x25595,x25596,x25597,x25591,x25598,x25599),f507(x25593,x25594,x25595,x25596,x25597,x25592,x25598,x25599))
% 15.02/14.81 [2560]~E(x25601,x25602)+E(f507(x25603,x25604,x25605,x25606,x25607,x25608,x25601,x25609),f507(x25603,x25604,x25605,x25606,x25607,x25608,x25602,x25609))
% 15.02/14.81 [2561]~E(x25611,x25612)+E(f507(x25613,x25614,x25615,x25616,x25617,x25618,x25619,x25611),f507(x25613,x25614,x25615,x25616,x25617,x25618,x25619,x25612))
% 15.02/14.81 [2562]~E(x25621,x25622)+E(f912(x25621,x25623,x25624,x25625),f912(x25622,x25623,x25624,x25625))
% 15.02/14.81 [2563]~E(x25631,x25632)+E(f912(x25633,x25631,x25634,x25635),f912(x25633,x25632,x25634,x25635))
% 15.02/14.81 [2564]~E(x25641,x25642)+E(f912(x25643,x25644,x25641,x25645),f912(x25643,x25644,x25642,x25645))
% 15.02/14.81 [2565]~E(x25651,x25652)+E(f912(x25653,x25654,x25655,x25651),f912(x25653,x25654,x25655,x25652))
% 15.02/14.81 [2566]~E(x25661,x25662)+E(f840(x25661,x25663,x25664,x25665,x25666,x25667,x25668,x25669),f840(x25662,x25663,x25664,x25665,x25666,x25667,x25668,x25669))
% 15.02/14.81 [2567]~E(x25671,x25672)+E(f840(x25673,x25671,x25674,x25675,x25676,x25677,x25678,x25679),f840(x25673,x25672,x25674,x25675,x25676,x25677,x25678,x25679))
% 15.02/14.81 [2568]~E(x25681,x25682)+E(f840(x25683,x25684,x25681,x25685,x25686,x25687,x25688,x25689),f840(x25683,x25684,x25682,x25685,x25686,x25687,x25688,x25689))
% 15.02/14.81 [2569]~E(x25691,x25692)+E(f840(x25693,x25694,x25695,x25691,x25696,x25697,x25698,x25699),f840(x25693,x25694,x25695,x25692,x25696,x25697,x25698,x25699))
% 15.02/14.81 [2570]~E(x25701,x25702)+E(f840(x25703,x25704,x25705,x25706,x25701,x25707,x25708,x25709),f840(x25703,x25704,x25705,x25706,x25702,x25707,x25708,x25709))
% 15.02/14.81 [2571]~E(x25711,x25712)+E(f840(x25713,x25714,x25715,x25716,x25717,x25711,x25718,x25719),f840(x25713,x25714,x25715,x25716,x25717,x25712,x25718,x25719))
% 15.02/14.81 [2572]~E(x25721,x25722)+E(f840(x25723,x25724,x25725,x25726,x25727,x25728,x25721,x25729),f840(x25723,x25724,x25725,x25726,x25727,x25728,x25722,x25729))
% 15.02/14.81 [2573]~E(x25731,x25732)+E(f840(x25733,x25734,x25735,x25736,x25737,x25738,x25739,x25731),f840(x25733,x25734,x25735,x25736,x25737,x25738,x25739,x25732))
% 15.02/14.81 [2574]~E(x25741,x25742)+E(f608(x25741,x25743,x25744),f608(x25742,x25743,x25744))
% 15.02/14.81 [2575]~E(x25751,x25752)+E(f608(x25753,x25751,x25754),f608(x25753,x25752,x25754))
% 15.02/14.81 [2576]~E(x25761,x25762)+E(f608(x25763,x25764,x25761),f608(x25763,x25764,x25762))
% 15.02/14.81 [2577]~E(x25771,x25772)+E(f230(x25771,x25773,x25774,x25775),f230(x25772,x25773,x25774,x25775))
% 15.02/14.81 [2578]~E(x25781,x25782)+E(f230(x25783,x25781,x25784,x25785),f230(x25783,x25782,x25784,x25785))
% 15.02/14.81 [2579]~E(x25791,x25792)+E(f230(x25793,x25794,x25791,x25795),f230(x25793,x25794,x25792,x25795))
% 15.02/14.81 [2580]~E(x25801,x25802)+E(f230(x25803,x25804,x25805,x25801),f230(x25803,x25804,x25805,x25802))
% 15.02/14.81 [2581]~E(x25811,x25812)+E(f847(x25811,x25813,x25814,x25815,x25816,x25817,x25818),f847(x25812,x25813,x25814,x25815,x25816,x25817,x25818))
% 15.02/14.81 [2582]~E(x25821,x25822)+E(f847(x25823,x25821,x25824,x25825,x25826,x25827,x25828),f847(x25823,x25822,x25824,x25825,x25826,x25827,x25828))
% 15.02/14.81 [2583]~E(x25831,x25832)+E(f847(x25833,x25834,x25831,x25835,x25836,x25837,x25838),f847(x25833,x25834,x25832,x25835,x25836,x25837,x25838))
% 15.02/14.81 [2584]~E(x25841,x25842)+E(f847(x25843,x25844,x25845,x25841,x25846,x25847,x25848),f847(x25843,x25844,x25845,x25842,x25846,x25847,x25848))
% 15.02/14.81 [2585]~E(x25851,x25852)+E(f847(x25853,x25854,x25855,x25856,x25851,x25857,x25858),f847(x25853,x25854,x25855,x25856,x25852,x25857,x25858))
% 15.02/14.81 [2586]~E(x25861,x25862)+E(f847(x25863,x25864,x25865,x25866,x25867,x25861,x25868),f847(x25863,x25864,x25865,x25866,x25867,x25862,x25868))
% 15.02/14.81 [2587]~E(x25871,x25872)+E(f847(x25873,x25874,x25875,x25876,x25877,x25878,x25871),f847(x25873,x25874,x25875,x25876,x25877,x25878,x25872))
% 15.02/14.81 [2588]~E(x25881,x25882)+E(f693(x25881,x25883,x25884),f693(x25882,x25883,x25884))
% 15.02/14.81 [2589]~E(x25891,x25892)+E(f693(x25893,x25891,x25894),f693(x25893,x25892,x25894))
% 15.02/14.81 [2590]~E(x25901,x25902)+E(f693(x25903,x25904,x25901),f693(x25903,x25904,x25902))
% 15.02/14.81 [2591]~E(x25911,x25912)+E(f671(x25911,x25913,x25914,x25915),f671(x25912,x25913,x25914,x25915))
% 15.02/14.81 [2592]~E(x25921,x25922)+E(f671(x25923,x25921,x25924,x25925),f671(x25923,x25922,x25924,x25925))
% 15.02/14.81 [2593]~E(x25931,x25932)+E(f671(x25933,x25934,x25931,x25935),f671(x25933,x25934,x25932,x25935))
% 15.02/14.81 [2594]~E(x25941,x25942)+E(f671(x25943,x25944,x25945,x25941),f671(x25943,x25944,x25945,x25942))
% 15.02/14.81 [2595]~E(x25951,x25952)+E(f793(x25951,x25953),f793(x25952,x25953))
% 15.02/14.81 [2596]~E(x25961,x25962)+E(f793(x25963,x25961),f793(x25963,x25962))
% 15.02/14.81 [2597]~E(x25971,x25972)+E(f43(x25971),f43(x25972))
% 15.02/14.81 [2598]~E(x25981,x25982)+E(f398(x25981,x25983,x25984),f398(x25982,x25983,x25984))
% 15.02/14.81 [2599]~E(x25991,x25992)+E(f398(x25993,x25991,x25994),f398(x25993,x25992,x25994))
% 15.02/14.81 [2600]~E(x26001,x26002)+E(f398(x26003,x26004,x26001),f398(x26003,x26004,x26002))
% 15.02/14.81 [2601]~E(x26011,x26012)+E(f541(x26011,x26013),f541(x26012,x26013))
% 15.02/14.81 [2602]~E(x26021,x26022)+E(f541(x26023,x26021),f541(x26023,x26022))
% 15.02/14.81 [2603]~E(x26031,x26032)+E(f559(x26031,x26033,x26034,x26035),f559(x26032,x26033,x26034,x26035))
% 15.02/14.81 [2604]~E(x26041,x26042)+E(f559(x26043,x26041,x26044,x26045),f559(x26043,x26042,x26044,x26045))
% 15.02/14.81 [2605]~E(x26051,x26052)+E(f559(x26053,x26054,x26051,x26055),f559(x26053,x26054,x26052,x26055))
% 15.02/14.81 [2606]~E(x26061,x26062)+E(f559(x26063,x26064,x26065,x26061),f559(x26063,x26064,x26065,x26062))
% 15.02/14.81 [2607]~E(x26071,x26072)+E(f555(x26071,x26073),f555(x26072,x26073))
% 15.02/14.81 [2608]~E(x26081,x26082)+E(f555(x26083,x26081),f555(x26083,x26082))
% 15.02/14.81 [2609]~E(x26091,x26092)+E(f292(x26091,x26093),f292(x26092,x26093))
% 15.02/14.81 [2610]~E(x26101,x26102)+E(f292(x26103,x26101),f292(x26103,x26102))
% 15.02/14.81 [2611]~E(x26111,x26112)+E(f757(x26111,x26113,x26114),f757(x26112,x26113,x26114))
% 15.02/14.81 [2612]~E(x26121,x26122)+E(f757(x26123,x26121,x26124),f757(x26123,x26122,x26124))
% 15.02/14.81 [2613]~E(x26131,x26132)+E(f757(x26133,x26134,x26131),f757(x26133,x26134,x26132))
% 15.02/14.81 [2614]~E(x26141,x26142)+E(f454(x26141,x26143,x26144,x26145,x26146),f454(x26142,x26143,x26144,x26145,x26146))
% 15.02/14.81 [2615]~E(x26151,x26152)+E(f454(x26153,x26151,x26154,x26155,x26156),f454(x26153,x26152,x26154,x26155,x26156))
% 15.02/14.81 [2616]~E(x26161,x26162)+E(f454(x26163,x26164,x26161,x26165,x26166),f454(x26163,x26164,x26162,x26165,x26166))
% 15.02/14.81 [2617]~E(x26171,x26172)+E(f454(x26173,x26174,x26175,x26171,x26176),f454(x26173,x26174,x26175,x26172,x26176))
% 15.02/14.81 [2618]~E(x26181,x26182)+E(f454(x26183,x26184,x26185,x26186,x26181),f454(x26183,x26184,x26185,x26186,x26182))
% 15.02/14.81 [2619]~E(x26191,x26192)+E(f363(x26191),f363(x26192))
% 15.02/14.81 [2620]~E(x26201,x26202)+E(f910(x26201,x26203,x26204,x26205,x26206),f910(x26202,x26203,x26204,x26205,x26206))
% 15.02/14.81 [2621]~E(x26211,x26212)+E(f910(x26213,x26211,x26214,x26215,x26216),f910(x26213,x26212,x26214,x26215,x26216))
% 15.02/14.81 [2622]~E(x26221,x26222)+E(f910(x26223,x26224,x26221,x26225,x26226),f910(x26223,x26224,x26222,x26225,x26226))
% 15.02/14.81 [2623]~E(x26231,x26232)+E(f910(x26233,x26234,x26235,x26231,x26236),f910(x26233,x26234,x26235,x26232,x26236))
% 15.02/14.81 [2624]~E(x26241,x26242)+E(f910(x26243,x26244,x26245,x26246,x26241),f910(x26243,x26244,x26245,x26246,x26242))
% 15.02/14.81 [2625]~E(x26251,x26252)+E(f420(x26251,x26253),f420(x26252,x26253))
% 15.02/14.81 [2626]~E(x26261,x26262)+E(f420(x26263,x26261),f420(x26263,x26262))
% 15.02/14.81 [2627]~E(x26271,x26272)+E(f818(x26271,x26273),f818(x26272,x26273))
% 15.02/14.81 [2628]~E(x26281,x26282)+E(f818(x26283,x26281),f818(x26283,x26282))
% 15.02/14.81 [2629]~E(x26291,x26292)+E(f447(x26291,x26293,x26294,x26295),f447(x26292,x26293,x26294,x26295))
% 15.02/14.81 [2630]~E(x26301,x26302)+E(f447(x26303,x26301,x26304,x26305),f447(x26303,x26302,x26304,x26305))
% 15.02/14.81 [2631]~E(x26311,x26312)+E(f447(x26313,x26314,x26311,x26315),f447(x26313,x26314,x26312,x26315))
% 15.02/14.81 [2632]~E(x26321,x26322)+E(f447(x26323,x26324,x26325,x26321),f447(x26323,x26324,x26325,x26322))
% 15.02/14.81 [2633]~E(x26331,x26332)+E(f259(x26331,x26333,x26334,x26335,x26336),f259(x26332,x26333,x26334,x26335,x26336))
% 15.02/14.81 [2634]~E(x26341,x26342)+E(f259(x26343,x26341,x26344,x26345,x26346),f259(x26343,x26342,x26344,x26345,x26346))
% 15.02/14.81 [2635]~E(x26351,x26352)+E(f259(x26353,x26354,x26351,x26355,x26356),f259(x26353,x26354,x26352,x26355,x26356))
% 15.02/14.81 [2636]~E(x26361,x26362)+E(f259(x26363,x26364,x26365,x26361,x26366),f259(x26363,x26364,x26365,x26362,x26366))
% 15.02/14.81 [2637]~E(x26371,x26372)+E(f259(x26373,x26374,x26375,x26376,x26371),f259(x26373,x26374,x26375,x26376,x26372))
% 15.02/14.81 [2638]~E(x26381,x26382)+E(f755(x26381,x26383,x26384),f755(x26382,x26383,x26384))
% 15.02/14.81 [2639]~E(x26391,x26392)+E(f755(x26393,x26391,x26394),f755(x26393,x26392,x26394))
% 15.02/14.81 [2640]~E(x26401,x26402)+E(f755(x26403,x26404,x26401),f755(x26403,x26404,x26402))
% 15.02/14.81 [2641]~E(x26411,x26412)+E(f644(x26411,x26413,x26414,x26415),f644(x26412,x26413,x26414,x26415))
% 15.02/14.81 [2642]~E(x26421,x26422)+E(f644(x26423,x26421,x26424,x26425),f644(x26423,x26422,x26424,x26425))
% 15.02/14.81 [2643]~E(x26431,x26432)+E(f644(x26433,x26434,x26431,x26435),f644(x26433,x26434,x26432,x26435))
% 15.02/14.81 [2644]~E(x26441,x26442)+E(f644(x26443,x26444,x26445,x26441),f644(x26443,x26444,x26445,x26442))
% 15.02/14.81 [2645]~E(x26451,x26452)+E(f765(x26451,x26453,x26454),f765(x26452,x26453,x26454))
% 15.02/14.81 [2646]~E(x26461,x26462)+E(f765(x26463,x26461,x26464),f765(x26463,x26462,x26464))
% 15.02/14.81 [2647]~E(x26471,x26472)+E(f765(x26473,x26474,x26471),f765(x26473,x26474,x26472))
% 15.02/14.81 [2648]~E(x26481,x26482)+E(f405(x26481),f405(x26482))
% 15.02/14.81 [2649]~E(x26491,x26492)+E(f622(x26491,x26493,x26494),f622(x26492,x26493,x26494))
% 15.02/14.81 [2650]~E(x26501,x26502)+E(f622(x26503,x26501,x26504),f622(x26503,x26502,x26504))
% 15.02/14.81 [2651]~E(x26511,x26512)+E(f622(x26513,x26514,x26511),f622(x26513,x26514,x26512))
% 15.02/14.81 [2652]~E(x26521,x26522)+E(f208(x26521,x26523,x26524,x26525,x26526,x26527,x26528),f208(x26522,x26523,x26524,x26525,x26526,x26527,x26528))
% 15.02/14.81 [2653]~E(x26531,x26532)+E(f208(x26533,x26531,x26534,x26535,x26536,x26537,x26538),f208(x26533,x26532,x26534,x26535,x26536,x26537,x26538))
% 15.02/14.81 [2654]~E(x26541,x26542)+E(f208(x26543,x26544,x26541,x26545,x26546,x26547,x26548),f208(x26543,x26544,x26542,x26545,x26546,x26547,x26548))
% 15.02/14.81 [2655]~E(x26551,x26552)+E(f208(x26553,x26554,x26555,x26551,x26556,x26557,x26558),f208(x26553,x26554,x26555,x26552,x26556,x26557,x26558))
% 15.02/14.81 [2656]~E(x26561,x26562)+E(f208(x26563,x26564,x26565,x26566,x26561,x26567,x26568),f208(x26563,x26564,x26565,x26566,x26562,x26567,x26568))
% 15.02/14.81 [2657]~E(x26571,x26572)+E(f208(x26573,x26574,x26575,x26576,x26577,x26571,x26578),f208(x26573,x26574,x26575,x26576,x26577,x26572,x26578))
% 15.02/14.81 [2658]~E(x26581,x26582)+E(f208(x26583,x26584,x26585,x26586,x26587,x26588,x26581),f208(x26583,x26584,x26585,x26586,x26587,x26588,x26582))
% 15.02/14.81 [2659]~E(x26591,x26592)+E(f649(x26591,x26593,x26594,x26595),f649(x26592,x26593,x26594,x26595))
% 15.02/14.81 [2660]~E(x26601,x26602)+E(f649(x26603,x26601,x26604,x26605),f649(x26603,x26602,x26604,x26605))
% 15.02/14.81 [2661]~E(x26611,x26612)+E(f649(x26613,x26614,x26611,x26615),f649(x26613,x26614,x26612,x26615))
% 15.02/14.81 [2662]~E(x26621,x26622)+E(f649(x26623,x26624,x26625,x26621),f649(x26623,x26624,x26625,x26622))
% 15.02/14.81 [2663]~E(x26631,x26632)+E(f817(x26631,x26633),f817(x26632,x26633))
% 15.02/14.81 [2664]~E(x26641,x26642)+E(f817(x26643,x26641),f817(x26643,x26642))
% 15.02/14.81 [2665]~E(x26651,x26652)+E(f533(x26651,x26653,x26654,x26655,x26656),f533(x26652,x26653,x26654,x26655,x26656))
% 15.02/14.81 [2666]~E(x26661,x26662)+E(f533(x26663,x26661,x26664,x26665,x26666),f533(x26663,x26662,x26664,x26665,x26666))
% 15.02/14.81 [2667]~E(x26671,x26672)+E(f533(x26673,x26674,x26671,x26675,x26676),f533(x26673,x26674,x26672,x26675,x26676))
% 15.02/14.81 [2668]~E(x26681,x26682)+E(f533(x26683,x26684,x26685,x26681,x26686),f533(x26683,x26684,x26685,x26682,x26686))
% 15.02/14.81 [2669]~E(x26691,x26692)+E(f533(x26693,x26694,x26695,x26696,x26691),f533(x26693,x26694,x26695,x26696,x26692))
% 15.02/14.81 [2670]~E(x26701,x26702)+E(f386(x26701,x26703),f386(x26702,x26703))
% 15.02/14.81 [2671]~E(x26711,x26712)+E(f386(x26713,x26711),f386(x26713,x26712))
% 15.02/14.81 [2672]~E(x26721,x26722)+E(f859(x26721),f859(x26722))
% 15.02/14.81 [2673]~E(x26731,x26732)+E(f682(x26731,x26733),f682(x26732,x26733))
% 15.02/14.81 [2674]~E(x26741,x26742)+E(f682(x26743,x26741),f682(x26743,x26742))
% 15.02/14.81 [2675]~E(x26751,x26752)+E(f636(x26751,x26753,x26754,x26755,x26756,x26757,x26758),f636(x26752,x26753,x26754,x26755,x26756,x26757,x26758))
% 15.02/14.81 [2676]~E(x26761,x26762)+E(f636(x26763,x26761,x26764,x26765,x26766,x26767,x26768),f636(x26763,x26762,x26764,x26765,x26766,x26767,x26768))
% 15.02/14.81 [2677]~E(x26771,x26772)+E(f636(x26773,x26774,x26771,x26775,x26776,x26777,x26778),f636(x26773,x26774,x26772,x26775,x26776,x26777,x26778))
% 15.02/14.81 [2678]~E(x26781,x26782)+E(f636(x26783,x26784,x26785,x26781,x26786,x26787,x26788),f636(x26783,x26784,x26785,x26782,x26786,x26787,x26788))
% 15.02/14.81 [2679]~E(x26791,x26792)+E(f636(x26793,x26794,x26795,x26796,x26791,x26797,x26798),f636(x26793,x26794,x26795,x26796,x26792,x26797,x26798))
% 15.02/14.81 [2680]~E(x26801,x26802)+E(f636(x26803,x26804,x26805,x26806,x26807,x26801,x26808),f636(x26803,x26804,x26805,x26806,x26807,x26802,x26808))
% 15.02/14.81 [2681]~E(x26811,x26812)+E(f636(x26813,x26814,x26815,x26816,x26817,x26818,x26811),f636(x26813,x26814,x26815,x26816,x26817,x26818,x26812))
% 15.02/14.81 [2682]~E(x26821,x26822)+E(f429(x26821,x26823,x26824,x26825,x26826),f429(x26822,x26823,x26824,x26825,x26826))
% 15.02/14.81 [2683]~E(x26831,x26832)+E(f429(x26833,x26831,x26834,x26835,x26836),f429(x26833,x26832,x26834,x26835,x26836))
% 15.02/14.81 [2684]~E(x26841,x26842)+E(f429(x26843,x26844,x26841,x26845,x26846),f429(x26843,x26844,x26842,x26845,x26846))
% 15.02/14.81 [2685]~E(x26851,x26852)+E(f429(x26853,x26854,x26855,x26851,x26856),f429(x26853,x26854,x26855,x26852,x26856))
% 15.02/14.81 [2686]~E(x26861,x26862)+E(f429(x26863,x26864,x26865,x26866,x26861),f429(x26863,x26864,x26865,x26866,x26862))
% 15.02/14.81 [2687]~E(x26871,x26872)+E(f741(x26871,x26873,x26874),f741(x26872,x26873,x26874))
% 15.02/14.81 [2688]~E(x26881,x26882)+E(f741(x26883,x26881,x26884),f741(x26883,x26882,x26884))
% 15.02/14.81 [2689]~E(x26891,x26892)+E(f741(x26893,x26894,x26891),f741(x26893,x26894,x26892))
% 15.02/14.81 [2690]~E(x26901,x26902)+E(f471(x26901,x26903,x26904,x26905),f471(x26902,x26903,x26904,x26905))
% 15.02/14.81 [2691]~E(x26911,x26912)+E(f471(x26913,x26911,x26914,x26915),f471(x26913,x26912,x26914,x26915))
% 15.02/14.81 [2692]~E(x26921,x26922)+E(f471(x26923,x26924,x26921,x26925),f471(x26923,x26924,x26922,x26925))
% 15.02/14.81 [2693]~E(x26931,x26932)+E(f471(x26933,x26934,x26935,x26931),f471(x26933,x26934,x26935,x26932))
% 15.02/14.81 [2694]~E(x26941,x26942)+E(f535(x26941),f535(x26942))
% 15.02/14.81 [2695]~E(x26951,x26952)+E(f875(x26951,x26953),f875(x26952,x26953))
% 15.02/14.81 [2696]~E(x26961,x26962)+E(f875(x26963,x26961),f875(x26963,x26962))
% 15.02/14.81 [2697]~E(x26971,x26972)+E(f204(x26971,x26973,x26974),f204(x26972,x26973,x26974))
% 15.02/14.81 [2698]~E(x26981,x26982)+E(f204(x26983,x26981,x26984),f204(x26983,x26982,x26984))
% 15.02/14.81 [2699]~E(x26991,x26992)+E(f204(x26993,x26994,x26991),f204(x26993,x26994,x26992))
% 15.02/14.81 [2700]~E(x27001,x27002)+E(f906(x27001,x27003),f906(x27002,x27003))
% 15.02/14.81 [2701]~E(x27011,x27012)+E(f906(x27013,x27011),f906(x27013,x27012))
% 15.02/14.81 [2702]~E(x27021,x27022)+E(f694(x27021,x27023,x27024,x27025,x27026),f694(x27022,x27023,x27024,x27025,x27026))
% 15.02/14.81 [2703]~E(x27031,x27032)+E(f694(x27033,x27031,x27034,x27035,x27036),f694(x27033,x27032,x27034,x27035,x27036))
% 15.02/14.81 [2704]~E(x27041,x27042)+E(f694(x27043,x27044,x27041,x27045,x27046),f694(x27043,x27044,x27042,x27045,x27046))
% 15.02/14.81 [2705]~E(x27051,x27052)+E(f694(x27053,x27054,x27055,x27051,x27056),f694(x27053,x27054,x27055,x27052,x27056))
% 15.02/14.81 [2706]~E(x27061,x27062)+E(f694(x27063,x27064,x27065,x27066,x27061),f694(x27063,x27064,x27065,x27066,x27062))
% 15.02/14.81 [2707]~E(x27071,x27072)+E(f205(x27071),f205(x27072))
% 15.02/14.81 [2708]~E(x27081,x27082)+E(f395(x27081,x27083),f395(x27082,x27083))
% 15.02/14.81 [2709]~E(x27091,x27092)+E(f395(x27093,x27091),f395(x27093,x27092))
% 15.02/14.81 [2710]~E(x27101,x27102)+E(f127(x27101,x27103,x27104,x27105,x27106),f127(x27102,x27103,x27104,x27105,x27106))
% 15.02/14.81 [2711]~E(x27111,x27112)+E(f127(x27113,x27111,x27114,x27115,x27116),f127(x27113,x27112,x27114,x27115,x27116))
% 15.02/14.81 [2712]~E(x27121,x27122)+E(f127(x27123,x27124,x27121,x27125,x27126),f127(x27123,x27124,x27122,x27125,x27126))
% 15.02/14.81 [2713]~E(x27131,x27132)+E(f127(x27133,x27134,x27135,x27131,x27136),f127(x27133,x27134,x27135,x27132,x27136))
% 15.02/14.81 [2714]~E(x27141,x27142)+E(f127(x27143,x27144,x27145,x27146,x27141),f127(x27143,x27144,x27145,x27146,x27142))
% 15.02/14.81 [2715]~E(x27151,x27152)+E(f853(x27151,x27153,x27154),f853(x27152,x27153,x27154))
% 15.02/14.81 [2716]~E(x27161,x27162)+E(f853(x27163,x27161,x27164),f853(x27163,x27162,x27164))
% 15.02/14.81 [2717]~E(x27171,x27172)+E(f853(x27173,x27174,x27171),f853(x27173,x27174,x27172))
% 15.02/14.81 [2718]~E(x27181,x27182)+E(f810(x27181,x27183),f810(x27182,x27183))
% 15.02/14.81 [2719]~E(x27191,x27192)+E(f810(x27193,x27191),f810(x27193,x27192))
% 15.02/14.81 [2720]~E(x27201,x27202)+E(f229(x27201,x27203,x27204),f229(x27202,x27203,x27204))
% 15.02/14.81 [2721]~E(x27211,x27212)+E(f229(x27213,x27211,x27214),f229(x27213,x27212,x27214))
% 15.02/14.81 [2722]~E(x27221,x27222)+E(f229(x27223,x27224,x27221),f229(x27223,x27224,x27222))
% 15.02/14.81 [2723]~E(x27231,x27232)+E(f727(x27231,x27233),f727(x27232,x27233))
% 15.02/14.81 [2724]~E(x27241,x27242)+E(f727(x27243,x27241),f727(x27243,x27242))
% 15.02/14.81 [2725]~E(x27251,x27252)+E(f246(x27251,x27253,x27254),f246(x27252,x27253,x27254))
% 15.02/14.81 [2726]~E(x27261,x27262)+E(f246(x27263,x27261,x27264),f246(x27263,x27262,x27264))
% 15.02/14.81 [2727]~E(x27271,x27272)+E(f246(x27273,x27274,x27271),f246(x27273,x27274,x27272))
% 15.02/14.81 [2728]~E(x27281,x27282)+E(f898(x27281,x27283,x27284),f898(x27282,x27283,x27284))
% 15.02/14.81 [2729]~E(x27291,x27292)+E(f898(x27293,x27291,x27294),f898(x27293,x27292,x27294))
% 15.02/14.81 [2730]~E(x27301,x27302)+E(f898(x27303,x27304,x27301),f898(x27303,x27304,x27302))
% 15.02/14.81 [2731]~E(x27311,x27312)+E(f542(x27311,x27313,x27314,x27315,x27316,x27317),f542(x27312,x27313,x27314,x27315,x27316,x27317))
% 15.02/14.81 [2732]~E(x27321,x27322)+E(f542(x27323,x27321,x27324,x27325,x27326,x27327),f542(x27323,x27322,x27324,x27325,x27326,x27327))
% 15.02/14.81 [2733]~E(x27331,x27332)+E(f542(x27333,x27334,x27331,x27335,x27336,x27337),f542(x27333,x27334,x27332,x27335,x27336,x27337))
% 15.02/14.81 [2734]~E(x27341,x27342)+E(f542(x27343,x27344,x27345,x27341,x27346,x27347),f542(x27343,x27344,x27345,x27342,x27346,x27347))
% 15.02/14.81 [2735]~E(x27351,x27352)+E(f542(x27353,x27354,x27355,x27356,x27351,x27357),f542(x27353,x27354,x27355,x27356,x27352,x27357))
% 15.02/14.81 [2736]~E(x27361,x27362)+E(f542(x27363,x27364,x27365,x27366,x27367,x27361),f542(x27363,x27364,x27365,x27366,x27367,x27362))
% 15.02/14.81 [2737]~E(x27371,x27372)+E(f563(x27371,x27373,x27374,x27375),f563(x27372,x27373,x27374,x27375))
% 15.02/14.81 [2738]~E(x27381,x27382)+E(f563(x27383,x27381,x27384,x27385),f563(x27383,x27382,x27384,x27385))
% 15.02/14.81 [2739]~E(x27391,x27392)+E(f563(x27393,x27394,x27391,x27395),f563(x27393,x27394,x27392,x27395))
% 15.02/14.81 [2740]~E(x27401,x27402)+E(f563(x27403,x27404,x27405,x27401),f563(x27403,x27404,x27405,x27402))
% 15.02/14.81 [2741]~E(x27411,x27412)+E(f293(x27411,x27413,x27414),f293(x27412,x27413,x27414))
% 15.02/14.81 [2742]~E(x27421,x27422)+E(f293(x27423,x27421,x27424),f293(x27423,x27422,x27424))
% 15.02/14.81 [2743]~E(x27431,x27432)+E(f293(x27433,x27434,x27431),f293(x27433,x27434,x27432))
% 15.02/14.81 [2744]~E(x27441,x27442)+E(f877(x27441,x27443,x27444,x27445,x27446),f877(x27442,x27443,x27444,x27445,x27446))
% 15.02/14.81 [2745]~E(x27451,x27452)+E(f877(x27453,x27451,x27454,x27455,x27456),f877(x27453,x27452,x27454,x27455,x27456))
% 15.02/14.81 [2746]~E(x27461,x27462)+E(f877(x27463,x27464,x27461,x27465,x27466),f877(x27463,x27464,x27462,x27465,x27466))
% 15.02/14.81 [2747]~E(x27471,x27472)+E(f877(x27473,x27474,x27475,x27471,x27476),f877(x27473,x27474,x27475,x27472,x27476))
% 15.02/14.81 [2748]~E(x27481,x27482)+E(f877(x27483,x27484,x27485,x27486,x27481),f877(x27483,x27484,x27485,x27486,x27482))
% 15.02/14.81 [2749]~E(x27491,x27492)+E(f335(x27491,x27493),f335(x27492,x27493))
% 15.02/14.81 [2750]~E(x27501,x27502)+E(f335(x27503,x27501),f335(x27503,x27502))
% 15.02/14.81 [2751]~E(x27511,x27512)+E(f824(x27511,x27513,x27514,x27515),f824(x27512,x27513,x27514,x27515))
% 15.02/14.81 [2752]~E(x27521,x27522)+E(f824(x27523,x27521,x27524,x27525),f824(x27523,x27522,x27524,x27525))
% 15.02/14.81 [2753]~E(x27531,x27532)+E(f824(x27533,x27534,x27531,x27535),f824(x27533,x27534,x27532,x27535))
% 15.02/14.81 [2754]~E(x27541,x27542)+E(f824(x27543,x27544,x27545,x27541),f824(x27543,x27544,x27545,x27542))
% 15.02/14.81 [2755]~E(x27551,x27552)+E(f562(x27551,x27553,x27554,x27555),f562(x27552,x27553,x27554,x27555))
% 15.02/14.81 [2756]~E(x27561,x27562)+E(f562(x27563,x27561,x27564,x27565),f562(x27563,x27562,x27564,x27565))
% 15.02/14.81 [2757]~E(x27571,x27572)+E(f562(x27573,x27574,x27571,x27575),f562(x27573,x27574,x27572,x27575))
% 15.02/14.81 [2758]~E(x27581,x27582)+E(f562(x27583,x27584,x27585,x27581),f562(x27583,x27584,x27585,x27582))
% 15.02/14.81 [2759]~E(x27591,x27592)+E(f536(x27591),f536(x27592))
% 15.02/14.81 [2760]~E(x27601,x27602)+E(f432(x27601,x27603),f432(x27602,x27603))
% 15.02/14.81 [2761]~E(x27611,x27612)+E(f432(x27613,x27611),f432(x27613,x27612))
% 15.02/14.81 [2762]~E(x27621,x27622)+E(f570(x27621,x27623,x27624,x27625),f570(x27622,x27623,x27624,x27625))
% 15.02/14.81 [2763]~E(x27631,x27632)+E(f570(x27633,x27631,x27634,x27635),f570(x27633,x27632,x27634,x27635))
% 15.02/14.81 [2764]~E(x27641,x27642)+E(f570(x27643,x27644,x27641,x27645),f570(x27643,x27644,x27642,x27645))
% 15.02/14.81 [2765]~E(x27651,x27652)+E(f570(x27653,x27654,x27655,x27651),f570(x27653,x27654,x27655,x27652))
% 15.02/14.81 [2766]~E(x27661,x27662)+E(f490(x27661,x27663),f490(x27662,x27663))
% 15.02/14.81 [2767]~E(x27671,x27672)+E(f490(x27673,x27671),f490(x27673,x27672))
% 15.02/14.81 [2768]~E(x27681,x27682)+E(f729(x27681,x27683,x27684),f729(x27682,x27683,x27684))
% 15.02/14.81 [2769]~E(x27691,x27692)+E(f729(x27693,x27691,x27694),f729(x27693,x27692,x27694))
% 15.02/14.81 [2770]~E(x27701,x27702)+E(f729(x27703,x27704,x27701),f729(x27703,x27704,x27702))
% 15.02/14.81 [2771]~E(x27711,x27712)+E(f770(x27711,x27713,x27714,x27715),f770(x27712,x27713,x27714,x27715))
% 15.02/14.81 [2772]~E(x27721,x27722)+E(f770(x27723,x27721,x27724,x27725),f770(x27723,x27722,x27724,x27725))
% 15.02/14.81 [2773]~E(x27731,x27732)+E(f770(x27733,x27734,x27731,x27735),f770(x27733,x27734,x27732,x27735))
% 15.02/14.81 [2774]~E(x27741,x27742)+E(f770(x27743,x27744,x27745,x27741),f770(x27743,x27744,x27745,x27742))
% 15.02/14.81 [2775]~E(x27751,x27752)+E(f275(x27751,x27753,x27754,x27755),f275(x27752,x27753,x27754,x27755))
% 15.02/14.81 [2776]~E(x27761,x27762)+E(f275(x27763,x27761,x27764,x27765),f275(x27763,x27762,x27764,x27765))
% 15.02/14.81 [2777]~E(x27771,x27772)+E(f275(x27773,x27774,x27771,x27775),f275(x27773,x27774,x27772,x27775))
% 15.02/14.81 [2778]~E(x27781,x27782)+E(f275(x27783,x27784,x27785,x27781),f275(x27783,x27784,x27785,x27782))
% 15.02/14.81 [2779]~E(x27791,x27792)+E(f558(x27791,x27793),f558(x27792,x27793))
% 15.02/14.81 [2780]~E(x27801,x27802)+E(f558(x27803,x27801),f558(x27803,x27802))
% 15.02/14.81 [2781]~E(x27811,x27812)+E(f607(x27811,x27813,x27814,x27815,x27816),f607(x27812,x27813,x27814,x27815,x27816))
% 15.02/14.81 [2782]~E(x27821,x27822)+E(f607(x27823,x27821,x27824,x27825,x27826),f607(x27823,x27822,x27824,x27825,x27826))
% 15.02/14.81 [2783]~E(x27831,x27832)+E(f607(x27833,x27834,x27831,x27835,x27836),f607(x27833,x27834,x27832,x27835,x27836))
% 15.02/14.81 [2784]~E(x27841,x27842)+E(f607(x27843,x27844,x27845,x27841,x27846),f607(x27843,x27844,x27845,x27842,x27846))
% 15.02/14.81 [2785]~E(x27851,x27852)+E(f607(x27853,x27854,x27855,x27856,x27851),f607(x27853,x27854,x27855,x27856,x27852))
% 15.02/14.81 [2786]~E(x27861,x27862)+E(f458(x27861,x27863,x27864,x27865),f458(x27862,x27863,x27864,x27865))
% 15.02/14.81 [2787]~E(x27871,x27872)+E(f458(x27873,x27871,x27874,x27875),f458(x27873,x27872,x27874,x27875))
% 15.02/14.81 [2788]~E(x27881,x27882)+E(f458(x27883,x27884,x27881,x27885),f458(x27883,x27884,x27882,x27885))
% 15.02/14.81 [2789]~E(x27891,x27892)+E(f458(x27893,x27894,x27895,x27891),f458(x27893,x27894,x27895,x27892))
% 15.02/14.81 [2790]~E(x27901,x27902)+E(f264(x27901,x27903,x27904),f264(x27902,x27903,x27904))
% 15.02/14.81 [2791]~E(x27911,x27912)+E(f264(x27913,x27911,x27914),f264(x27913,x27912,x27914))
% 15.02/14.81 [2792]~E(x27921,x27922)+E(f264(x27923,x27924,x27921),f264(x27923,x27924,x27922))
% 15.02/14.81 [2793]~E(x27931,x27932)+E(f211(x27931,x27933,x27934,x27935),f211(x27932,x27933,x27934,x27935))
% 15.02/14.81 [2794]~E(x27941,x27942)+E(f211(x27943,x27941,x27944,x27945),f211(x27943,x27942,x27944,x27945))
% 15.02/14.81 [2795]~E(x27951,x27952)+E(f211(x27953,x27954,x27951,x27955),f211(x27953,x27954,x27952,x27955))
% 15.02/14.81 [2796]~E(x27961,x27962)+E(f211(x27963,x27964,x27965,x27961),f211(x27963,x27964,x27965,x27962))
% 15.02/14.81 [2797]~E(x27971,x27972)+E(f723(x27971,x27973,x27974),f723(x27972,x27973,x27974))
% 15.02/14.81 [2798]~E(x27981,x27982)+E(f723(x27983,x27981,x27984),f723(x27983,x27982,x27984))
% 15.02/14.81 [2799]~E(x27991,x27992)+E(f723(x27993,x27994,x27991),f723(x27993,x27994,x27992))
% 15.02/14.81 [2800]~E(x28001,x28002)+E(f801(x28001),f801(x28002))
% 15.02/14.81 [2801]~E(x28011,x28012)+E(f212(x28011,x28013,x28014,x28015,x28016,x28017,x28018),f212(x28012,x28013,x28014,x28015,x28016,x28017,x28018))
% 15.02/14.81 [2802]~E(x28021,x28022)+E(f212(x28023,x28021,x28024,x28025,x28026,x28027,x28028),f212(x28023,x28022,x28024,x28025,x28026,x28027,x28028))
% 15.02/14.81 [2803]~E(x28031,x28032)+E(f212(x28033,x28034,x28031,x28035,x28036,x28037,x28038),f212(x28033,x28034,x28032,x28035,x28036,x28037,x28038))
% 15.02/14.81 [2804]~E(x28041,x28042)+E(f212(x28043,x28044,x28045,x28041,x28046,x28047,x28048),f212(x28043,x28044,x28045,x28042,x28046,x28047,x28048))
% 15.02/14.81 [2805]~E(x28051,x28052)+E(f212(x28053,x28054,x28055,x28056,x28051,x28057,x28058),f212(x28053,x28054,x28055,x28056,x28052,x28057,x28058))
% 15.02/14.81 [2806]~E(x28061,x28062)+E(f212(x28063,x28064,x28065,x28066,x28067,x28061,x28068),f212(x28063,x28064,x28065,x28066,x28067,x28062,x28068))
% 15.02/14.81 [2807]~E(x28071,x28072)+E(f212(x28073,x28074,x28075,x28076,x28077,x28078,x28071),f212(x28073,x28074,x28075,x28076,x28077,x28078,x28072))
% 15.02/14.81 [2808]~E(x28081,x28082)+E(f652(x28081,x28083),f652(x28082,x28083))
% 15.02/14.81 [2809]~E(x28091,x28092)+E(f652(x28093,x28091),f652(x28093,x28092))
% 15.02/14.81 [2810]~E(x28101,x28102)+E(f524(x28101,x28103,x28104),f524(x28102,x28103,x28104))
% 15.02/14.81 [2811]~E(x28111,x28112)+E(f524(x28113,x28111,x28114),f524(x28113,x28112,x28114))
% 15.02/14.81 [2812]~E(x28121,x28122)+E(f524(x28123,x28124,x28121),f524(x28123,x28124,x28122))
% 15.02/14.81 [2813]~E(x28131,x28132)+E(f408(x28131,x28133),f408(x28132,x28133))
% 15.02/14.81 [2814]~E(x28141,x28142)+E(f408(x28143,x28141),f408(x28143,x28142))
% 15.02/14.81 [2815]~E(x28151,x28152)+E(f331(x28151),f331(x28152))
% 15.02/14.81 [2816]~E(x28161,x28162)+E(f605(x28161,x28163,x28164,x28165),f605(x28162,x28163,x28164,x28165))
% 15.02/14.81 [2817]~E(x28171,x28172)+E(f605(x28173,x28171,x28174,x28175),f605(x28173,x28172,x28174,x28175))
% 15.02/14.81 [2818]~E(x28181,x28182)+E(f605(x28183,x28184,x28181,x28185),f605(x28183,x28184,x28182,x28185))
% 15.02/14.81 [2819]~E(x28191,x28192)+E(f605(x28193,x28194,x28195,x28191),f605(x28193,x28194,x28195,x28192))
% 15.02/14.81 [2820]~E(x28201,x28202)+E(f350(x28201,x28203),f350(x28202,x28203))
% 15.02/14.81 [2821]~E(x28211,x28212)+E(f350(x28213,x28211),f350(x28213,x28212))
% 15.02/14.81 [2822]~E(x28221,x28222)+E(f413(x28221),f413(x28222))
% 15.02/14.81 [2823]~E(x28231,x28232)+E(f332(x28231),f332(x28232))
% 15.02/14.81 [2824]~E(x28241,x28242)+E(f456(x28241,x28243,x28244),f456(x28242,x28243,x28244))
% 15.02/14.81 [2825]~E(x28251,x28252)+E(f456(x28253,x28251,x28254),f456(x28253,x28252,x28254))
% 15.02/14.81 [2826]~E(x28261,x28262)+E(f456(x28263,x28264,x28261),f456(x28263,x28264,x28262))
% 15.02/14.81 [2827]~E(x28271,x28272)+E(f354(x28271,x28273,x28274,x28275,x28276),f354(x28272,x28273,x28274,x28275,x28276))
% 15.02/14.81 [2828]~E(x28281,x28282)+E(f354(x28283,x28281,x28284,x28285,x28286),f354(x28283,x28282,x28284,x28285,x28286))
% 15.02/14.81 [2829]~E(x28291,x28292)+E(f354(x28293,x28294,x28291,x28295,x28296),f354(x28293,x28294,x28292,x28295,x28296))
% 15.02/14.81 [2830]~E(x28301,x28302)+E(f354(x28303,x28304,x28305,x28301,x28306),f354(x28303,x28304,x28305,x28302,x28306))
% 15.02/14.81 [2831]~E(x28311,x28312)+E(f354(x28313,x28314,x28315,x28316,x28311),f354(x28313,x28314,x28315,x28316,x28312))
% 15.02/14.81 [2832]~E(x28321,x28322)+E(f351(x28321),f351(x28322))
% 15.02/14.81 [2833]~E(x28331,x28332)+E(f452(x28331,x28333,x28334,x28335,x28336),f452(x28332,x28333,x28334,x28335,x28336))
% 15.02/14.81 [2834]~E(x28341,x28342)+E(f452(x28343,x28341,x28344,x28345,x28346),f452(x28343,x28342,x28344,x28345,x28346))
% 15.02/14.81 [2835]~E(x28351,x28352)+E(f452(x28353,x28354,x28351,x28355,x28356),f452(x28353,x28354,x28352,x28355,x28356))
% 15.02/14.81 [2836]~E(x28361,x28362)+E(f452(x28363,x28364,x28365,x28361,x28366),f452(x28363,x28364,x28365,x28362,x28366))
% 15.02/14.81 [2837]~E(x28371,x28372)+E(f452(x28373,x28374,x28375,x28376,x28371),f452(x28373,x28374,x28375,x28376,x28372))
% 15.02/14.81 [2838]~E(x28381,x28382)+E(f278(x28381,x28383,x28384,x28385),f278(x28382,x28383,x28384,x28385))
% 15.02/14.81 [2839]~E(x28391,x28392)+E(f278(x28393,x28391,x28394,x28395),f278(x28393,x28392,x28394,x28395))
% 15.02/14.81 [2840]~E(x28401,x28402)+E(f278(x28403,x28404,x28401,x28405),f278(x28403,x28404,x28402,x28405))
% 15.02/14.81 [2841]~E(x28411,x28412)+E(f278(x28413,x28414,x28415,x28411),f278(x28413,x28414,x28415,x28412))
% 15.02/14.81 [2842]~E(x28421,x28422)+E(f124(x28421),f124(x28422))
% 15.02/14.81 [2843]~E(x28431,x28432)+E(f223(x28431,x28433,x28434),f223(x28432,x28433,x28434))
% 15.02/14.81 [2844]~E(x28441,x28442)+E(f223(x28443,x28441,x28444),f223(x28443,x28442,x28444))
% 15.02/14.81 [2845]~E(x28451,x28452)+E(f223(x28453,x28454,x28451),f223(x28453,x28454,x28452))
% 15.02/14.81 [2846]~E(x28461,x28462)+E(f566(x28461,x28463),f566(x28462,x28463))
% 15.02/14.81 [2847]~E(x28471,x28472)+E(f566(x28473,x28471),f566(x28473,x28472))
% 15.02/14.81 [2848]~E(x28481,x28482)+E(f411(x28481),f411(x28482))
% 15.02/14.81 [2849]~E(x28491,x28492)+E(f480(x28491,x28493,x28494,x28495),f480(x28492,x28493,x28494,x28495))
% 15.02/14.81 [2850]~E(x28501,x28502)+E(f480(x28503,x28501,x28504,x28505),f480(x28503,x28502,x28504,x28505))
% 15.02/14.81 [2851]~E(x28511,x28512)+E(f480(x28513,x28514,x28511,x28515),f480(x28513,x28514,x28512,x28515))
% 15.02/14.81 [2852]~E(x28521,x28522)+E(f480(x28523,x28524,x28525,x28521),f480(x28523,x28524,x28525,x28522))
% 15.02/14.81 [2853]~P1(x28531)+P1(x28532)+~E(x28531,x28532)
% 15.02/14.81 [2854]~P106(x28541)+P106(x28542)+~E(x28541,x28542)
% 15.02/14.81 [2855]P25(x28552,x28553,x28554)+~E(x28551,x28552)+~P25(x28551,x28553,x28554)
% 15.02/14.81 [2856]P25(x28563,x28562,x28564)+~E(x28561,x28562)+~P25(x28563,x28561,x28564)
% 15.02/14.81 [2857]P25(x28573,x28574,x28572)+~E(x28571,x28572)+~P25(x28573,x28574,x28571)
% 15.02/14.81 [2858]~P107(x28581)+P107(x28582)+~E(x28581,x28582)
% 15.02/14.81 [2859]P19(x28592,x28593,x28594)+~E(x28591,x28592)+~P19(x28591,x28593,x28594)
% 15.02/14.81 [2860]P19(x28603,x28602,x28604)+~E(x28601,x28602)+~P19(x28603,x28601,x28604)
% 15.02/14.81 [2861]P19(x28613,x28614,x28612)+~E(x28611,x28612)+~P19(x28613,x28614,x28611)
% 15.02/14.81 [2862]~P120(x28621)+P120(x28622)+~E(x28621,x28622)
% 15.02/14.81 [2863]~P102(x28631)+P102(x28632)+~E(x28631,x28632)
% 15.02/14.81 [2864]~P108(x28641)+P108(x28642)+~E(x28641,x28642)
% 15.02/14.81 [2865]~P109(x28651)+P109(x28652)+~E(x28651,x28652)
% 15.02/14.81 [2866]P14(x28662,x28663)+~E(x28661,x28662)+~P14(x28661,x28663)
% 15.02/14.81 [2867]P14(x28673,x28672)+~E(x28671,x28672)+~P14(x28673,x28671)
% 15.02/14.81 [2868]~P6(x28681)+P6(x28682)+~E(x28681,x28682)
% 15.02/14.81 [2869]~P68(x28691)+P68(x28692)+~E(x28691,x28692)
% 15.02/14.81 [2870]~P127(x28701)+P127(x28702)+~E(x28701,x28702)
% 15.02/14.81 [2871]P32(x28712,x28713,x28714)+~E(x28711,x28712)+~P32(x28711,x28713,x28714)
% 15.02/14.81 [2872]P32(x28723,x28722,x28724)+~E(x28721,x28722)+~P32(x28723,x28721,x28724)
% 15.02/14.81 [2873]P32(x28733,x28734,x28732)+~E(x28731,x28732)+~P32(x28733,x28734,x28731)
% 15.02/14.81 [2874]~P110(x28741)+P110(x28742)+~E(x28741,x28742)
% 15.02/14.81 [2875]P40(x28752,x28753)+~E(x28751,x28752)+~P40(x28751,x28753)
% 15.02/14.81 [2876]P40(x28763,x28762)+~E(x28761,x28762)+~P40(x28763,x28761)
% 15.02/14.81 [2877]~P129(x28771)+P129(x28772)+~E(x28771,x28772)
% 15.02/14.81 [2878]~P67(x28781)+P67(x28782)+~E(x28781,x28782)
% 15.02/14.81 [2879]~P2(x28791)+P2(x28792)+~E(x28791,x28792)
% 15.02/14.81 [2880]P26(x28802,x28803,x28804,x28805)+~E(x28801,x28802)+~P26(x28801,x28803,x28804,x28805)
% 15.02/14.81 [2881]P26(x28813,x28812,x28814,x28815)+~E(x28811,x28812)+~P26(x28813,x28811,x28814,x28815)
% 15.02/14.81 [2882]P26(x28823,x28824,x28822,x28825)+~E(x28821,x28822)+~P26(x28823,x28824,x28821,x28825)
% 15.02/14.81 [2883]P26(x28833,x28834,x28835,x28832)+~E(x28831,x28832)+~P26(x28833,x28834,x28835,x28831)
% 15.02/14.81 [2884]P33(x28842,x28843,x28844)+~E(x28841,x28842)+~P33(x28841,x28843,x28844)
% 15.02/14.81 [2885]P33(x28853,x28852,x28854)+~E(x28851,x28852)+~P33(x28853,x28851,x28854)
% 15.02/14.81 [2886]P33(x28863,x28864,x28862)+~E(x28861,x28862)+~P33(x28863,x28864,x28861)
% 15.02/14.81 [2887]~P3(x28871)+P3(x28872)+~E(x28871,x28872)
% 15.02/14.81 [2888]~P101(x28881)+P101(x28882)+~E(x28881,x28882)
% 15.02/14.81 [2889]P17(x28892,x28893,x28894)+~E(x28891,x28892)+~P17(x28891,x28893,x28894)
% 15.02/14.81 [2890]P17(x28903,x28902,x28904)+~E(x28901,x28902)+~P17(x28903,x28901,x28904)
% 15.02/14.81 [2891]P17(x28913,x28914,x28912)+~E(x28911,x28912)+~P17(x28913,x28914,x28911)
% 15.02/14.81 [2892]P149(x28922,x28923,x28924)+~E(x28921,x28922)+~P149(x28921,x28923,x28924)
% 15.02/14.81 [2893]P149(x28933,x28932,x28934)+~E(x28931,x28932)+~P149(x28933,x28931,x28934)
% 15.02/14.81 [2894]P149(x28943,x28944,x28942)+~E(x28941,x28942)+~P149(x28943,x28944,x28941)
% 15.02/14.81 [2895]~P4(x28951)+P4(x28952)+~E(x28951,x28952)
% 15.02/14.81 [2896]P148(x28962,x28963,x28964)+~E(x28961,x28962)+~P148(x28961,x28963,x28964)
% 15.02/14.81 [2897]P148(x28973,x28972,x28974)+~E(x28971,x28972)+~P148(x28973,x28971,x28974)
% 15.02/14.81 [2898]P148(x28983,x28984,x28982)+~E(x28981,x28982)+~P148(x28983,x28984,x28981)
% 15.02/14.81 [2899]~P66(x28991)+P66(x28992)+~E(x28991,x28992)
% 15.02/14.81 [2900]P11(x29002,x29003,x29004,x29005,x29006)+~E(x29001,x29002)+~P11(x29001,x29003,x29004,x29005,x29006)
% 15.02/14.81 [2901]P11(x29013,x29012,x29014,x29015,x29016)+~E(x29011,x29012)+~P11(x29013,x29011,x29014,x29015,x29016)
% 15.02/14.81 [2902]P11(x29023,x29024,x29022,x29025,x29026)+~E(x29021,x29022)+~P11(x29023,x29024,x29021,x29025,x29026)
% 15.02/14.81 [2903]P11(x29033,x29034,x29035,x29032,x29036)+~E(x29031,x29032)+~P11(x29033,x29034,x29035,x29031,x29036)
% 15.02/14.81 [2904]P11(x29043,x29044,x29045,x29046,x29042)+~E(x29041,x29042)+~P11(x29043,x29044,x29045,x29046,x29041)
% 15.02/14.81 [2905]~P5(x29051)+P5(x29052)+~E(x29051,x29052)
% 15.02/14.81 [2906]~P94(x29061)+P94(x29062)+~E(x29061,x29062)
% 15.02/14.81 [2907]~P80(x29071)+P80(x29072)+~E(x29071,x29072)
% 15.02/14.81 [2908]~P69(x29081)+P69(x29082)+~E(x29081,x29082)
% 15.02/14.81 [2909]~P111(x29091)+P111(x29092)+~E(x29091,x29092)
% 15.02/14.81 [2910]~P70(x29101)+P70(x29102)+~E(x29101,x29102)
% 15.02/14.81 [2911]P37(x29112,x29113,x29114)+~E(x29111,x29112)+~P37(x29111,x29113,x29114)
% 15.02/14.81 [2912]P37(x29123,x29122,x29124)+~E(x29121,x29122)+~P37(x29123,x29121,x29124)
% 15.02/14.81 [2913]P37(x29133,x29134,x29132)+~E(x29131,x29132)+~P37(x29133,x29134,x29131)
% 15.02/14.81 [2914]P54(x29142,x29143,x29144)+~E(x29141,x29142)+~P54(x29141,x29143,x29144)
% 15.02/14.81 [2915]P54(x29153,x29152,x29154)+~E(x29151,x29152)+~P54(x29153,x29151,x29154)
% 15.02/14.81 [2916]P54(x29163,x29164,x29162)+~E(x29161,x29162)+~P54(x29163,x29164,x29161)
% 15.02/14.81 [2917]~P78(x29171)+P78(x29172)+~E(x29171,x29172)
% 15.02/14.81 [2918]P57(x29182,x29183,x29184)+~E(x29181,x29182)+~P57(x29181,x29183,x29184)
% 15.02/14.81 [2919]P57(x29193,x29192,x29194)+~E(x29191,x29192)+~P57(x29193,x29191,x29194)
% 15.02/14.81 [2920]P57(x29203,x29204,x29202)+~E(x29201,x29202)+~P57(x29203,x29204,x29201)
% 15.02/14.81 [2921]~P146(x29211)+P146(x29212)+~E(x29211,x29212)
% 15.02/14.81 [2922]~P99(x29221)+P99(x29222)+~E(x29221,x29222)
% 15.02/14.81 [2923]P39(x29232,x29233)+~E(x29231,x29232)+~P39(x29231,x29233)
% 15.02/14.81 [2924]P39(x29243,x29242)+~E(x29241,x29242)+~P39(x29243,x29241)
% 15.02/14.81 [2925]~P65(x29251)+P65(x29252)+~E(x29251,x29252)
% 15.02/14.81 [2926]~P72(x29261)+P72(x29262)+~E(x29261,x29262)
% 15.02/14.81 [2927]P34(x29272,x29273,x29274,x29275)+~E(x29271,x29272)+~P34(x29271,x29273,x29274,x29275)
% 15.02/14.81 [2928]P34(x29283,x29282,x29284,x29285)+~E(x29281,x29282)+~P34(x29283,x29281,x29284,x29285)
% 15.02/14.81 [2929]P34(x29293,x29294,x29292,x29295)+~E(x29291,x29292)+~P34(x29293,x29294,x29291,x29295)
% 15.02/14.81 [2930]P34(x29303,x29304,x29305,x29302)+~E(x29301,x29302)+~P34(x29303,x29304,x29305,x29301)
% 15.02/14.81 [2931]P41(x29312,x29313)+~E(x29311,x29312)+~P41(x29311,x29313)
% 15.02/14.81 [2932]P41(x29323,x29322)+~E(x29321,x29322)+~P41(x29323,x29321)
% 15.02/14.81 [2933]~P84(x29331)+P84(x29332)+~E(x29331,x29332)
% 15.02/14.81 [2934]P16(x29342,x29343)+~E(x29341,x29342)+~P16(x29341,x29343)
% 15.02/14.81 [2935]P16(x29353,x29352)+~E(x29351,x29352)+~P16(x29353,x29351)
% 15.02/14.81 [2936]P36(x29362,x29363,x29364,x29365,x29366)+~E(x29361,x29362)+~P36(x29361,x29363,x29364,x29365,x29366)
% 15.02/14.81 [2937]P36(x29373,x29372,x29374,x29375,x29376)+~E(x29371,x29372)+~P36(x29373,x29371,x29374,x29375,x29376)
% 15.02/14.81 [2938]P36(x29383,x29384,x29382,x29385,x29386)+~E(x29381,x29382)+~P36(x29383,x29384,x29381,x29385,x29386)
% 15.02/14.81 [2939]P36(x29393,x29394,x29395,x29392,x29396)+~E(x29391,x29392)+~P36(x29393,x29394,x29395,x29391,x29396)
% 15.02/14.81 [2940]P36(x29403,x29404,x29405,x29406,x29402)+~E(x29401,x29402)+~P36(x29403,x29404,x29405,x29406,x29401)
% 15.02/14.81 [2941]~P73(x29411)+P73(x29412)+~E(x29411,x29412)
% 15.02/14.81 [2942]P9(x29422,x29423,x29424)+~E(x29421,x29422)+~P9(x29421,x29423,x29424)
% 15.02/14.81 [2943]P9(x29433,x29432,x29434)+~E(x29431,x29432)+~P9(x29433,x29431,x29434)
% 15.02/14.81 [2944]P9(x29443,x29444,x29442)+~E(x29441,x29442)+~P9(x29443,x29444,x29441)
% 15.02/14.81 [2945]P53(x29452,x29453)+~E(x29451,x29452)+~P53(x29451,x29453)
% 15.02/14.81 [2946]P53(x29463,x29462)+~E(x29461,x29462)+~P53(x29463,x29461)
% 15.02/14.81 [2947]~P74(x29471)+P74(x29472)+~E(x29471,x29472)
% 15.02/14.81 [2948]P28(x29482,x29483)+~E(x29481,x29482)+~P28(x29481,x29483)
% 15.02/14.81 [2949]P28(x29493,x29492)+~E(x29491,x29492)+~P28(x29493,x29491)
% 15.02/14.81 [2950]~P95(x29501)+P95(x29502)+~E(x29501,x29502)
% 15.02/14.81 [2951]~P71(x29511)+P71(x29512)+~E(x29511,x29512)
% 15.02/14.81 [2952]P20(x29522,x29523,x29524,x29525)+~E(x29521,x29522)+~P20(x29521,x29523,x29524,x29525)
% 15.02/14.81 [2953]P20(x29533,x29532,x29534,x29535)+~E(x29531,x29532)+~P20(x29533,x29531,x29534,x29535)
% 15.02/14.81 [2954]P20(x29543,x29544,x29542,x29545)+~E(x29541,x29542)+~P20(x29543,x29544,x29541,x29545)
% 15.02/14.81 [2955]P20(x29553,x29554,x29555,x29552)+~E(x29551,x29552)+~P20(x29553,x29554,x29555,x29551)
% 15.02/14.81 [2956]~P77(x29561)+P77(x29562)+~E(x29561,x29562)
% 15.02/14.81 [2957]~P85(x29571)+P85(x29572)+~E(x29571,x29572)
% 15.02/14.81 [2958]P31(x29582,x29583,x29584)+~E(x29581,x29582)+~P31(x29581,x29583,x29584)
% 15.02/14.81 [2959]P31(x29593,x29592,x29594)+~E(x29591,x29592)+~P31(x29593,x29591,x29594)
% 15.02/14.81 [2960]P31(x29603,x29604,x29602)+~E(x29601,x29602)+~P31(x29603,x29604,x29601)
% 15.02/14.81 [2961]P59(x29612,x29613)+~E(x29611,x29612)+~P59(x29611,x29613)
% 15.02/14.81 [2962]P59(x29623,x29622)+~E(x29621,x29622)+~P59(x29623,x29621)
% 15.02/14.81 [2963]~P86(x29631)+P86(x29632)+~E(x29631,x29632)
% 15.02/14.81 [2964]~P112(x29641)+P112(x29642)+~E(x29641,x29642)
% 15.02/14.81 [2965]~P62(x29651)+P62(x29652)+~E(x29651,x29652)
% 15.02/14.81 [2966]~P76(x29661)+P76(x29662)+~E(x29661,x29662)
% 15.02/14.81 [2967]P29(x29672,x29673)+~E(x29671,x29672)+~P29(x29671,x29673)
% 15.02/14.81 [2968]P29(x29683,x29682)+~E(x29681,x29682)+~P29(x29683,x29681)
% 15.02/14.81 [2969]~P113(x29691)+P113(x29692)+~E(x29691,x29692)
% 15.02/14.81 [2970]~P42(x29701)+P42(x29702)+~E(x29701,x29702)
% 15.02/14.81 [2971]~P135(x29711)+P135(x29712)+~E(x29711,x29712)
% 15.02/14.81 [2972]~P143(x29721)+P143(x29722)+~E(x29721,x29722)
% 15.02/14.81 [2973]~P140(x29731)+P140(x29732)+~E(x29731,x29732)
% 15.02/14.81 [2974]P58(x29742,x29743,x29744,x29745,x29746)+~E(x29741,x29742)+~P58(x29741,x29743,x29744,x29745,x29746)
% 15.02/14.81 [2975]P58(x29753,x29752,x29754,x29755,x29756)+~E(x29751,x29752)+~P58(x29753,x29751,x29754,x29755,x29756)
% 15.02/14.81 [2976]P58(x29763,x29764,x29762,x29765,x29766)+~E(x29761,x29762)+~P58(x29763,x29764,x29761,x29765,x29766)
% 15.02/14.81 [2977]P58(x29773,x29774,x29775,x29772,x29776)+~E(x29771,x29772)+~P58(x29773,x29774,x29775,x29771,x29776)
% 15.02/14.81 [2978]P58(x29783,x29784,x29785,x29786,x29782)+~E(x29781,x29782)+~P58(x29783,x29784,x29785,x29786,x29781)
% 15.02/14.81 [2979]~P141(x29791)+P141(x29792)+~E(x29791,x29792)
% 15.02/14.81 [2980]~P133(x29801)+P133(x29802)+~E(x29801,x29802)
% 15.02/14.81 [2981]~P82(x29811)+P82(x29812)+~E(x29811,x29812)
% 15.02/14.81 [2982]~P114(x29821)+P114(x29822)+~E(x29821,x29822)
% 15.02/14.81 [2983]~P7(x29831)+P7(x29832)+~E(x29831,x29832)
% 15.02/14.81 [2984]~P100(x29841)+P100(x29842)+~E(x29841,x29842)
% 15.02/14.81 [2985]P27(x29852,x29853,x29854,x29855,x29856)+~E(x29851,x29852)+~P27(x29851,x29853,x29854,x29855,x29856)
% 15.02/14.81 [2986]P27(x29863,x29862,x29864,x29865,x29866)+~E(x29861,x29862)+~P27(x29863,x29861,x29864,x29865,x29866)
% 15.02/14.82 [2987]P27(x29873,x29874,x29872,x29875,x29876)+~E(x29871,x29872)+~P27(x29873,x29874,x29871,x29875,x29876)
% 15.02/14.82 [2988]P27(x29883,x29884,x29885,x29882,x29886)+~E(x29881,x29882)+~P27(x29883,x29884,x29885,x29881,x29886)
% 15.02/14.82 [2989]P27(x29893,x29894,x29895,x29896,x29892)+~E(x29891,x29892)+~P27(x29893,x29894,x29895,x29896,x29891)
% 15.02/14.82 [2990]~P87(x29901)+P87(x29902)+~E(x29901,x29902)
% 15.02/14.82 [2991]P60(x29912,x29913,x29914,x29915)+~E(x29911,x29912)+~P60(x29911,x29913,x29914,x29915)
% 15.02/14.82 [2992]P60(x29923,x29922,x29924,x29925)+~E(x29921,x29922)+~P60(x29923,x29921,x29924,x29925)
% 15.02/14.82 [2993]P60(x29933,x29934,x29932,x29935)+~E(x29931,x29932)+~P60(x29933,x29934,x29931,x29935)
% 15.02/14.82 [2994]P60(x29943,x29944,x29945,x29942)+~E(x29941,x29942)+~P60(x29943,x29944,x29945,x29941)
% 15.02/14.82 [2995]~P81(x29951)+P81(x29952)+~E(x29951,x29952)
% 15.02/14.82 [2996]~P93(x29961)+P93(x29962)+~E(x29961,x29962)
% 15.02/14.82 [2997]P15(x29972,x29973,x29974)+~E(x29971,x29972)+~P15(x29971,x29973,x29974)
% 15.02/14.82 [2998]P15(x29983,x29982,x29984)+~E(x29981,x29982)+~P15(x29983,x29981,x29984)
% 15.02/14.82 [2999]P15(x29993,x29994,x29992)+~E(x29991,x29992)+~P15(x29993,x29994,x29991)
% 15.02/14.82 [3000]~P136(x30001)+P136(x30002)+~E(x30001,x30002)
% 15.02/14.82 [3001]P8(x30012,x30013)+~E(x30011,x30012)+~P8(x30011,x30013)
% 15.02/14.82 [3002]P8(x30023,x30022)+~E(x30021,x30022)+~P8(x30023,x30021)
% 15.02/14.82 [3003]~P116(x30031)+P116(x30032)+~E(x30031,x30032)
% 15.02/14.82 [3004]P30(x30042,x30043,x30044)+~E(x30041,x30042)+~P30(x30041,x30043,x30044)
% 15.02/14.82 [3005]P30(x30053,x30052,x30054)+~E(x30051,x30052)+~P30(x30053,x30051,x30054)
% 15.02/14.82 [3006]P30(x30063,x30064,x30062)+~E(x30061,x30062)+~P30(x30063,x30064,x30061)
% 15.02/14.82 [3007]P61(x30072,x30073)+~E(x30071,x30072)+~P61(x30071,x30073)
% 15.02/14.82 [3008]P61(x30083,x30082)+~E(x30081,x30082)+~P61(x30083,x30081)
% 15.02/14.82 [3009]P56(x30092,x30093,x30094)+~E(x30091,x30092)+~P56(x30091,x30093,x30094)
% 15.02/14.82 [3010]P56(x30103,x30102,x30104)+~E(x30101,x30102)+~P56(x30103,x30101,x30104)
% 15.02/14.82 [3011]P56(x30113,x30114,x30112)+~E(x30111,x30112)+~P56(x30113,x30114,x30111)
% 15.02/14.82 [3012]~P64(x30121)+P64(x30122)+~E(x30121,x30122)
% 15.02/14.82 [3013]~P130(x30131)+P130(x30132)+~E(x30131,x30132)
% 15.02/14.82 [3014]~P88(x30141)+P88(x30142)+~E(x30141,x30142)
% 15.02/14.82 [3015]~P144(x30151)+P144(x30152)+~E(x30151,x30152)
% 15.02/14.82 [3016]P51(x30162,x30163)+~E(x30161,x30162)+~P51(x30161,x30163)
% 15.02/14.82 [3017]P51(x30173,x30172)+~E(x30171,x30172)+~P51(x30173,x30171)
% 15.02/14.82 [3018]~P83(x30181)+P83(x30182)+~E(x30181,x30182)
% 15.02/14.82 [3019]~P119(x30191)+P119(x30192)+~E(x30191,x30192)
% 15.02/14.82 [3020]P52(x30202,x30203)+~E(x30201,x30202)+~P52(x30201,x30203)
% 15.02/14.82 [3021]P52(x30213,x30212)+~E(x30211,x30212)+~P52(x30213,x30211)
% 15.02/14.82 [3022]P35(x30222,x30223,x30224)+~E(x30221,x30222)+~P35(x30221,x30223,x30224)
% 15.02/14.82 [3023]P35(x30233,x30232,x30234)+~E(x30231,x30232)+~P35(x30233,x30231,x30234)
% 15.02/14.82 [3024]P35(x30243,x30244,x30242)+~E(x30241,x30242)+~P35(x30243,x30244,x30241)
% 15.02/14.82 [3025]P23(x30252,x30253,x30254,x30255,x30256,x30257)+~E(x30251,x30252)+~P23(x30251,x30253,x30254,x30255,x30256,x30257)
% 15.02/14.82 [3026]P23(x30263,x30262,x30264,x30265,x30266,x30267)+~E(x30261,x30262)+~P23(x30263,x30261,x30264,x30265,x30266,x30267)
% 15.02/14.82 [3027]P23(x30273,x30274,x30272,x30275,x30276,x30277)+~E(x30271,x30272)+~P23(x30273,x30274,x30271,x30275,x30276,x30277)
% 15.02/14.82 [3028]P23(x30283,x30284,x30285,x30282,x30286,x30287)+~E(x30281,x30282)+~P23(x30283,x30284,x30285,x30281,x30286,x30287)
% 15.02/14.82 [3029]P23(x30293,x30294,x30295,x30296,x30292,x30297)+~E(x30291,x30292)+~P23(x30293,x30294,x30295,x30296,x30291,x30297)
% 15.02/14.82 [3030]P23(x30303,x30304,x30305,x30306,x30307,x30302)+~E(x30301,x30302)+~P23(x30303,x30304,x30305,x30306,x30307,x30301)
% 15.02/14.82 [3031]~P63(x30311)+P63(x30312)+~E(x30311,x30312)
% 15.02/14.82 [3032]~P122(x30321)+P122(x30322)+~E(x30321,x30322)
% 15.02/14.82 [3033]~P142(x30331)+P142(x30332)+~E(x30331,x30332)
% 15.02/14.82 [3034]~P134(x30341)+P134(x30342)+~E(x30341,x30342)
% 15.02/14.82 [3035]~P131(x30351)+P131(x30352)+~E(x30351,x30352)
% 15.02/14.82 [3036]P12(x30362,x30363,x30364,x30365)+~E(x30361,x30362)+~P12(x30361,x30363,x30364,x30365)
% 15.02/14.82 [3037]P12(x30373,x30372,x30374,x30375)+~E(x30371,x30372)+~P12(x30373,x30371,x30374,x30375)
% 15.02/14.82 [3038]P12(x30383,x30384,x30382,x30385)+~E(x30381,x30382)+~P12(x30383,x30384,x30381,x30385)
% 15.02/14.82 [3039]P12(x30393,x30394,x30395,x30392)+~E(x30391,x30392)+~P12(x30393,x30394,x30395,x30391)
% 15.02/14.82 [3040]~P145(x30401)+P145(x30402)+~E(x30401,x30402)
% 15.02/14.82 [3041]~P147(x30411)+P147(x30412)+~E(x30411,x30412)
% 15.02/14.82 [3042]~P123(x30421)+P123(x30422)+~E(x30421,x30422)
% 15.02/14.82 [3043]~P89(x30431)+P89(x30432)+~E(x30431,x30432)
% 15.02/14.82 [3044]~P96(x30441)+P96(x30442)+~E(x30441,x30442)
% 15.02/14.82 [3045]~P124(x30451)+P124(x30452)+~E(x30451,x30452)
% 15.02/14.82 [3046]~P128(x30461)+P128(x30462)+~E(x30461,x30462)
% 15.02/14.82 [3047]P45(x30472,x30473)+~E(x30471,x30472)+~P45(x30471,x30473)
% 15.02/14.82 [3048]P45(x30483,x30482)+~E(x30481,x30482)+~P45(x30483,x30481)
% 15.02/14.82 [3049]P24(x30492,x30493,x30494,x30495,x30496,x30497)+~E(x30491,x30492)+~P24(x30491,x30493,x30494,x30495,x30496,x30497)
% 15.02/14.82 [3050]P24(x30503,x30502,x30504,x30505,x30506,x30507)+~E(x30501,x30502)+~P24(x30503,x30501,x30504,x30505,x30506,x30507)
% 15.02/14.82 [3051]P24(x30513,x30514,x30512,x30515,x30516,x30517)+~E(x30511,x30512)+~P24(x30513,x30514,x30511,x30515,x30516,x30517)
% 15.02/14.82 [3052]P24(x30523,x30524,x30525,x30522,x30526,x30527)+~E(x30521,x30522)+~P24(x30523,x30524,x30525,x30521,x30526,x30527)
% 15.02/14.82 [3053]P24(x30533,x30534,x30535,x30536,x30532,x30537)+~E(x30531,x30532)+~P24(x30533,x30534,x30535,x30536,x30531,x30537)
% 15.02/14.82 [3054]P24(x30543,x30544,x30545,x30546,x30547,x30542)+~E(x30541,x30542)+~P24(x30543,x30544,x30545,x30546,x30547,x30541)
% 15.02/14.82 [3055]~P104(x30551)+P104(x30552)+~E(x30551,x30552)
% 15.02/14.82 [3056]~P97(x30561)+P97(x30562)+~E(x30561,x30562)
% 15.02/14.82 [3057]~P138(x30571)+P138(x30572)+~E(x30571,x30572)
% 15.02/14.82 [3058]~P79(x30581)+P79(x30582)+~E(x30581,x30582)
% 15.02/14.82 [3059]P49(x30592,x30593,x30594)+~E(x30591,x30592)+~P49(x30591,x30593,x30594)
% 15.02/14.82 [3060]P49(x30603,x30602,x30604)+~E(x30601,x30602)+~P49(x30603,x30601,x30604)
% 15.02/14.82 [3061]P49(x30613,x30614,x30612)+~E(x30611,x30612)+~P49(x30613,x30614,x30611)
% 15.02/14.82 [3062]~P137(x30621)+P137(x30622)+~E(x30621,x30622)
% 15.02/14.82 [3063]~P103(x30631)+P103(x30632)+~E(x30631,x30632)
% 15.02/14.82 [3064]~P98(x30641)+P98(x30642)+~E(x30641,x30642)
% 15.02/14.82 [3065]~P121(x30651)+P121(x30652)+~E(x30651,x30652)
% 15.02/14.82 [3066]P44(x30662,x30663,x30664,x30665,x30666,x30667)+~E(x30661,x30662)+~P44(x30661,x30663,x30664,x30665,x30666,x30667)
% 15.02/14.82 [3067]P44(x30673,x30672,x30674,x30675,x30676,x30677)+~E(x30671,x30672)+~P44(x30673,x30671,x30674,x30675,x30676,x30677)
% 15.02/14.82 [3068]P44(x30683,x30684,x30682,x30685,x30686,x30687)+~E(x30681,x30682)+~P44(x30683,x30684,x30681,x30685,x30686,x30687)
% 15.02/14.82 [3069]P44(x30693,x30694,x30695,x30692,x30696,x30697)+~E(x30691,x30692)+~P44(x30693,x30694,x30695,x30691,x30696,x30697)
% 15.02/14.82 [3070]P44(x30703,x30704,x30705,x30706,x30702,x30707)+~E(x30701,x30702)+~P44(x30703,x30704,x30705,x30706,x30701,x30707)
% 15.02/14.82 [3071]P44(x30713,x30714,x30715,x30716,x30717,x30712)+~E(x30711,x30712)+~P44(x30713,x30714,x30715,x30716,x30717,x30711)
% 15.02/14.82 [3072]~P117(x30721)+P117(x30722)+~E(x30721,x30722)
% 15.02/14.82 [3073]P21(x30732,x30733,x30734,x30735)+~E(x30731,x30732)+~P21(x30731,x30733,x30734,x30735)
% 15.02/14.82 [3074]P21(x30743,x30742,x30744,x30745)+~E(x30741,x30742)+~P21(x30743,x30741,x30744,x30745)
% 15.02/14.82 [3075]P21(x30753,x30754,x30752,x30755)+~E(x30751,x30752)+~P21(x30753,x30754,x30751,x30755)
% 15.02/14.82 [3076]P21(x30763,x30764,x30765,x30762)+~E(x30761,x30762)+~P21(x30763,x30764,x30765,x30761)
% 15.02/14.82 [3077]~P115(x30771)+P115(x30772)+~E(x30771,x30772)
% 15.02/14.82 [3078]~P139(x30781)+P139(x30782)+~E(x30781,x30782)
% 15.02/14.82 [3079]~P125(x30791)+P125(x30792)+~E(x30791,x30792)
% 15.02/14.82 [3080]~P38(x30801)+P38(x30802)+~E(x30801,x30802)
% 15.02/14.82 [3081]P18(x30812,x30813,x30814)+~E(x30811,x30812)+~P18(x30811,x30813,x30814)
% 15.02/14.82 [3082]P18(x30823,x30822,x30824)+~E(x30821,x30822)+~P18(x30823,x30821,x30824)
% 15.02/14.82 [3083]P18(x30833,x30834,x30832)+~E(x30831,x30832)+~P18(x30833,x30834,x30831)
% 15.02/14.82 [3084]~P132(x30841)+P132(x30842)+~E(x30841,x30842)
% 15.02/14.82 [3085]P13(x30852,x30853,x30854,x30855,x30856,x30857)+~E(x30851,x30852)+~P13(x30851,x30853,x30854,x30855,x30856,x30857)
% 15.02/14.82 [3086]P13(x30863,x30862,x30864,x30865,x30866,x30867)+~E(x30861,x30862)+~P13(x30863,x30861,x30864,x30865,x30866,x30867)
% 15.02/14.82 [3087]P13(x30873,x30874,x30872,x30875,x30876,x30877)+~E(x30871,x30872)+~P13(x30873,x30874,x30871,x30875,x30876,x30877)
% 15.02/14.82 [3088]P13(x30883,x30884,x30885,x30882,x30886,x30887)+~E(x30881,x30882)+~P13(x30883,x30884,x30885,x30881,x30886,x30887)
% 15.02/14.82 [3089]P13(x30893,x30894,x30895,x30896,x30892,x30897)+~E(x30891,x30892)+~P13(x30893,x30894,x30895,x30896,x30891,x30897)
% 15.02/14.82 [3090]P13(x30903,x30904,x30905,x30906,x30907,x30902)+~E(x30901,x30902)+~P13(x30903,x30904,x30905,x30906,x30907,x30901)
% 15.02/14.82 [3091]P50(x30912,x30913,x30914)+~E(x30911,x30912)+~P50(x30911,x30913,x30914)
% 15.02/14.82 [3092]P50(x30923,x30922,x30924)+~E(x30921,x30922)+~P50(x30923,x30921,x30924)
% 15.02/14.82 [3093]P50(x30933,x30934,x30932)+~E(x30931,x30932)+~P50(x30933,x30934,x30931)
% 15.02/14.82 [3094]P46(x30942,x30943)+~E(x30941,x30942)+~P46(x30941,x30943)
% 15.02/14.82 [3095]P46(x30953,x30952)+~E(x30951,x30952)+~P46(x30953,x30951)
% 15.02/14.82 [3096]~P91(x30961)+P91(x30962)+~E(x30961,x30962)
% 15.02/14.82 [3097]P150(x30972,x30973)+~E(x30971,x30972)+~P150(x30971,x30973)
% 15.02/14.82 [3098]P150(x30983,x30982)+~E(x30981,x30982)+~P150(x30983,x30981)
% 15.02/14.82 [3099]~P47(x30991)+P47(x30992)+~E(x30991,x30992)
% 15.02/14.82 [3100]P22(x31002,x31003,x31004,x31005,x31006)+~E(x31001,x31002)+~P22(x31001,x31003,x31004,x31005,x31006)
% 15.02/14.82 [3101]P22(x31013,x31012,x31014,x31015,x31016)+~E(x31011,x31012)+~P22(x31013,x31011,x31014,x31015,x31016)
% 15.02/14.82 [3102]P22(x31023,x31024,x31022,x31025,x31026)+~E(x31021,x31022)+~P22(x31023,x31024,x31021,x31025,x31026)
% 15.02/14.82 [3103]P22(x31033,x31034,x31035,x31032,x31036)+~E(x31031,x31032)+~P22(x31033,x31034,x31035,x31031,x31036)
% 15.02/14.82 [3104]P22(x31043,x31044,x31045,x31046,x31042)+~E(x31041,x31042)+~P22(x31043,x31044,x31045,x31046,x31041)
% 15.02/14.82 [3105]~P105(x31051)+P105(x31052)+~E(x31051,x31052)
% 15.02/14.82 [3106]~P75(x31061)+P75(x31062)+~E(x31061,x31062)
% 15.02/14.82 [3107]~P90(x31071)+P90(x31072)+~E(x31071,x31072)
% 15.02/14.82 [3108]P10(x31082,x31083,x31084)+~E(x31081,x31082)+~P10(x31081,x31083,x31084)
% 15.02/14.82 [3109]P10(x31093,x31092,x31094)+~E(x31091,x31092)+~P10(x31093,x31091,x31094)
% 15.02/14.82 [3110]P10(x31103,x31104,x31102)+~E(x31101,x31102)+~P10(x31103,x31104,x31101)
% 15.02/14.82 [3111]~P92(x31111)+P92(x31112)+~E(x31111,x31112)
% 15.02/14.82 [3112]P48(x31122,x31123)+~E(x31121,x31122)+~P48(x31121,x31123)
% 15.02/14.82 [3113]P48(x31133,x31132)+~E(x31131,x31132)+~P48(x31133,x31131)
% 15.02/14.82 [3114]P43(x31142,x31143,x31144,x31145)+~E(x31141,x31142)+~P43(x31141,x31143,x31144,x31145)
% 15.02/14.82 [3115]P43(x31153,x31152,x31154,x31155)+~E(x31151,x31152)+~P43(x31153,x31151,x31154,x31155)
% 15.02/14.82 [3116]P43(x31163,x31164,x31162,x31165)+~E(x31161,x31162)+~P43(x31163,x31164,x31161,x31165)
% 15.02/14.82 [3117]P43(x31173,x31174,x31175,x31172)+~E(x31171,x31172)+~P43(x31173,x31174,x31175,x31171)
% 15.02/14.82 [3118]~P118(x31181)+P118(x31182)+~E(x31181,x31182)
% 15.02/14.82 [3119]P55(x31192,x31193)+~E(x31191,x31192)+~P55(x31191,x31193)
% 15.02/14.82 [3120]P55(x31203,x31202)+~E(x31201,x31202)+~P55(x31203,x31201)
% 15.02/14.82 [3121]~P126(x31211)+P126(x31212)+~E(x31211,x31212)
% 15.02/14.82
% 15.02/14.82 %-------------------------------------------
% 15.02/14.82 cnf(10487,plain,
% 15.02/14.82 ($false),
% 15.02/14.82 inference(scs_inference,[],[4517,4757]),
% 15.02/14.82 ['proof']).
% 15.02/14.82 % SZS output end Proof
% 15.02/14.82 % Total time :0.480000s
%------------------------------------------------------------------------------